Transcript

1 ARISTOTELEIO PANEPISTHMIO JESSALONIKHS SQOLH JETIKWN EPISTHMWN TMHMA PLHROFORIKHS TEQNIKES PARAMORFWSIMWN MONTELWN SE PROBLHMATA TEQNHTHS ORASHS, EPEXERGASIAS EIKONAS KAI BINTEO Didaktorik Diatrib MIQAHL KRHNIDH PtuqioÔqou Plhroforik c JessalonÐkh 2009

2

3 MIQAHL KRHNIDH TEQNIKES PARAMORFWSIMWN MONTELWN SE PROBLHMATA TEQNHTHS ORASHS, EPEXERGASIAS EIKONAS KAI BINTEO DIDAKTORIKH DIATRIBH Upobl jhke sto Tm ma Plhroforik c, Tomèac Yhfiak n Mèswn HmeromhnÐa Proforik c Exètashc: 18 MartÐou, 2009 Exetastik Epitrop Kajhght c I. P tac, Epiblèpwn Anap. Kajhght c K. Kotrìpouloc, Mèloc TrimeloÔc Sumb. Epitrop c Anap. Kajhg tria E. Karatz, Mèloc TrimeloÔc Sumb. Epitrop c Kajhght c M. StrÐntzhc, Exetast c Kajhght c K. KaranÐkac, Exetast c Epik. Kajhght c N. Nikolaòdhc, Exetast c Lèktorac A. Tèfac, Exetast c

4

5 cflmiqa l D. KrhnÐdhc cfla.p.j. Teqnikèc Paramorf simwn Montèlwn se Probl mata Teqnht c 'Orashc, EpexergasÐa Eikìnac kai BÐnteo ISBN H ègkrish thc paroôsac Didaktorik c Diatrib c apì to Tm ma Plhroforik c tou AristoteleÐou PanepisthmÐou JessalonÐkhc den upodhl nei apodoq twn gnwm n tou suggrafèwc} (N. 5343/1932, rjro 202, par. 2)

6

7 Afierwmèno, stouc goneðc mou Dhm trh kai NÐkh, sth gunaðka mou Alex ndra, sta paidi mou Dhm trh kai NÐkh, sth jeða mou KaterÐna kai ston aderfì mou Stèlio. cfl COPYRIGHT 2008, MIQAHL KRHNIDHS

8

9 PROLOGOS H ergasða aut ekpon jhke sto ergast rio Teqnht c NohmosÔnhc kai An lushc Plhrofori n tou tm matoc Plhroforik c tou AristoteleÐou PanepisthmÐou JessalonÐkhc. H ereunhtik ergasða xekðnhse ton Septèmbrio tou 2002 upì thn epðbleyh tou kajhght tou tm matoc Plhroforik c A.P.J., k. Iw nnh P ta kai twn mel n thc trimeloôc sumbouleutik c epitrop c touc kajhghtèc tou tm matoc Plhroforik c A.P.J., k. KwnstantÐno Kotrìpoulo kai k. Elènh Karatz. H ergasða pou parousi zetai se aut th didaktorik diatrib proèkuye met apì shmantikì kìpo, anaz thsh kai melèth tou suggrafèa all kai me thn polôtimh sumbol poll n llwn anjr pwn. Ja jela na euqarist sw jerm ton epiblèponta kajhght tou didaktorikoô kai kajhght tou Tm matoc Plhroforik c A.P.J., k. Iw nnh P ta gia thn polôtimh kajod ghs tou, tic anex ntlhtec gn seic tou, th suneq sunergasða tou mazð mou kaj c kai thn paroq twn mèswn tou ergasthrðou, kaj' ìlh thn di rkeia ekpìnhshc thc diatrib c. Ja jela epðshc na euqarist sw jerm kai touc llouc dôo kajhghtèc tou Tm matoc Plhroforik c A.P.J. kai mèlh thc trimeloôc sumbouleutik c mou epitrop c, k. KwnstantÐno Kotrìpoulo kai k. Elènh Karatz, gia thn exðsou shmantik sumbol kai enj rruns touc. Ja jela akìma na euqarist sw ton epðkouro kajhght tou Tm matoc Plhroforik c A.P.J. k. Nikìlao NikolaÐdh gia th sunepðbleyh tou kaj' ìlh th di rkeia thc ergasðac. PolÔ shmantik sumbol epðshc, eðqe o Dr. Stèlioc KrhnÐdhc pou me tic polôtimec sumboulèc kai tic parotrônseic tou èdwse shmantik jhsh sthn prìodo thc ergasðac. EpÐshc, ja jela na euqarist sw gia thn polôtimh sunergasða kai antallag apìyewn, ìla ta mèlh tou ErgasthrÐou Teqnht c NohmosÔnhc kai An lushc Plhrofori n tou Tm matoc Plhroforik c A.P.J., tèwc kai nun: thn Dr. Eir nh K -

10 iv tsia gia thn sumpar stash kai bo jeia thc se ìlh thn di rkeia ekpìnhshc thc diatrib c mou, to Lèktora tou tm matoc Plhroforik c Anast sio Tèfa, to Dr. BasÐleio SolaqÐdh, ton k. Ge rgio St mou, ton k. Nikìlao Brèto, thn ka. Zuzana Cernekova kaj c kai ìla ta upìloipa mèlh tou ergasthrðou. Tèloc, ja jela na anafèrw ìti aut h ergasða apoteleð to epistègasma thc foithtik c mou parousðac epð dèka olìklhra qrìnia sto tm ma Plhroforik c A.P.J., apì to 1998 wc proptuqiakìc foitht c mèqri kai to 2008 pou oloklhr jhke h didaktorik diatrib. 'Etsi, ja jela na euqarist sw ìla ta mèlh D.E.P. kaj c kai to upìloipo proswpikì tou tm matoc Plhroforik c A.P.J, gia thn polôtimh sunergasða ìla aut taqrìnia. JessalonÐkh, Noèmbrioc 2008

11 PERILHYH H paroôsa didaktorik diatrib me jèma Teqnikèc Paramorf simwn Montèlwn se Probl mata Teqnht c 'Orashc kai EpexergasÐac Eikìnac kai BÐnteo} apoteleð to apotèlesma mðac poluetoôc episthmonik c ergasðac se jèmata pou aforoôn th teqnht ìrash kai thn epexergasða eikìnac kai bðnteo. Pio sugkekrimèna, h diatrib perilamb nei mða nèa mèjodo epilog c kai parakoloôjhshc qarakthristik n shmeðwn se disdi stata antikeðmena. H mèjodoc aut basðzetai se èna endi meso st dio twn exis sewn paramìrfwshc enìc montèlou epif neiac pou upìkeitai stouc nìmouc kai tic idiìthtec thc fusik c kai to opoðo parametropoieð thn epif neia miac eikìnac. H mèjodoc efarmìsthke sthn parakoloôjhsh anjr pinwn pros pwn kai sugkrinìmenh me llec mejìdouc petuqaðnei kal kai poiotik apotelèsmata. En suneqeða, proteðnetai ènac monodi statoc kai disdi statoc, diakritìc, mh diaqwrðsimoc metasqhmatismìc shm twn o opoðoc proèrqetai apì thn epðlush twn exis sewn enìc paramorf simou montèlou epif neiac me thn teqnik thc an lushc idioqarakthristik n. O proteinìmenoc metasqhmatismìc èqei parìmoia dom me ton diakritì metasqhmatismì sunhmðtonou afoô ton perilamb nei kai san eidik perðptwsh kai èqei sunep c parìmoiec idiìthtec. 'Epeita, parousi zetai mða nèa mèjodoc ektðmhshc prosanatolismoô tou anjr pinou kefalioô se bðnteo. H mèjodoc eðnai basismènh sthn epðlush twn exis sewn diakubèrnhshc twn paramorf sewn twn montèlwn, pou anaparistoôn thn epif neia thc trèqousac eikìnac tou bðnteo kai sth qr sh aktinik n sunart sewn b shc.

12 vi Tèloc, parousi zetai mða nèa mèjodoc kat tmhshc ègqrwmwn eikìnwn sundu zontac th qwrik plhroforða thc eikìnac me th fwteinìthta thc. O algìrijmoc kat tmhshc apoteleðtai apì duo basik mèrh. To pr to afor thn kbantopoðhsh qr matoc pou efarmìzetai sthn eikìna kai to deôtero thn kat tmhsh thc eikìnac me b sh mia nèa sun rthsh enèrgeiac pou ekfr zei thn topik omalìthta twn perioq n thc eikìnac.

13 DEFORMABLE MODEL TECHNIQUES IN COMPUTER VISION PROBLEMS AND IMAGE AND VIDEO PROCESSING vii SUMMARY The main research focus of this Ph.D. thesis are newly developed deformable model techniques in computer vision problems and image and video processing. More specifically, a new method for the automatic selection and tracking of characteristic feature points on 2D objects, is presented. This method is based on 3D deformable surface models, which parameterize the image surface. Additionally, a1d and 2D discrete, non-separable, signal transforms and their inverse formula are introduced. The proposed 1D and 2D transforms are an intermediate result of the deformation procedure of a 2D and 3D physics-based deformable model respectively and they are DCT-like transforms since they include the DCT as a special case and thus exhibit similar properties to DCT. Moreover, a novel approach for estimating 3D head pose in single-view video sequences is proposed. Following initialization by a face detector, a tracking technique that utilizes a 3D deformable surface model to approximate the facial image intensity is used to track the face in the video sequence. Head pose estimation is performed by using a feature vector which is a byproduct of the equations that govern the deformation of the surface model used in the tracking. The afore-mentioned vector is

14 viii used as input in a Radial Basis Function (RBF) interpolation network in order to estimate the 3D head pose. Finally, a novel approach for the segmentation of color textured images, which is based on a novel energy function, is presented. The proposed energy function expresses the local smoothness of an image area and is derived by exploiting modal analysis techniques that are utilized in order to describe and analyze the deformations of a 3D deformable surface model. The external forces that attract the 3D deformable surface model, combine the intensity of the image pixels with the spatial information of local image regions. The proposed image segmentation algorithm has two steps. Firstly, a color quantization scheme, which is based on the node displacements of the deformable surface model, is utilized in order to decrease the number of colors in the image. Then, the proposed energy function is used as a criterion for a region growing algorithm. The final segmentation of the image is derived by a region merge approach.

15 ix Kef laia se BiblÐa DHMOSIEUSEIS 1. G. Stamou, M. Krinidis, E. Loutas, N. Nikolaidis and I. Pitas, 2D and 3D Motion Tracking in Digital Video", in The Handbook of Image and Video Processing, 2nd edition, edited by Al Bovic, Elsevier, N. Nikolaidis, M. Krinidis, G. Stamou and I. Pitas, Motion Tracking in Video", Essential Video, edited by Al Bovic, 'Arjra se Episthmonik Periodik 1. M. Krinidis, N. Nikolaidis and I. Pitas, 2D Feature Point Selection and Tracking Using 3D Physics-Based Deformable Surfaces", IEEE Transactions on Circuits and Systems for Video Technology, vol. 17, no. 7, pp , July M. Krinidis, N. Nikolaidis and I. Pitas, The Discrete Modal Transform and its Application to Image Compression", Signal Processing: Image Communication, Elsevier, vol.22, issue 5, pp , June M. Krinidis, N. Nikolaidis and I. Pitas, 3D Head Pose Estimation in Monocular Video Sequences Using Deformable Surfaces and Radial Basis Functions", IEEE Transactions on Circuits and Systems for Video Technology,vol. 19, no. 2, pages , February 2009.

16 x 4. M. Krinidis and I. Pitas, Color-Texture Image Segmentation U- sing Deformable Surfaces", accepted for publication in IEEE Transactions on Image Processing, February 'Arjra se Episthmonik Sunèdria 1. M. Krinidis, G. Stamou, H. Teutsch, S. Spors, N. Nikolaidis, R. Rabenstein and I. Pitas, An Audio-Visual Database For Evaluating Person Tracking Algorithms", In Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing" (ICASSP 2005), vol. 2, pp , Philadelphia, March, G. Stamou, M. Krinidis, N. Nikolaidis, and I. Pitas, A monocular system for automatic face detection and tracking", In Proceedings of Visual Communications and Image Processing" (VCIP 2005), Beijing, China, July, M. Krinidis, N. Nikolaidis and I. Pitas, Feature-based tracking u- sing 3D physics-based deformable surfaces", In Proceedings of EU- RASIP European Signal Processing Conference" (EUSIPCO 2005), Antalya, Turkey, 4-8 September, L. Goldmann, M. Krinidis, N. Nikolaidis, S. Asteriadis and T. Sikora, An Integrated System for Face Detection and Tracking", In Proceedings of Workshop ICOB2005", Berlin, Germany, October, M. Krinidis, N. Nikolaidis and I. Pitas, Using Deformable Surface Models to Derive a DCT-Like 2DTransform", In Proceedings of

17 xi International Conference on Multimedia and Expo" (ICME 2007), Beijing, China, July 2-5, M. Krinidis, N. Nikolaidis and I. Pitas, 3D Head Pose Estimation Using Support Vector Machines and Physics-Based Deformable Surfaces", In Proceedings of International Symposium on Signal Processing and its Applications" (ISSPA 2007), Sharaj, United Emirates, February, 2007.

18

19 Perieqìmena 1 Eisagwg Paramorf sima Montèla Teqnikèc mh-basizìmenec sth Fusik Teqnikèc Basizìmenec sth Fusik Fusikèc Teqnikèc ProseggÐsewn Suz thsh Epilog kai ParakoloÔjhsh Qarakthristik n ShmeÐwn Qrhsimopoi ntac Trisdi stata Paramorf sima Montèla Epif neiac pou Upìkeintai stouc Nìmouc kai Idiìthtec thc Fusik c Eisagwg Paramorf simo Montèlo Epilog ShmeÐwn ParakoloÔjhsh ShmeÐwn Peir mata Sumper smata O Diakritìc Metasqhmatismìc Idioqarakthristik n kai h Efarmog tou se mia Teqnik SumpÐeshc Eikìnac me Ap leia PlhroforÐac Eisagwg xiii

20 xiv Perieqìmena 3.2 Paramorf simo Montèlo Epif neiac Diakritìc Metasqhmatismìc Idioqarakthristik n Idiìthtec MetasqhmatismoÔ Sugkèntrwsh Enèrgeiac kai Ikanìthta Aposusqètishc Efarmog se SumpÐesh Eikìnac Sumper smata EktÐmhsh Trisdi statou ProsanatolismoÔ Anjr pinou KefalioÔ se Eikonoseirèc me Qr sh Paramorf simwn Montèlwn kai Aktinik n Sunart sewn B sewn Eisagwg Paramorf simo Montèlo Epif neiac DhmiourgÐa DianÔsmatoc ProsanatolismoÔ Parembol Aktinik n Sunart sewn B shc Axiolìghsh tou Proteinìmenou sust matoc Prwtìkollo kai Dedomèna Axiolìghshc Peiramatik Apotelèsmata Sumper smata Kat tmhsh 'Egqrwmwn Eikìnwn Basismènh sthn Enèrgeia Idioqarakthristik n Paramorf simwn Montèlwn Eisagwg An lush Idioqarakthristik n kai Sun rthsh Enèrgeiac Kb ntish Qr matoc Kat tmhsh eikìnac Peiramatik Apotelèsmata Prwtìkollo kai Dedomèna Axiolìghshc Peiramatik Apotelèsmata Sumper smata Par rthma 198

21 Perieqìmena xv A Upologismìc AntÐstrofou MetasqhmatismoÔ DMT 199 B Orjokanonikìthta tou ZeugarioÔ pou OrÐzetai apì ton EujÔ kai AntÐstrofo Metasqhmatismì DMT 201

22

23 Kef laio 1 Eisagwg Tic teleutaðec dekaetðec tou eikostoô ai na parathr jhke mða katakìrufh aôxhsh tou endiafèrontoc gia th diaqeðrish, an lush, met dosh kai epexergasða yhfiak n mèswn (akðnhtwn eikìnwn, trisdi statwn eikìnwn, bðnteo, qwn, keimènou) se pagkìsmio epðpedo. H sôgqronh teqnologða èdwse th dunatìthta gia th yhfiopoðhsh diafìrwn tôpwn dedomènwn, oi opoðec anaparistoôn eðte disdi stata eðte trisdi stata antikeðmena kai e- mperièqoun exeidikeumèna dedomèna ìpwc eðnai h akrib c jèsh enìc antikeimènou se mia eikonoseir kai o prosanatolismìc tou anjr pinou kefalioô se k poia eikìna. EÐnai fanerì ìti nèec teqnologðec gia thn anapar stash, epexergasða kai an lush twn sugkekrimènwn tôpwn dedomènwn èqoun èrjei sto prosk nio. H shmantikìterh Ðswc phg plhroforðac eðnai h optik, dhlad, h eikìna eðte aut eðnai kinoômenh eðte akðnhth. Despìzousa, loipìn, jèsh metaxô twn diafìrwn morf n thc yhfiak c plhroforðac katèqei h yhfiak eikìna kai ìqi dika, kaj c prosfèrei kalôterh poiìthta, eukolìterh kai pio apotelesmatik apoj keush kai met dosh, se sunduasmì me ikanèc teqnikèc yhfiak c sumpðeshc kai ekpomp c, apait ntac ligìtero q ro apoj keushc eôroc suqnot twn gia met dosh, kaj c kai polô pio eu- 1

24 2 Kef laio 1. Eisagwg èlikth kai gr gorh diaqeðrish kai epexergasða. Idiaitèrwc ta teleutaða qrìnia, me thn di dosh tou pagkìsmiou istoô, h eikìna katèqei despìzousa jèsh stic perissìterec istoselðdec. Autìc eðnai kai o kôrioc lìgoc gia thn an gkh ikan n algorðjmwn sumpðeshc eikìnac. 'Ena akìma yhfiakì mèso, to opoðo gnwrðzei exðsou meg lh njhsh, eðnai to yhfiakì bðnteo. Den prèpei na xeqn me ìti plèon oi yhfiakèc plhroforðec mporoôn kai sundu zontai me ton qo, par gontac ta gnwst se ìlouc yhfiak polumèsa, ta opoða apoteloôn pio oloklhrwmènec phgèc plhrofori n kai qrhsimopoioôntai kat kìron stic yhfiakèc efarmogèc. Oi allhlepidrastikèc anjrwpokentrikèc efarmogèc twn polumèswn, se sunduasmì me tic uyhlèc taqôthtec met doshc tou DiadiktÔou, èqoun kerdðsei to endiafèron twn episthmìnwn. DÔo apì touc perissìtero suzhthmènouc kai axiìlogouc stìqouc twn efarmog n aut n eðnai h parakoloôjhsh anjr pwn se yhfiakì bðnteo kaj c kai h ektðmhsh prosanatolismoô tou anjr pinou kefalioô. Tìso sthn epexergasða yhfiakoô bðnteo ìso kai sthn epexergasða yhfiak c eikìnac, ènac shmantikìc episthmonikìc kl doc eðnai h teqnht ìrash. 'Ena basikì prìblhma thc teqnht c ìrashc eðnai o trìpoc perigraf c twn qarakthristik n gnwrism twn, epifanei n kai twn upì exètash antikeimènwn, ètsi ste na mporoôn na katatmhjoôn, na anagnwristoôn, na sumpiestoôn, na parakoloujhjoôn na upostoôn opoiad pote llh parìmoia diadikasða. To prìblhma autì od ghse touc epist monec sth qr sh twn paramorf simwn montèlwn, ta opoða kalôptoun èna eurô f sma efarmog n thc teqnht c ìrashc. 'Eqoun protajeð kat kairoôc poll n eid n paramorf sima montèla, pou sthn pleioyhfða touc qrhsimopoioôntai kai leitourgoôn me parìmoio trìpo kai gia thn antimet pish Ðdiwn problhm twn, ìpwc gia par deigma sthn parakoloôjhsh perioq n kai sthn perigraf sqhm twn kai eikìnwn.

25 1.1. Paramorf sima Montèla Paramorf sima Montèla Sth di rkeia twn teleutaðwn dekati n, h perioq twn paramorf simwn montèlwn apotèlese to kaðrio jèma miac èntonhc èreunac kai suz thshc. H katakìrufh aôxhsh tou endiafèrontoc gia thn perigraf, thn an lush kai thn epexergasða thc montelopoðhshc yhfiak n mèswn (akðnhtwn eikìnwn, trisdi statwn eikìnwn, bðnteo, qwn), ofeðletai stic anarðjmhtec efarmogèc touc se polu rijma episthmonik pedða. H mhqanik ìrash (an lush eikìnac kai bðnteo, kat tmhsh eikìnac, parakoloôjhsh kðnhshc), h apeikìnish antikeimènwn (anapar stash sqhm twn kai antistoðqish plhrofori n) kai ta grafik upologist n (montelopoðhsh sqhm twn, prosomoðwsh kai sqediasmìc kðnhshc) apoteloôn k poia apì ta pedða pou brðskoun efarmog ta paramorf sima montèla. EÐnai fanerì ìti oi nèec teqnologðec gia thn anapar stash kai epexergasða twn sugkekrimènwn montèlwn èqoun èrjei sto prosk nio. Mèqri tic arqèc tou 1980, oi teqnikèc montelopoðhshc stouc upologistèc, periorðzontan mìno se kampta antikeðmena. To 1984, o Barr eis gage th qr sh gewmetrik n telest n gia thn paramìrfwsh enìc stereoô antikeimènou, metasqhmatðzontac to sôsthma suntetagmènwn tou antikeimènou [1]. Sta epìmena qrìnia, o Kass prìteine thn teqnik twn energ n perigramm twn [2] pou sôntoma genikeôthke sthn trisdi stath perðptwsh apì ton Terzìpoulo [3], o opoðoc kai eis gage ton ìro fiparamorf sima Montèlafl. To kolossiaðo eôroc twn paramorf simwn montèlwn, ègine gr gora antilhptì kai oi parap nw eisagwgikèc teqnikèc apotèlesan to pedðo ereun n kai ergasðac gia thn kataskeu disdi statwn kai trisdi - statwn eikonik n montèlwn. Oi shmerinèc teqnikèc paramìrfwshc antikeimènwn, perilamb noun stoiqeða apì gewmetrða, fusik, prohgmèna majhmatik, proseggistikèc jewrðec kai statistik. H poluplokìthta twn teqnik n paramìrfwshc u- p rxe o prwteôon par gontac pou periìrize thn an ptuxh twn parap nw

26 4 Kef laio 1. Eisagwg teqnik n, eidik se efarmogèc pragmatikoô qrìnou. 'Otan h akrðbeia eðnai uyðsthc shmasðac, oi aplopoi seic den eðnai epitreptèc. Stic mèrec mac, ta paramorf sima montèla qrhsimopoioôntai ston èlegqo antoq c sugkrouìmenwn autokðnhtwn, sthn parakoloôjhsh kðnhshc se bðnteo epit rhshc, se diaisjhtik, eikonik perib llonta gluptik c. EpÐshc, prohgmèna montèla, qrhsimopoioôntai se epist mec ìpwc h iatrik, h biologða kaihbio atrik se efarmogèc ìpwc an lush iatrik n eikìnwn, prosomoðwsh iatrik n egqeir sewn kai trisdi stath anapar stash apì bio atrikèc eikìnec. Ta paramorf sima montèla mporoôn na kathgoriopoihjoôn sômfwna me thn teqnik pou qrhsimopoieðtai gia thn epðlush thc paramìrfwshc Teqnikèc mh-basizìmenec sth Fusik Oi teqnikèc pou den basðzontai sth fusik eðnai mèjodoi pou k noun qr sh gewmetrik n stoiqeðwn me skopì na paramorf soun eikonik montèla. Se autèc tic peript seic, den eðnai aparaðthth h gn sh tou ulikoô apì to opoðo eðnai kataskeuasmèno to antikeðmeno proc paramìrfwsh kai gðnetai mia prosp jeia na diathrhjeð h isorropða metaxô thc akrðbeiac pou q netai kai thc poluplokìthtac twn pr xewn pou aplopoieðtai. KampÔlec kai Epir mmata Oi kampôlec kai ta epir mmata (splines and patches) eðnai sônjeta, suneq perigr mmata ta opoða mporoôn na perigrafoôn me poluwnumikèc exis seic. Up rqoun di foroi tôpoi kampôlwn, kajènac ek twn opoðwn èqei tic dikèc tou, exèqontec idiìthtec oi opoðec kajorðzontai apì ta polu numa pou qrhsimopoioôntai, ìpwc oi Bezier Splines kampôlec, oi Mh-Omoiìmorfec Rational B-Spline kampôlec kai llec. Wstìso, parìlo tic diaforèc pou up rqoun metaxô twn diafìrwn eid n twn kampul n, h diadikasða kataskeu c k je tôpou miac kampôlhc eðnai parìmoia.

27 1.1. Paramorf sima Montèla 5 Oi kampôlec anaparðstantai apì èna sônolo apì èna plègma shmeðwn elègqou. Aut ta shmeða elègqou qrhsimopoioôntai wc b rh se èna grammikì jroisma aktinik n sunart sewn pou exart tai apì to eðdoc thc kampôlhc. Oi aktinikèc sunart seic eðnai sunart seic k poiwn paramètrwn pou kajorðzoun tic idiìthtec tou ek stote montèlou. EleÔjerh MorfopoÐhsh Paramìrfwshc H eleôjerh morfopoðhsh paramìrfwshc (free form deformation) eðnai è- nac q roc pou èqei gðnei polô shmantikìc ta teleutaða qrìnia sto gewmetrikì sqediasmì kai sth sqediokðnhsh (animation). Sth sugkekrimènh teqnik, h paramìrfwsh epitugq netai apì èna sônolo telest n (k myh, kwnik klðsh, strèblwsh, epim kunsh) oi opoðoi eðnai anex rthtoi a- pì ta shmeða elègqou. H eleôjerh morfopoðhsh paramìrfwshc arqik uiojet jhke apì sust mata sqediasmoô upologist n (Computer Aided Design (CAD)), wstìso, akìma kai stic mèrec mac, qrhsimopoieðtai se polô sônjetec montelopoi seic ìpwc se paramorf seic eikonik n montèlwn anjr pinwn pros pwn kai se prosomoi seic sônjetwn iatrik n epemb - sewn Teqnikèc Basizìmenec sth Fusik Me thn p rodo twn qrìnwn, h upologistik ikanìthta suneq c auxanìtan, opìte dìjhke h dunatìthta gia teqnikèc montelopoðhshc apì touc upologistèc. EÐnai plèon dunatì, oi arqèc thc mhqanik c na enswmatwjoôn se gewmetrikoôc sqhmatismoôc enìc montèlou, me skopì thn epðteuxh enìc pio realistikoô kai peistikoô paramorf simou montèlou. Diakrit Montèla: Mèjodoi elathrðwn m zac-apìsbeshc 'Opwc upodhl nei kai o tðtloc thc enìthtac, èna montèlo pou upìkeitai stouc nìmouc thc fusik c anaparist èna sônolo apì shmeða ta opoða

28 6 Kef laio 1. Eisagwg sundèontai metaxô touc apì elat ria se èna diktuwtì plègma. Ta montèla pou upìkeintai stouc nìmouc thc fusik c eðnai dunamik montèla kai oi dun meic twn elathrðwn eðnai grammikèc. Autì shmaðnei ìti h dônamh twn elathrðwn eðnai an logh thc metatìpishc twn elathrðwn apì th jèsh isorropðac touc. Suneq Montèla: Mèjodoi Peperasmènwn StoiqeÐwn Oi mèjodoi peperasmènwn stoiqeðwn qrhsimopoioôn ektetamèna majhmatikèc fìrmoulec gia na proseggðsoun tic merikèc diaforikèc exis seic twn paramorf sewn. Ta perissìtera fusik fainìmena mporoôn na montelopoihjoôn qrhsimopoi ntac parag gouc kai oloklhr mata. Wstìso, to eôroc aut n twn exis sewn pou mporoôn na epilujoôn eðnai austhr periorismèno kajist ntac tic lôseic aut n twn exis sewn polô dôskolec. Autì to prìblhma mporeð na prosperasteð qrhsimopoi ntac majhmatikèc mejìdouc diakrit n tim n twn anex rthtwn metablht n. Parìla aut, autèc oi mèjodoi eðnai exairetik qronobìrec. Wstìso, oi sôgqronoi hlektronikoð upologistèc èqoun fèrei epan stash stic majhmatikèc mejìdouc kai èqoun dieukolônei thn epexergasða meg lwn problhm twn pou palaiìtera h lôsh touc tan apagoreutik. Oi mèjodoi peperasmènwn stoiqeðwn eðnai parìmoioi me tic mejìdouc diaforik n exis sewn Fusikèc Teqnikèc ProseggÐsewn Oi Fusikèc Teqnikèc ProseggÐsewn den proèrqontai mesa apì tic e- xis seic suneq n mhqanism n. Wstìso, apoteloôn efalt rio fusik n kin trwn. Energ Montèla Perigramm twn/fðdia 'Ena energì montèlo perigr mmatoc eðnai mia kampôlh pou elaqistopoieð k poia enèrgeia, h opoða sun jwc èqei kat llhlh dom ste na proseg-

29 1.2. Suz thsh 7 gðsei mia epijumht paramìrfwsh. Aut ta montèla suqn onom zontai kai fðdia, afoô emfanðzontai san na tulðgontai p nw stic yhfiakèc eikìnec. EÐnai èna par deigma thc genikeumènhc teqnik c tairi smatoc enìc paramorf simou montèlou se mia eikìna qrhsimopoi ntac k poia teqnik elaqistopoðhshc enèrgeiac. Ta fðdia eis qjhsan arqik apì ton Kass [2] kai èlusan poll probl mata sthn teqnht ìrash, ìpwc h anðqneush akm n kai kðnhshc se yhfiakèc eikìnec kai bðnteo. 1.2 Suz thsh Sthn didaktorik aut diatrib melet ntai ta proanaferjènta probl mata kai proteðnontai kainotìmec mèjodoi gia thn apotelesmatik antimet pish touc me th qr sh paramorf simwn montèlwn. Eidikìtera, parousi zontai prwtìtupec teqnikèc gia thn epilog kai parakoloôjhsh qarakthristik n shmeðwn se disdi stata antikeðmena. Akìma, eis getai ènac monodi statoc kai disdi statoc diakritìc metasqhmatismìc pou è- qei parìmoia dom me ton diakritì metasqhmatismì sunhmðtonou afoô ton perilamb nei kai san eidik perðptwsh kai èqei sunep c parìmoiec idiìthtec. Epiplèon, perigr fetai mia kainotìmoc mèjodoc gia thn ektðmhsh prosanatolismoô anjr pinou pros pou se bðnteo. H proteinìmenh mèjodoc k nei qr sh twn exis sewn paramorf simwn montèlwn kai aktinik n sunart sewn b shc. Tèloc, parousi zetai mða teqnik kat tmhshc ègqrwmwn eikìnwn pou sundu zei th qwrik plhroforða thc eikìnac me th fwteinìthtac thc. H mèjodoc k nei qr sh miac kainoôrgiac sun rthshc enèrgeiac pou ekfr zei thn topik omalìthta twn perioq n thc eikìnac. Pio sugkekrimèna, sto Kef laio 2 parousi zetai mia nèa prosèggish gia thn epilog kai thn parakoloôjhsh qarakthristik n shmeðwn se akoloujðec eikìnwn. Se aut n thn mèjodo, h fwteinìthta thc eikìnac antiproswpeôetai apì èna 3D paramorf simo montèlo epif neiac. H proteinìmenh prosèggish sthrðzetai sthn epilog kai parakoloôjhsh qarakthristi-

30 8 Kef laio 1. Eisagwg k n shmeðwn me thn ekmet lleush enìc dianôsmatoc, apokaloômeno kai wc genikeumèno di nusma metatopðsewn, pou emfanðzetai stic exis seic paramìrfwshc tou montèlou. Autì to di nusma apodeiknôetai ìti eðnai ènac sunduasmìc di forwn mask n anðqneushc gramm n kai akm n, odhg ntac kat sunèpeia se eudi krita kai emfan qarakthristik shmeða. Hprotei- nìmenh mèjodoc sugkrðjhke se akrðbeia kai eurwstða parakoloôjhshc, me èna gnwstì algìrijmo parakoloôjhshc (KLT) kai ènan algìrijmo parakoloôjhshc basismèno sta SIFT qarakthristik shmeða. Hproteinìmenh mèjodoc apodeðqjhke peiramatik ìti eðnai akribèsterh kai pio anjektik apì ton KLT kai ton SIFT. Epiplèon, o algìrijmoc epilog c qarakthristik n shmeðwn exet sthke en ntia se SIFT kai Harris qarakthristik shmeða kai apodeðqjhke pwc parèqei kalôtera apotelèsmata. Sto Kef laio 3 proteðnetai o Diakritìc Metasqhmatismìc Idioqarakthristik n (DMT), ènac 1D kai 2D diakritìc, mh diaqwrðsimoc metasqhmatismìc gia epexergasða s matoc, o opoðoc apì majhmatik c apìyewc, mporeð na jewrhjeð san mia genðkeush tou gnwstoô, DiakritoÔ MetasqhmatismoÔ SunhmÐtonou (DCT). 'Ena 3D paramorf simo montèlo epif - neiac qrhsimopoieðtai gia na anaparast sei thn epif neia fwteinot twn thc eikìnac. Oproteinìmenoc metasqhmatismìc eðnai èna pro ìn twn exis sewn diakubèrnhshc twn paramorf sewn. Oi idiìthtec tou proteinìmenou metasqhmatismoô eðnai parìmoiec me tou DCT.Gia na dieukrinistoôn autèc oi idiìthtec, o proteinìmenoc metasqhmatismìc efarmìzetai se èna prìtupo sumpðeshc eikìnac me ap leia plhroforðac. Ta apotelèsmata aut c thc efarmog c sugkrðjhkan me apotelèsmata enìc protôpou sumpðeshc pou basðzetai ston DCT. Ta peiramatik apotelèsmata deðqnoun pwc o DMT, o opoðoc emperièqei èna enswmatwmèno mhqanismì kajorismoô tou epipèdou sumpðeshc, èqei exairetikèc ikanìthtec sugkèntrwshc enèrgeiac kai epitugq nei sugkrðsima apotelèsmata meton DCT se qamhl epðpeda sumpðeshc, en eðnai, genikìtera, kalôteroc se uyhl epðpeda sumpðeshc. Sto Kef laio 4 thc didaktorik c diatrib c to endiafèron strèfetai

31 1.2. Suz thsh 9 sthn exètash miac nèac prosèggishc gia ton upologismì tou trisdi statou prosanatolismoô tou anjr pinou kefalioô se disdi statec eikonoseirèc. AkoloujoÔmenh thc qr sh enìc aniqneut pros pou, qrhsimopoieðtai mia teqnik parakoloôjhshc pros pwn se eikonoseirèc pou basðzetai se è- na trisdi stato paramorf simo montèlo to opoðo proseggðzei th fwteinìthta thc eikìnac. H ektðmhsh tou prosanatolismoô tou anjr pinou kefalioô basðzetai sth qr sh enìc dianôsmatoc qarakthristik n gnwrism twn, pou qrhsimopoieðtai gia thn parakoloôjhsh tou pros pou. To proanaferjèn di nusma qrhsimopoieðtai san eðsodoc se èna dðktuo parembol c aktinik n sunart sewn b shc (Radial Basis Functions interpolation network) prokeimènou na upologisteð o prosanatolismìc tou anjr pinou kefalioô. H proteinìmenh mèjodoc exet sthke sth b sh dedomènwn IDIAP pou perièqei bajmonomhmèna apotelèsmata ektðmhshc prosanatolismoô anjr pinwn pros pwn. Ta epiteuqjènta apotelèsmata deðqnoun ìti h mèjodoc mporeð na upologðsei th trisdi stath kateôjunsh tou kefalioô me polô kal akrðbeia. Tèloc, sto Kef laio 5 perigr fetai mia nèa teqnik kat tmhshc ègqrwmwn eikìnwn, h opoða basðzetai se mia prwtìtuph sun rthsh enèrgeiac. H proteinìmenh sun rthsh enèrgeiac ekfr zei thn topik omalìthta miac perioq c thc eikìnac kai par getai apì thn ekmet lleush enìc endi mesou b matoc thc an lushc idioqarakthristik n, pou qrhsimopoieðtai prokeimènou na perigrafoôn kai na analujoôn oi paramorf seic enìc 3D paramorf simou montèlou epif neiac. Oi exwterikèc dun meic pou proselkôoun to 3D paramorf simo montèlo epif neiac, sundu zoun thn èntash twn eikonostoiqeðwn thc eikìnac me tic qwrikèc plhroforðec twn topik n perioq n thc. O proteinìmenoc algìrijmoc kat tmhshc eikìnac apoteleðtai apì dôo b mata. Arqik, mia teqnik kb ntishc qr matoc, pou basðzetai stic metatopðseic kìmbwn tou paramorf simou montèlou epif - neiac, qrhsimopoieðtai prokeimènou na meiwjeð o arijmìc qrwm twn sthn eikìna. Katìpin, h proteinìmenh sun rthsh enèrgeiac qrhsimopoieðtai wc

32 10 Kef laio 1. Eisagwg krit rio gia ènan algìrijmo sunènwshc perioq n. H telik kat tmhsh thc eikìnac par getai met thn efarmog miac teqnik c sugq neushc perioq n. H proteinìmenh mèjodoc efarmìsthke sth b sh dedomènwn kat tmhshc tou Mpèrkleô. Ta epiteuqjènta apotelèsmata parousi zoun kal eurwstða sugkrinìmena me llouc algorðjmouc sthn episthmonik perioq thc kat tmhshc eikìnac.

33 BibliografÐa [1] A. Barr, Global and local deformations of solid primitives," in Proceedings of the 11th annual conference on Computer graphics and interactive techniques, pp , New York, NY, USA, 1984, ACM Press. [2] M. Kass, A. Witkin and D. Terzopoulos, Snakes: Active contour models. International Journal of Computer Vision," International Journal of Computer Visio, vol. 1, no. 4, pp , [3] D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer, Elastically deformable models," Computer Graphics (Proc. SIGGRAPH" 87), vol. 21, no. 4, pp ,

34 12 BibliografÐa

35 Kef laio 2 Epilog kai ParakoloÔjhsh Qarakthristik n ShmeÐwn Qrhsimopoi ntac Trisdi stata Paramorf sima Montèla Epif neiac pou Upìkeintai stouc Nìmouc kai Idiìthtec thc Fusik c 2.1 Eisagwg H parakoloôjhsh antikeimènwn se eikonoseirèc eðnai ènac suqn antimetwpðsimoc stìqoc se efarmogèc pou epexerg zontai to bðnteo, ìpwc h 13

36 14 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn epit rhsh diafìrwn katast sewn, h anagn rish qeironomðac qeri n, h allhlepðdrash anjr pou-upologist, ta èxupna perib llonta, h anagn rish kðnhshc sthn eikonik pragmatikìthta kai sta grafik upologist n, h epexergasða eikonoseir n, h iatrik kai h metewrologða kai h apeikìnish 3D plhroforðac apì mh bajmonomhmèno bðnteo. Kat sunèpeia, stic dôo teleutaðec dekaetðec, entatik episthmonik èreuna èqei diexaqjeð se aut n thn perioq. H oikodìmhsh enìc sust matoc parakoloôjhshc den eðnai mia apl diadikasða lìgw diafìrwn problhm twn, ìpwc oi diaforèc ston fwtismì, oi merikèc olikèc epikalôyeic antikeimènwn, o jìruboc sthn eikìna, h aprìblepth kðnhsh, k.lp. Mèqri t ra, di fora sust mata parakoloôjhshc anjr pwn, pros pwn kai antikeimènwn èqoun parousiasteð sthn episthmonik bibliografða. Aut ta sust mata mporoôn na diairejoôn eurèwc se tèsseric kathgorðec: ffl parakoloôjhsh basismènh sto qr ma, ffl parakoloôjhsh basismènh se prìtupa, ffl parakoloôjhsh perigr mmatoc, ffl parakoloôjhsh basismènh se qarakthristik shmeða. Epiprìsjetec plhroforðec gia tic proanaferjeðsec kathgorðec parakoloôjhshc mporoôn na brejoôn stic ristec dhmosieôseic anaskìphshc pou èqoun emfanisteð sth bibliografða [1]-[5]. To qr ma eðnai èna diakritikì qarakthristikì gn risma twn antikeimènwn kai epomènwc, eðnai qr simo ston entopismì touc se eikìnec kai eikonoseirèc. H plhroforða qr matoc par gei ikanopoihtik apotelèsmata sthn parakoloôjhsh antikeimènwn kai epitrèpei th gr gorh epexergasða, h opoða eðnai shmantik gia èna sôsthma parakoloôjhshc pou prèpei na leitourgeð se èna logikì qronikì plaðsio. Pollèc proseggðseic eðnai basismènec sta istìgramma qr matoc en merikèc llec qrhsimopoioôn olik prìtupa anafor c qr matoc [6]-[7].

37 2.1. Eisagwg 15 Oi teqnikèc antistoðqishc protôpwn qrhsimopoioôntai apì polloôc e- reunhtèc sthn parakoloôjhsh antikeimènwn, akolouj ntac tic Ðdiec arqèc me tic teqnikèc antistoðqishc protôpwn pou axiopoioôntai sthn anagn rish antikeimènwn [8] -[9]. H parakoloôjhsh basismènh se prìtupa perilamb nei th qr sh pollapl n protôpwn th paramìrfwsh protôpwn gia na prosarmìsei tic allagèc sto antikeðmeno tou endiafèrontoc. H diadikasða tou kajorismoô antistoiqi n metaxô eikìnac kai protôpou eðnai upologistik meg lh all parèqei ikanopoihtik apotelèsmata parakoloôjhshc. H parakoloôjhsh pou basðzetai se plhroforðec perigr mmatoc tou a- ntikeimènou endiafèrontoc eðnai eukolìterh apì to na diamorfwjeð kai na parakoloujhjeð olìklhro to antikeðmeno, p.q. ìpwc ìtan qrhsimopoieðtai to qr ma. Epiplèon, h parakoloôjhsh perigr mmatoc eðnai pio akrib c se sqèsh me thn apl parakoloôjhsh gwni n akm n, dedomènou ìti mporeð na prosarmosteð ste na antimetwpðsei peript seic ìpou to upì parakoloôjhsh antikeðmeno epikalôptetai merik c sthn exetazìmenh eikonoseir. H energìc anapar stash perigr mmatoc pou eis getai apì ton Kass [10], eðnai h dhmofilèsterh mèjodoc gia th skiagr fhsh kai thn parakoloôjhsh perigr mmatoc. H parakoloôjhsh pou basðzetai se shmeða eðnai mia suqn qrhsimopoihmènh prosèggish, sthn opoða ta kinoômena antikeðmena antiproswpeôontai apì qarakthristik shmeða pou aniqneôontai prin apì thn parakoloôjhsh kat th di rkeia thc parakoloôjhshc. Autì to eðdoc parakoloôjhshc, an kai eðnai epirrepèc se l jh parakoloôjhshc, mporeð na efarmosteð polô apotelesmatik kai autì eðnai shmantikì se pollèc krðsimec efarmogèc ìpou o qrìnoc eðnai kajoristikìc. H epilog twn qarakthristik n gnwrism twn exart tai apì ton ek stote algìrijmo kai basðzetai sun jwc se sugkekrimèna qarakthristik gnwrðsmata shmeðwn (topikèc idiìthtec eikìnac). 'Enac shmantikìc arijmìc algorðjmwn parakoloôjhshc shmeðwn prospajeð na susqetðsei qarakthristik se diado-

38 16 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn qikèc eikìnec. Sthn ergasða [11], ta qarakthristik shmeða epilègontai stoqastik me b sei thn enèrgeia twn suntelest n metasqhmatismoô Gabor kum twn. Holik topojèthsh twn qarakthristik n shmeðwn kajorðzetai apì èna 2D plègma, qrhsimopoi ntac thn perioq twn trig nwn pou diamorf nontai apì ta qarakthristik shmeða. Aut h mèjodoc qrhsimopoieð èna topikì qarakthristikì di nusma pou perièqei touc suntelestèc metasqhmatismoô Gabor kum twn kai èna olikì di nusma qarakthristik n shmeðwn pou perièqei tic perioqèc trig nwn. Prokeimènou na brejoôn ta antðstoiqa qarakthristik gnwrðsmata sthn epìmenh qronik eikìna, o 2D qrusìc algìrijmoc tmhm twn ( golden section algorithm) uiojeteðtai. K poia qarakthristik gnwrðsmata mesaðou epipèdou (strokes) qrhsimopoioôntai sto [12], antð qamhloô epipèdou shmeða ìpwc oi akmèc. Aut ta shmeða oloklhr nontai me thn org nwsh twn akm n mèsw miac leitourgðac sôndeshc touc. DÔo katast seic (ègkuroc/ kuroc) qrhsimopoioôntai gia k je qarakthristikì shmeðo kai mia pijanìthta ekqwreðtai sto kajèna. Kat' autì ton trìpo, ìla ta shmeða sumb lloun sthn parakoloôjhsh tou kinoômenou antikeimènou all me diaforetik b rh to kajèna. Sthn teqnik pou parousi zetai sto [13], pollapl qarakthristik shmeða qrhsimopoi jhkan prokeimènou na belti soun thn akrðbeia kai thn eurwstða enìc sust matoc parakoloôjhshc ikanì na leitourg sei se pragmatikì qrìno. Pio sugkekrimèna, qarakthristik shmeða istogramm twn qr matoc sundu sthkan me qarakthristik shmeða morf c basismèna se akmèc klðshc (edge-gradient) ste na sumb lloun sthn parakoloôjhsh tou a- ntikeimènou endiafèrontoc se èna Monte Carlo plaðsio ergasðac. Mia sôgkrish tess rwn algorðjmwn parakoloôjhshc basismènoi se qarakthristik shmeða dðnetai sto [14]. PolloÐ ereunhtèc, antð na prospaj soun na belti soun thn apìdosh parakoloôjhshc antikeimènou mèsw thc epinìhshc eufuèsterwn qarakthristik n gnwrism twn, ekmetalleôthkan th gn sh gia to p c douleôei èna sôsthma parakoloôjhshc kai prosp jhsan na epib loun di forouc periorismoôc ste na beltiwjeð h parako-

39 2.1. Eisagwg 17 loôjhsh twn qarakthristik n shmeðwn [15, 16, 17]. Stic perissìterec peript seic, èna b ma arqikopoðhshc, pou exart - tai apì ton algìrijmo parakoloôjhshc, efarmìzetai prin apì thn parakoloôjhsh kai kajorðzei thn perioq twn shmeðwn endiafèrontoc. Stouc algorðjmouc pou basðzontai se qarakthristik shmeða, poikðlec strathgikèc epilog c shmeðwn mporoôn na qrhsimopoihjoôn. O stìqoc eðnai na lhfjoôn qarakthristik shmeða sthn eikìna pou eðnai kat llhla gia parakoloôjhsh. Poll apì aut ta qarakthristik shmeða qrhsimopoioôntai epðshc kai gia teqnikèc antistoðqhshc eikìnwn, p.q., gia thn eôresh antistoiqi n metaxô dôo diaforetik n ìyewn thc Ðdiac skhn c. O Lowe prìteine ta shmeða SIFT ( Scale Invariant Feature Transform) [18], ta opoða eðnai amet blhta se klim kwsh, peristrof kai allagèc fwtismoô. Ta SIFT shmeða qrhsimopoi jhkan sthn anðqneush antistoiqi n se eikìnec kai sthn an kthsh eikìnac. O Harris [19] prìteine ènan sunduasmèno aniqneut akm n kai gwni n pou parèqei qarakthristik shmeða ploôsia se plhroforða akm n kai ètsi eðnai kat llhla gia parakoloôjhsh antikeimènwn. Sthn teqnik pou parousi sthke sto [20], ta qarakthristik shmeða ex gontai basizìmena stic idiotimèc miac m trac klðshc thc eikìnac pou kataskeu zetai gia mia perioq gôrw apì to upoy fio qarakthristikì shmeðo. E n h el qisth idiotim aut c thc m trac eðnai megalôterh apì èna prokajorismèno apì to qr sth kat fli, to qarakthristikì shmeðo jewreðtai kalì gia parakoloôjhsh. Ta epilegmèna shmeða me b sh thn parap nw mèjodo eðnai bèltista gia ton algìrijmo parakoloôjhshc pou parousi zetai sto Ðdio èggrafo. Epiplèon, èna llo sq ma epilog c qarakthristik n shmeðwn proc parakoloôjhsh prot jhke sto [21]. Lamb nontac upìyh èna sônolo qarakthristik n gnwrism twn, upologðsthkan oi analogðec pijanìthtac twn puknot twn twn deigm twn apì ta antikeðmena tou endiafèrontoc all kai tou fìntou, gia na diamorf soun èna nèo sônolo upoy fiwn qarakthristik n gnwrism twn pou prosarmìsthkan sthn di krish antikeimènou/fìntou. Ta posost analogðac twn

40 18 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn duo kl sewn qrhsimopoioôntai gia na kathgoriopoi soun aut ta nèa qarakthristik gnwrðsmata sômfwna me to pìso kal qwrðzoun ta deðgmata twn eikonostoiqeðwn tou antikeimènou endiafèrontoc kai tou fìntou. Autìc o mhqanismìc axiolìghshc qarakthristik n gnwrism twn enswmat netai se èna sôsthma mèsou-metatìpishc (mean-sift) parakoloôjhshc pou epilègei prosarmostik ta qarakthristik gnwrðsmata gia thn parakoloôjhsh. 'Enac kainotìmoc algìrijmoc epilog c kai parakoloôjhshc qarakthristik n shmeðwn proteðnetai se autì to kef laio. Efalt rio aut c thc mejìdou apotèlesan oi teqnikèc pou parousi sthkan sta [22]-[24]. O Nastar [22] qrhsimopoðhse paramorf sima montèla gia na proseggðsei tic dunamikèc akoloujðec paramorf sewn epif neiac antikeimènou se eikonoseirèc plhrofori n ìgkou (dhl. 3D akoloujðec stoiqeðwn) kai ef rmose thn teqnik an lushc idioqarakthristik n (Modal Analysis) (mia tupopoihmènh teqnik sth mhqanik pou epitrèpei apotelesmatikìterouc upologismoôc kai parèqei kleistèc lôseic sthn diadikasða paramìrfwshc) prokeimènou na perigrafoôn kai na analujoôn oi paramorf seic se bðoiatrikèc eikìnec. To plaðsio ergasðac pou proteðnetai se autì to kef laio èqei qrhsimopoihjeð epðshc sthn eujugr mmish seiriak epðkthtwn tom n [24], sthn polômorfh an lush eikìnac egkef lou [23] kai sthn kat tmhsh 2D antikeimènwn [25]. Sthn prokeimènh perðptwsh, o sqhmatismìc twn paramorf simwn montèlwn qrhsimopoieðtai se mia entel c diaforetik kai nèa efarmog, dhlad aut thc epilog c kai parakoloôjhshc qarakthristik n shmeðwn. Upojètontac ìti h fwteinìthta thc eikìnac se k je eikìna tou bðnteo mporeð na proseggisteð apì mia paramorf simh epif - neia, k poioc mporeð na epilèxei kai na parakolouj sei qarakthristik shmeða. H proteinìmenh teqnik ekmetalleôetai èna upopro ìn twn exis sewn diakubèrnhshc pou kajorðzoun tic paramorf seic tou montèlou epif neiac, prokeimènou na epilegoôn kai na parakoloujhjoôn qarakthristik shmeða. Pio sugkekrimèna, h diadikasða epilog c qarakthristik n

41 2.1. Eisagwg 19 shmeðwn qrhsimopoieð to apokaloômeno genikeumèno di nusma metatopðsewn (generalized displacementvector) [22], pou apodeiknôetai ìti eðnai ènac kainotìmoc sunduasmìc paragwg c di forwn mask n anðqneushc gramm n kai akm n kai ètsi eðnai ikanì na par gei qarakthristik shmeða pou antistoiqoôn se topikèc akmèc, grammèc, gwnðec lla qarakthristik gnwrðsmata miac eikìnac pou eðnai kat llhla gia parakoloôjhsh. H sôndesh metaxô tou paramorf simou montèlou epif neiac kai twn aniqneut n gramm n/akm n eðnai mia shmantik èkbash autoô tou kefalaðou. Met thn epilog qarakthristik n shmeðwn, o proteinìmenoc algìrijmoc parakoloujeð ta shmeða basizìmenoc sth mètrhsh kai sthn antistoðqhsh tou genikeumènou dianôsmatoc metatopðsewn twn qarakthristik n shmeðwn se diadoqikèc eikìnec miac eikonoseir c. En suntomða, h kainotomða tou sugkekrimènou kefalaðou ègkeitai sth qr sh enìc paramorf simou montèlou epif neiac to opoðo proseggðzei thn epif neia fwteinìthtac miac eikìnac kai sthn metèpeita qr sh enìc ìrou pou emfanðzetai sthn diadikasða paramìrfwshc ste na epilèxei kai na parakolouj sei qarakthristik shmeða. 'Oson afor to paramorf simo montèlo kai thn teqnik an lus c tou ìpwc eis qjhke sta [26, 22] kai peraitèrw qrhsimopoi jhke sta [23, 24], h kainotomða brðsketai sth qr sh tou montèlou gia mia diaforetik efarmog (dhlad aut thc epilog c kai parakoloôjhshc qarakthristik n shmeðwn), sth qr sh diaforetik n exwterik n dun mewn pou proselkôoun to montèlo proc th fwteinìthta thc eikìnac (ìpwc ja perigrafeð sthn Par grafo 2.2) kai sth qr sh enìc endi mesou apotelèsmatoc (to genikeumèno di nusma metatopðsewn) thc diadikasðac paramìrfwshc tou montèlou antð na qrhsimopoihjeð to montèlo autì kaj' eautì. Sugkrinìmeno me up rqontec algorðjmouc epilog c kai parakoloôjhshc qarakthristik n shmeðwn, ìpwc ton Kanade-Lucas-Tomasi (KLT) [27] kai to SIFT [28], hproteinìmenh mèjodoc epitugq nei kalôterh apìdosh apì thn poyh thc parakoloôjhshc enìc antikeimènou se akrðbeia

42 20 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn kai eurwstða. Ta apotelèsmata deðqnoun ìti h proteinìmenh mèjodoc eðnai dunat en ntia se peristrofèc, klimak seic, enallagèc fwtismoô kai èntonec skièc kai mporeð na akolouj sei ta epilegmèna qarakthristik shmeða gia makr qronik diast mata. Epiplèon, to tm ma algorðjmou thc epilog c qarakthristik n shmeðwn, sugkrðjhke me llouc algorðjmouc epilog c qarakthristik n shmeðwn, ìpwc o SIFT [18] kai oi aniqneutèc akm n kai gwni n tou Harris [19] kai apodeðqjhke ìti parèqei kalôtera apotelèsmata sthn metèpeita parakoloôjhsh touc. To upìloipo tou kefalaðou organ netai wc ex c. Sthn Par grafo 2.2 parousi zetai mia sunoptik perigraf thc diadikasðac paramìrfwshc b sei thc teqnik c an lushc idioqarakthristik n. H diadikasða epilog c qarakthristik n shmeðwn eis getai sthn Par grafo 2.3. O algìrijmoc parakoloôjhshc perigr fetai sthn Par grafo 2.4. H apìdosh thc proteinìmenhc teqnik c, kaj c epðshc kai mia sôgkrish metaxô tou proteinìmenou algorðjmou kai tou eurèwc diadedomènou sthn bibliografða algorðjmou parakoloôjhshc KLT [27], tou algorðjmou epilog c shmeðwn kai parakoloôjhshc SIFT [18] kai tou aniqneut qarakthristik n shmeðwn Harris [19] parousi zontai sthn Par grafo 2.5. Ta telik sumper smata sun gontai sthn Par grafo Trisdi stato Paramorf simo Montèlo Epif neiac pou Upìkeitai stouc Nìmouc thc Fusik c H fwteinìthta miac eikìnac I(x; y) mporeð na jewrhjeð ìti kajorðzei mia epif neia p nw apì thn perioq thc eikìnac (x; y) pou ja kaleðtai sth sunèqeia epif neia fwteinot twn (sq ma 2.2b). H proteinìmenh mèjodoc parakoloôjhshc antikeimènou sthrðzetai sthn parametropoðhsh enìc 3D q rou pou orðzetai apì to (x; y; I(x; y)) kai kaleðtai XY I q roc [29].

43 2.2. Paramorf simo Montèlo 21 'Ena 3D paramorf simo montèlo epif neiac pou upìkeitai stouc nìmouc thc fusik c kai qrhsimopoi jhke sta [22, 23, 26], uiojeteðtai gia autìn to skopì. Se aut thn Par grafo, h mejodologða pou perigr fhke stic proanaferjeðsec ergasðec ja anajewrhjeð en suntomða, ste na katasteð autì to kef laio autìnomo kai eparkèc. Gia perissìterec leptomèreiec, sumperilambanomènwn kai twn upojèsewn pou èqoun lhfjeð, oi endiaferìmenoi anagn stec mporoôn na sumbouleujoôn tic proanaferjeðsec ergasðec. k l o m c N w N h Sq ma 2.1: Tetr pleuro montèlo epif neiac. To paramorf simo montèlo epif neiac apoteleðtai apì èna omoiìmorfo tetr pleuro plègma N = N h N w kìmbwn, ìpwc faðnetai kai sto sq ma 2.1. Se aut thn par grafo, upojètoume ìti ta N h, N w eðnai Ðsa me to Ôyoc kai to pl toc thc eikìnac antðstoiqa (se eikonostoiqeða), sunep c k je eikonostoiqeðo thc eikìnac antistoiqeð se ènan kìmbo tou plègmatoc. Oi suntetagmènec twn kìmbwn tou upì exètash montèlou susswreôontai se èna di nusma:

44 22 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn v (fi ) = h r (fi ) 11;:::;r (fi ) ; T 1 Nw r(fi 21;:::;r ) (fi jj0;:::;r NhNwi ) (fi ) = h i T = r (fi ) 1 ;:::;r (fi ) i ;:::;r (fi ) N ; (2.1) ìpou N = N h N w, j 2 f1; 2;:::;N h g, j 0 2 f1; 2;:::;N w g, i = (j 1)N w + j 0 kai i 2 f1; 2;:::;Ng, r (fi ) i = [x (fi ) i ; y (fi ) i ; z (fi ) i ]. To stoiqeðo z (fi ) i antistoiqeð sth fwteinìthta thc eikìnac, dhlad z (fi ) i = I(x (fi ) i ;y (fi ) i ). To fi dhl nei th qronik stigm paramìrfwshc. K je kìmboc tou montèlou upotðjetai ìti èqei mia m za m kai sundèetai me touc geitonikoôc tou kìmbouc me tèleia elat ria Ðdiac sklhrìthtac k, fusikoô m kouc l 0 suntelest apìsbeshc c. K tw apì thn epðdrash eswterik n kai exwterik n dun mewn, to sôsthma m za-elathrðwn paramorf netai se èna 3D plègma anaparist ntac thn epif neiac thc eikìnac, ìpwc mporeð na dei k poioc sto sq ma 2.2d. To upì melèth montèlo eðnai èna sôsthma pou upìkeitai stouc nìmouc thc fusik c kai kubern tai apì th jemeli dh exðswsh dunamik c: f el (r (fi ) i )+f d (r (fi ) i )+f ext (r (fi ) i )=m i r (fi ) i, i =1; 2;:::;N; (2.2) ìpou r (fi ) i eðnai to i-stì stoiqeðo tou dianôsmatoc v (fi ), dhlad oi suntetagmènec tou i-stoô kìmbou, m i h m za kai r (fi ) i h epit quns pou apoktiètai upì thn ep reia thc sunolik dônamhc pou askeðtai sto montèlo. H f d ( ) eðnai h dônamh apìsbeshc h opoða eðnai an logh thc taqôthtac twn kìmbwn _r (fi ) i. To f ext ( ) eðnai to exwterikì fortðo dônamhc pou dèqetai k je kìmboc wc apotèlesma thc èlxhc tou montèlou apì th fwteinìthta thc eikìnac, kai suqn basðzetai sthn eukleðdeia apìstash metaxô thc fwteinìthtac enìc eikonostoiqeðou thc eikìnac, tou opoðou h antipros peush sto XY I q ro eðnai (x ij ;y ij ;I(x ij )) kai stic suntetagmènec twn kìmbwn [30, 31]. H f el ( ) eðnai to jroisma twn elastik n dun mewn pou efarmìzontai ston i-stì kìmbo. kai

45 2.2. Paramorf simo Montèlo 23 Se orismènec peript seic, pou mporoôn na brejoôn sto [22], to paramorf simo montèlo epif neiac kuberneðtai apì thn dunamik exðswsh (lagrangian dynamics) [32]: Mü (fi ) + C _u (fi ) + Ku (fi ) = f (fi ) ; (2.3) ìpou u (fi ) eðnai to di nusma me tic metatopðseic twn kìmbwn u (fi ) = v (fi ) v (fi 0). Oi M, C, kai K [33] eðnai, antðstoiqa, oi N N pðnakec m zac, apìsbeshc kai sklhrìthtac twn elathrðwn tou montèlou kai f (fi ) eðnai to di nusma me tic exwterikèc dun meic. E n h arqik kai telik kat stash paramìrfwshc eðnai gnwst, mporoôme na upojèsoume ìti èna stajerì fortðo dônamhc f efarmìzetai sto montèlo epif neiac [23]. Aut h upìjesh isqôei kai sthn sugkekrimènh perðptwsh pou exet zetai se autì to kef laio, ìpou h arqik kat stash eðnai h arqik diamìrfwsh tou montèlou (sq ma 2.2g) kai h telik, epijumht kat stash eðnai h epif neia fwteinìthtac thc eikìnac, pou parousi zetai sto sq ma 2.2b. Kat sunèpeia, h exðswsh (2.3) metasqhmatðzetai sthn exðswsh diakubèrnhshc se kat stash isorropðac (equilibrium governing equation) kai antistoiqeð sto statikì prìblhma: Ku = f: (2.4) AntÐ na brejeð mesa h lôsh thc exðswshc sthn kat stash isorropðac (2.4), k poioc mporeð na th metasqhmatðsei me mia allag b shc [34]: u = Ψ~u; (2.5) ìpou Ψ eðnai ènac tetragwnikìc mh-antistrèyimoc pðnakac metasqhmatismoô, t xewc N, proc kajorismì kai to ~u anafèretai wc to genikeumèno di nusma metatopðsewn. 'Enac apotelesmatikìc trìpoc epilog c tou Ψ eðnai na tejeð Ðso me ton pðnaka Φ, tou opoðou oi st lec eðnai ta idiodianôsmata ffi i tou genikeumènou idioprobl matoc: Kffi i =! 2 i Mffi i ; (2.6)

46 24 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn u (fi ) = Φ~u (fi ) = N =NhNw X i=1 ffi i ~u (fi ) i : (2.7) To i-stì idiodi nusma ffi i, dhlad, h i-st st lh Φ kaleðtai epðshc kai i-stì idiodi nusma tal ntwshc. To ~u i eðnai to i-stì stoiqeðo tou ~u kai! i eðnai h antðstoiqh idiotim (pou apokaleðtai kai suqnìthta tal ntwshc). H exðswsh (2.5) (kai en suneqeða (2.7) ) eðnai gnwst wc exðswsh epallhlðac twn idioqarakthristik n tou montèlou. 'Ena shmantikì pleonèkthma thc an lushc idioqarakthristik n, eðnai ìti ta idiodianôsmata ffi i kai oi idiotimèc! i miac epðpedhc topologðac è- qoun mia rht diatôpwsh [22] kai den eðnai aparaðthto na upologistoôn qrhsimopoi ntac tic teqnikèc idio-aposônjeshc:! 2 (j; j 0 )= 4k m ffi n;n 0(j; j 0 ) = cos» sin 2 ßj 2N h + sin 2 ßj 0 2N w ; (2.8) ßj(2n 1) N h cos ßj0 (2n 0 1) N w ; (2.9) ìpou j = 0; 1;:::;N h 1, j 0 = 0; 1;:::;N w 1, n = 1; 2;:::;N h, n 0 = 1; 2;:::;N w,! 2 (j; j 0 ) =! 2 jnw+j0, ffi n;n 0(j; j 0 ) eðnai to (n; n 0 )-stì stoiqeðo tou pðnaka ffi(j; j 0 ), ìpou ffi(j; j 0 )=ffi jn w+j0. Sto q ro twn idioqarakthristik n, h exðswsh (2.4) mporeð na grafteð wc ex c: ~K~u = ~ f; (2.10) ìpou ~K = Φ T KΦ kai ~ f = Φ T f, f eðnai to di nusma exwterik n dun mewn. Wc ek toôtou, qrhsimopoi ntac tic exis seic (2.7), (2.8) kai (2.9), h exðswsh (2.10) aplopoieðtai se 3N bajmwtèc exis seic:! 2 i ~u i;j = ~ f i;j : (2.11) Ta stoiqeða twn dun mewn sto di nusma f kat m koc twn axìnwn x kai y jewr jhkan ìti eðnai Ðsa me mhdèn, dhlad f i;x = f i;y =0. Ta stoiqeða aut n twn dun mewn kat ton xona z ( xonac fwteinìthtac) jewroôntai

47 2.2. Paramorf simo Montèlo 25 (a) (b) (g) (d) Sq ma 2.2: (a) Eikìna pouapeikonðzei èna prìswpo, (b) anapar stash thc epif neiac fwteinot twn thc eikìnac, (g) to arqikì montèlo se kat stash isorropðac, (d) to metasqhmatismèno montèlo epif neiac pou proseggðzei thn epif neia fwteinot twn thc eikìnac. an loga thc eukleðdeiac apìstashc metaxô tou shmeðou (x; y; I(x; y)) thc epif neiac fwteinot twn kai thc antðstoiqhc jèshc tou kìmbou sto montèlo sthn arqik diamìrfws tou (x; y; 0), dhlad, Ðso me thn fwteinìthta I(x; y) tou eikonostoiqeðou (x; y): f (x 1)N w +y;z = f(x; y) =I(x; y), ìpou

48 26 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn f (x 1)N w +y;z eðnai tostoiqeðo ston xona z tou (x 1)N w +y-stoô stoiqeðou tou dianôsmatoc f. Upì autèc tic sunj kec, to montèlo paramorf netai mìno kat m koc tou xona z. Sthn perðptwsh pou exet zetai se autì to kef laio, k je eikìna thc eikonoseir c perigr fetai apì talant seic enìc arqikoô montèlou. sq ma 2.2 xedialônei ton trìpo tal ntwshc miac 2D eikìnac enìc anjr pinou pros pou pou apeikonðzetai sto sq ma 2.2a. H anapar stash thc epif neiac fwteinot twn thc eikìnac faðnetai sto sq ma 2.2b. To mègejoc tou montèlou (se kìmbouc) pou qrhsimopoi jhke gia na proseggðzei thn epif neia thc eikìnac tan Ðso me to mègejoc thc eikìnac (se eikonostoiqeða). To tetr pleuro plègma tou montèlou arqikopoieðtai (sq ma 2.2g) kai ta stoiqeða ~u ij upologðzontai wc ex c: ~u ij = P N h n=1 P N w (1 +! 2 (i; j))q PN h n=1 n0 =1 I(n; n 0 )ffi n;n 0(i; j) P N w n0 =1 ffi 2 n;n0(i; j) To : (2.12) Prèpei na shmeiwjeð ìti to paramorf simo montèlo epitugq nei mìno mia prosèggish thc epif neiac fwteinot twn thc exetazìmenhc eikìnac. To genikeumèno di nusma metatopðsewn ~u (t) (x; y) thc exðswshc (2.10) qrhsimopoieðtai, ìpwc parousi zetai stic epìmenec Paragr fouc, prokeimènou na epileqtoôn kai na parakoloujhjoôn qarakthristik shmeða se 2D eikìnec. Autì to di nusma ja kaleðtai qarakthristikì di nusma shmeðwn (QDS).'Ena di gramma ro c tou proteinìmenou algorðjmou parousi zetai sto sq ma 2.3. Oi leptomèreiec tou algorðjmou anafèrontai stic epìmenec Paragr fouc autoô tou kefalaðou. 2.3 Algìrijmoc Epilog c Qarakthristik n ShmeÐwn se Eikìnec Se aut n thn Par grafo, eis getai o algìrijmoc me ton opoðo 3D paramorf sima montèla epif neiac pou upìkeintai stouc nìmouc thc fusik c

49 2.3. Epilog ShmeÐwn 27 Εικόνα εισόδου Χειροκίνητη επιλογή περιοχής ενδιαφέροντος Αριθμός χαρακτηριστικών σημείων προς επιλογή ( M), μέγεθος της αρχικής περιοχής αναζήτησης( Rt), μέγεθος του παραμορφώσιμου μοντέλου ( N x N ) Παράμετροι που καθορίζει ο χρήστης h w Για κάθε εικονοστοιχείο στην επιλεγμένη περιοχή υπολογίζεται το χαρακτηριστικό διάνυσμα (CFV) Επιλογή χαρακτηριστικών σημείων: τα εικονοστοιχεία με την μεγαλύτερη απολύτη τιμή του αθροίσματος των στοιχείων του CFV Παρακολούθηση χαρακτηριστικών σημείων Το CFV υπολογίζεται για κάθε εικονοστοιχείο στην περιοχή αναζήτησης της επόμενης χρονικά εικόνας Το ταίριασμα των χαρακτηριστικών σημείων γίνεται με τη χρήση της απόλυτης τιμής του αθροίσματος των στοιχείων του CFV Ικανοποιητική ποιότητα ταιριάσματος Ναι Νέες θέσεις στην επόμενη χρονικά εικόνα Όχι Το μέγεθος της περιοχής αναζήτησης αυξάνεται Είναι το μέγεθος της περιοχής αναζήτησης μικρότερο από το κατώφλι; Όχι Το χαρακτηριστικό σημείο θεωρείται χαμένο Ναι Θέσεις παρακολούθησης για κάθε εικόνα του βίντεο Sq ma 2.3: Di gramma ro c tou proteinìmenou algorðjmou epilog c kai parakoloôjhshc qarakthristik n shmeðwn. mporoôn na qrhsimopoihjoôn ste na epilèxoun qarakthristik shmeða se mia eikìna. Aut h diadikasða epilog c qarakthristik n shmeðwn mporeð na efarmosteð sthn pr th eikìna miac eikonoseir c prokeimènou na arqikopoihjeð mia diadikasða parakoloôjhshc enìc antikeimènou pou ja perigrafeð leptomer c sthn epìmenh Par grafo. H Ðdia diadikasða mporeð na qrhsimopoihjeð gia na arqikopoi sei xan k poion algìrijmo parakoloôjhshc se peript seic ìpou k ti tètoio apaiteðtai, p.q. ìtan

50 28 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn exafanðzetai to upì parakoloôjhsh antikeðmeno kai epanemfanðzetai sth skhn. Prokeimènou na epilegeð èna eikonostoiqeðo (x; y) sthn eikìna I t th qronik stigm t san qarakthristikì shmeðo, qrhsimopoieðtai to qarakthristikì di nusma shmeðwn ~u (t) (x; y) thc exðswshc (2.10), ta stoiqeða tou opoðou upologðzontai apì thn exðswsh (2.12). Gia ton kajorismì tou QDS enìc eikonostoiqeðou (x; y) miac eikìnac I t apì èna bðnteo, èna paramorf simo montèlo epif neiac, megèjouc N H N W (N H» N h, N W» N w, oi N H kai N W eðnai perittoð arijmoð), efarmìzetai se mia perioq thc eikìnac D t tou idðou megèjouc (N H N W ), me kèntro to eikonostoiqeðo (x; y). To QDS ~u (t) (x; y) gia èna sugkekrimèno eikonostoiqeðo (x; y) eðnai: ~u (t) (x; y) =[k (t) 11(x; y); k (t) 12(x; y);:::;k (t) NH NW (x; y)]t ; (2.13) ìpou k (t) i;j(x; y) =[~u (t) xi;j(x; y); ~u (t) yi;j(x; y); ~u (t) zi;j(x; y)] T,to opoðo paðrnei timèc an efarmosteð h diadikasða paramìrfwshc, h opoða perigr fhke sthn Par grafo 2.2, sthn perioq thc eikìnac D t. 'Opwc anafèrjhke dh sthn prohgoômenh Par grafo, kamða paramìrfwsh den gðnetai kat m koc twn axìnwn x kai y, dhlad paramorf seic emfanðzontai mìno ston xona twn fwteinot twn (z xonac), oi opoðec ofeðlontai stic fwteinìthtec thc eikìnac. Kat sunèpeia, ~u (t) xij(x; y) =~u (t) yij(x; y) =0kai to QDS aplopoieðtai sthn parak tw morf : ~u (t) (x; y) =[~u (t) 11(x; y);:::;~u (t) NHNW (x; y)]t ; (2.14) ìpou to ~u (t) ij (x; y), ~u (t) zij(x; y). Qrhsimopoi ntac thn exðswsh (2.12), k - poioc mporeð na diapist sei ìti to ~u (t) ij (x; y) mporeð na ekfrasteð wc ex c: X ~u (t) ij (x; y) = NH 1 k=0 NW 1 X l=0 ij (k; l)i t x N W 1 + k; y N H 1 + l ; 2 2 (2.15)

51 2.3. Epilog ShmeÐwn 29 ìpou: ij (k; l) = ffi k;l (i; j) (1 +! 2 (i; j))q PN H k=1 P N W l=1 ffi2 k;l (i; j) ; 0» k» N H 1; 0» l» N W 1: (2.16) Oi timèc twn pin kwn ij (2.16) gia qarakthristikèc timèc twn N H, N W, (p.q. 3, 5) od ghsan sto sumpèrasma ìti autoð oi pðnakec (W ij ) antistoiqoôn se gnwstèc m skec epexergasðac eikìnac, ìpwc aniqneutèc gramm n kai akm n, klimakwmènec me mia stajer a ij, h tim thc opoðac exart - tai apì tic idiìthtec tou paramorf simou montèlou epif neiac, dhlad th sklhrìthta twn elathrðwn kai th m za twn kìmbwn: ij (k; l) =a ij W ij (k; l): (2.17) Gia thn pio apl perðptwsh ìpou N H = N W =3kai gia èna montèlo me k =1kai m =1,to di nusma ~u (t) (x; y) upologðzetai an dojoôn oi timèc sta a ij kai W ij pou emfanðzontai ston PÐnaka 2.1. Pr gmati, eðnai olof nero ìti autèc oi m skec antistoiqoôn se m skec epexergasðac eikìnac. Oi m skec W 12 kai W 21 eðnai oi m skec anðqneushc akm n Prewitt [35], oi opoðoi aniqneôoun orizìntiec kai k jetec akmèc antðstoiqa. Epiplèon, oi m skec W 13 kai W 31 eðnai k jetoi kai orizìntioi aniqneutèc akm n [35]. Akìma, oi m skec W 23 kai W 32 eðnai aniqneutèc akm n [36] kai h m ska W 33 eðnai h Laplacian m ska anðqneushc gramm n. Oi m skec kai oi stajerèc sthn perðptwsh pou N H = N W = 5 parousi zontai ston PÐnaka 2.2. Autèc oi m skec antistoiqoôn epðshc se m skec anðqneushc gramm n kai akm n. Kat sunèpeia, ta stoiqeða tou QDS, axiolog jhkan qrhsimopoi ntac thn exðswsh (2.15) p nw se mia perioq eikìnac kentrarismènh sto eikonostoiqeðo (x; y) kai me kat llhlouc suntelestèc kai apodeðqjhke pwc eðnai m skec anðqneushc gramm n kai akm n. H sôndesh metaxô tou qarakthristikoô dianôsmatoc shmeðwn

52 30 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn PÐnakac 2.1: Oi stajerèc a ij kai oi m skec W ij (pðnakec) diast sewn a 11 =0:1111 a 12 =0:0962 a 13 =0:0278 W 11 = W 12 = W 13 = a 21 =0:0962 a 22 =0:1111 a 23 =0:0385 W 21 = W 22 = W 23 = 64 a 31 =0:0278 a 32 =0:0385 a 33 =0:0159 W 31 = W 32 = W 33 = (dhlad tou genikeumènou dianôsmatoc metatopðsewn tou paramorf simou montèlou) kai twn mask n anðqneushc akm n/gramm n tan mia apì tic pio endiafèrousec ekb seic autoô tou KefalaÐou. Aut h sôndesh mporeð na apodojeð ston trìpo me ton opoðo h teqnik thc an lushc idioqarakthristik n leitourgeð. Sthn ousða, h exðswsh an lushc idioqarakthristik n (2.5) ekteleð mia suqnotik aposônjesh enìc sq matoc, dhlad to aposunjètei se èna suqnotik auxanìmeno sônolo talant sewn (pou eðnai orjokanonikèc sunart seic kai antistoiqoôn se basik sq mata) pou sundu zontai grammik apì ta eôrh twn idioqarakthristik n [22]. Oi m - skec pou sqetðzontai me thn axiolìghsh tou QDS parèqoun plhroforðec gia to suqnotikì perieqìmeno thc eikìnac ( kmec, grammèc kai mèsh tim thc fwteinìthtac ton DC ìro) pou eisèrqetai sthn aposônjesh suqnìthtac mèsw twn eôrwn twn idioqarakthristik n ~u i sthn exðswsh (2.7). Ston proteinìmeno algìrijmo epilog c qarakthristik n shmeðwn, upologðzoume to QDS~u (t) (1; 1); ~u (t) (1; 2); :::; ~u (t) (N Hreg ;N Wreg ), gia k je eikonostoiqeðo (x; y) miac perioq c thc eikìnac R t pou parakoloujeðtai th qronik stigm t, ìpou N Hreg N Wreg eðnai to mègejoc thc perioq c thc eikìnac. Sth sunèqeia, to di nusma S (t) tou opoðou ta stoiqeða S (t) x;y eð-

53 2.3. Epilog ShmeÐwn 31 PÐnakac 2.2: Oi stajerèc a ij kai oi m skec W ij (pðnakec) diast sewn 5 5. W ij a ij w 00...w 04 w 10...w 14 w 20...w 24 w 30...w 34 w 40...w 44 W W nai to jroisma twn apìlutwn tim n twn stoiqeðwn tou QDS ~u (t) (x; y) upologðzetai wc ex c: S (t) =[S (t) 11;S (t) 12;:::;S (t) NHregNWreg ]T ; (2.18) S (t) xy, NHX NWX (k;l)6=(1;1) fi fi fi~u (t) k;l (x; y) fi fifi : (2.19) To stoiqeðo ~u (t) 1;1(x; y) exaireðtai apì touc upologismoôc mèsa sthn (2.19), dedomènou ìti autì to stoiqeðo antistoiqeð sth m ska W 11, h opoða u- pologðzei apl ton topikì mèso ìro twn fwteinot twn thc eikìnac kai epomènwc den perièqei k poia shmantik plhroforða. 'Etsi, se k je eikonostoiqeðo (x; y) thc upì exètash eikìnac ( thc perioq c thc eikìnac) anatðjetai mia tim. Prokeimènou na epilegoôn ta M pio emfan qarakthristik shmeða (eikonostoiqeða) sthn eikìna, epilègontai ta M eikono-

54 32 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn stoiqeða pou antistoiqoôn stic M megalôterec timèc tou S (t) xy, dedomènou ìti mia meg lh tim tou S (t) xy upodhl nei pwc h N H N W perioq thc eikìnac gôrw apì to eikonostoiqeðo (x; y) perièqei kmec, grammèc, gwnðec lla qarakthristik stoiqeða kai epomènwc, to antðstoiqo eikonostoiqeðo eðnai kat llhlo gia parakoloôjhsh. (a) (b) Sq ma 2.4: (a) Oi jèseic twn qarakthristik n shmeðwn pou antistoiqoôn stic 300 megalôterec timèc tou S (t) xy me mègejoc montèlou N H = N W =7, (b) oi jèseic twn qarakthristik n shmeðwn pou antistoiqoôn stic 300 megalôterec timèc tou S (t) xy pou brðskontai se apìstash toul qiston 7 eikonostoiqeðwn metaxô touc (ston orizìntio kai katakìrufo xona). 'Opwc eðnai anamenìmeno, merik apì ta M epilegmèna qarakthristik shmeða brðskontai kont to èna sto llo (sq ma 2.4a), p nw stic akmèc, tic grammèc kai tic gwnðec thc eikìnac. 'Otan ìmwc ta epilegmèna qarakthristik shmeða sugkentr nontai se mia mikr geitoni, tìte emfanðzontai probl mata sthn epakìloujh diadikasða parakoloôjhshc tou antikeimènou, p.q., sthn perðptwsh merik n allhloepikalôyewn antikeimènwn, ìpou

55 2.3. Epilog ShmeÐwn 33 Sq ma 2.5: Oi epif neiec fwteinot twn thc arqik c eikìnac gia 9apì ta epilegmèna shmeða pouapeikonðzontai sto sq ma 2.4 (me mègejoc montèlou N H = N W = 7). O sunolikìc arijmìc twn epilegmènwn shmeðwn eðnai 300). ìla ta qarakthristik shmeða mporeð na qajoôn monomi c. 'Etsi, ta M shmeða p (t), i 2 f1; 2;:::; Mg pou epilègontai telik, eðnai aut pou èqoun i mègisth tim tou S (t) xy all, sugqrìnwc, diathroôn mia orismènh eukleðdeia apìstash D = kp (t) i p (t) j k > D thres metaxô touc (sq ma 2.4b). Pio sugkekrimèna, taxinomoôme ta qarakthristik shmeða sômfwna me to S (t) xy kai epilègoume autì me th megalôterh tim tou S (t) xy. Sth sunèqeia, epilègoume wc deôtero qarakthristikì shmeðo autì me thn amèswc mikrìterh tim tou S (t) xy kai to opoðo brðsketai se mia el qisth epijumht apìstash D thres apì to pr to. H diadikasða suneqðzetai èwc ìtou epiteuqjeð o e- pijumhtìc arijmìc shmeðwn. O arijmìc twn M qarakthristik n shmeðwn pou ja epilegoôn kajorðzetai apì to qr sth. To sq ma 2.5 apeikonðzei tic epif neiec fwteinìthtac thc arqik c eikìnac gia merik apì ta epilegmèna qarakthristik shmeða pou parousi zontai sto sq ma 2.4b. Oi timèc

56 34 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn (a) (b) (g) (d) Sq ma 2.6: (a) H arqik eikìna, (b) 15 epilegmèna shmeða sthn arqik eikìna, (g) h èxodoc tou Canny aniqneut akm n, (d) 15 epilegmèna shmeða p nw sthn èxodo tou Canny aniqneut akm n. twn fwteinot twn brðskontai ston k jeto xona. K poioc mporeð na parathr sei ìti h fwteinìthta thc eikìnac mèsa sthn 7 7 geitoni aut n twn qarakthristik n shmeðwn èqei meg lec apoklðseic. Kat sunèpeia, aut ta shmeða anamènetai na eðnai kat llhla gia parakoloôjhsh, ìpwc ja apodeiqjeð kai sta peir mata sthsunèqeia autoô tou KefalaÐou. H diadikasða epilog c qarakthristik n shmeðwn se mia eikìna eðnai m llon mia qronobìra diadikasða (wstìso ìqi kai exairetik polô), a- foô gia k je eikonostoiqeðo thc eikìnac èna paramorf simo montèlo e-

57 2.4. ParakoloÔjhsh ShmeÐwn 35 pif neiac megèjouc N H N W prèpei na qrhsimopoihjeð. H upologistik poluplokìthta gia k je eikonostoiqeðo eðnai thc t xewc O(N 4 ) gia paramorf simo montèlo megèjouc N N. Autìc o arijmìc poluplokìthtac mporeð na prokôyei apì thn exðswsh (2.12), dedomènou ìti gia k je ènan apì touc N 2 kìmbouc tou paramorf simou montèlou epif neiac, apaitoôntai 2N 2 +1 prosjèseic kai4n 2 +5 pollaplasiasmoð. Gia exoikonìmhsh qrìnou, mporeð k poioc na qrhsimopoi sei ton algìrijmo aniqneut n akm n Canny [37] wc ex c: o Canny aniqneut c akm n efarmìzetai sthn eikìna kai h epilog tou sunìlou twn qarakthristik n shmeðwn (sq ma 2.6b) periorðzetai mìno metaxô twn eikonostoiqeðwn thc eikìnac ìpou h èxodoc tou Canny èqei epishm nei ìti brðskontai akmèc (sq ma 2.6g). Aut h diadikasða prosfèrei mia grhgorìterh all ìqi tìso akrib c epilog qarakthristik n shmeðwn. Se kanèna apì ta peir mata pou anafèretai se autì to Kef laio den qrhsimopoi jhke aut h grhgorìterh èkdosh tou algorðjmou epilog c qarakthristik n shmeðwn, dedomènou ìti h poluplokìthta tan deutereôousac shmasðac. 2.4 Algìrijmoc ParakoloÔjhshc ShmeÐwn se Eikonoseir To prìblhma thc parakoloôjhshc 2D qarakthristik n shmeðwn eðnai i- sodônamo me thn eôresh thc antðstoiqhc jèshc qarakthristik n shmeðwn se diadoqikèc eikìnec miac eikonoseir c. Jewr ntac mia tètoia akoloujða I = I 1 ;I 2 ;:::;I T kai èna qarakthristikì shmeðo p (t) = (x i i ;y i ); t 2 f1; 2;:::; Tg sthn t-st eikìna, to prìblhma parakoloôjhshc mporeð na diatupwjeð wc h eôresh enìc dianôsmatoc d (t) i = d (t) i (x);d (t) i (y), ìpou d (t) i (x);d (t) i (y) eðnai ta stoiqeða twn metatopðsewn tou shmeðou p (t) kat m koc k je xona antðstoiqa, prokeimènou na ektimhjeð h jèsh i tou

58 36 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn p (t+1) i =(x 0 ;y 0 ) sthn epìmenh qronik eikìna: p (t+1) i = p (t) i + d (t) i : (2.20) O proteinìmenoc algìrijmoc parakoloôjhshc upologðzei gia k je qarakthristikì shmeðo p (t) i =(x i ;y i ) apì to sônolo twn epilegmènwn qarakthristik n shmeðwn p (t) = [p (t); 1 p(t) 2 ;:::;p(t) M ]T sthn eikìna I t, to QDS ~u (t) (x; y) gia mia N H N W perioq thc eikìnac kai sth sunèqeia upologðzei to S (t) (x; y): S (t) x;y = NHX N WX (k;l)6=(1;1) fi fi fi~u (t) k;l (x; y) fi fifi : (2.21) Prokeimènou na brejeð h jèsh p (t+1) = (x 0 i i;yi) 0 tou i-stoô qarakthristikoô shmeðou sthn epìmenh qronik eikìna I t+1 thc eikonoseir c, o algìrijmoc upologðzei to QDS ~u (t+1) (k; l) gia k je eikonostoiqeðo miac N S H N SW (N SH, N SW eðnai perittoð arijmoð) perioq c anaz thshc R h opoða eðnai kentrarismènh sto shmeðo (x; y) sthn eikìna I t+1. H nèa jèsh tou i-stoô qarakthristikoô shmeðou dðnetai apì: p (t+1) i =(x 0 i;yi) 0! arg min(js (t) xy S (t+1) kl j); (2.22) kl ìpou k 2 fx N S H 1 2 ; :::; x+ N S H 1 2 g kai l 2 fy N S W 1 2 ; :::; y+ N S W 1 2 g. H qr sh thc apìluthc diafor c (2.22) sto S (t) x;y (2.21) gia ton kajorismì thc omoiìthtac twn qarakthristik n shmeðwn kat th di rkeia thc parakoloôjhshc, epilèqthke antð llwn pijan n metrik n, ìpwc o susqetismìc (correlation) metaxô twn QDS, kai apofasðsthke met apì thn peiramatik sôgkrish tètoiwn metrik n. Prokeimènou na prosdioristoôn ta qarakthristik shmeða pou èqoun q sei to shmeðo pou parakoloujoôsan kai na afairejoôn apì thn diadikasða thc parakoloôjhshc, qrhsimopoi jhke èna mètro amoibaðac plhroforðac ( mutual information), pou ekfr zei kat pìso parakoloujoôntai

59 2.4. ParakoloÔjhsh ShmeÐwn 37 swst ta qarakthristik shmeða stic diadoqikèc eikìnec I t kai I t+1. 'Estw ìti C (t) ; C (t+1) eðnai dôo tuqaðec metablhtèc me P (c (t) i );P(c (t+1) i ) kai P (c (t) i ;c (t+1) i ) oi oriakèc kai koinèc sunart seic puknìthtac pijanìtht c touc. Sthn perðptws pou exet zetai, c (t) i = I t (p (t) ), c (t+1) i i = I t+1 (p (t+1) i kai p (t) 2 p (t), p (t+1) 2 p (t+1). Me lla lìgia, oi dôo tuqaðec metablhtèc i i eðnai oi fwteinìthtec tou Ðdiou qarakthristikoô shmeðou se dôo diadoqikèc eikìnec. Kat sunèpeia, h sqetik pijanìthta P (c (t) i ) upologðzetai apì to istìgramma thc eikìnac H ist (c (t) i ), dhlad P (c (t) i ) = H ist(c (t) i ). H koin NhNw pijanìthta upologðzetai apì to koinì 2D istìgramma twn duo diadoqik n eikìnwn dhlad P (c (t) i ;c (t+1) j ) = H ist(c (t) i ;c (t+1) j ) NhNw, ìpou H ist (c (t) i ) ;c (t+1) j ) eðnai to pl joc twn antðstoiqwn eikonostoiqeðwn (eikonostoiqeða sthn Ðdia qwrik jèsh) pou èqoun fwteinìthta c (t) i sthn eikìna I t kai fwteinìthta c (t+1) j sthn eikìna I t+1. H amoibaða plhroforða C (t) ; C (t+1) orðzetai wc ex c: L(C (t) ;C (t+1) )= Nmax X i=1 Nmax X j=1 P (c (t) i ;c (t+1) P (c (t) i j ) log 2 ;c (t+1) j ) P (c (t) i )P (c (t+1) j ) ; (2.23) ìpou N max eðnaiomègistoc arijmìc twn diajèsimwn epipèdwn tou gkri sthn eikìna. 'Ena qarakthristikì shmeðo shmei netai wc apotuqhmèno (èqase ton stìqo pou parakoloujoôse) an loga me thn parak tw metrik : 'Otan to E (t) m E (t) m = fi fi L(C t 1 ;C (t) ) L(C (t) ;C (t+1) ) fi fi : (2.24) Th (ìpou Th eðnai èna prokajorismèno kat fli), to antðstoiqo qarakthristikì shmeðo jewreðtai san apotuqhmèno kai o algìrijmoc stamat na to parakoloujeð. To kat fli Th tèjhke Ðso me 1:6, epeid peiramatik apodeðqjhke ìti autì to kat tato ìrio mporeð na diaqwrðsei apotelesmatik ta qarakthristik shmeða pou parakoloujoôn ton stìqo touc swst apì aut pou ton èqoun q sei. H peiramatik axiolìghsh tou katwflðou ègine me thn ektèlesh tou proteinìmenou algorðjmou parakoloôjhshc gia di fora qarakthristik shmeða se poikðlec

60 38 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn eikonoseirèc. Htim tou E (t) m axiolog jhke èpeita apì anjr pinh parat rhsh twn apotelesm twn, sthn opoða diaqwrðsthkan ìlec oi peript seic pou o stìqoc parakoloôjhshc eðqe qajeð. To kat fli Th p re thn el - qisth tim apì ìlec tic timèc pou katagr fhkan, dedomènou ìti aut h tim tan arket megalôterh apì tic antðstoiqec timèc twn qarakthristik n shmeðwn pou parakoloujoôsan epituq c ton stìqo touc. 'Ena par deigma thc diadikasðac anðqneushc qarakthristik n shmeðwn pou q noun to stìqo touc parousi zetai sto sq ma 2.7. Dekapènte qarakthristik shmeða epilèqthkan sthn pr th eikìna miac eikonoseir c kai parakolouj jhkan sthn upìloiph eikonoseir. Oi timèc tou E (t) m kat thn di rkeia tou qrìnou gia dôo qarakthristik shmeða apeikonðzetai sta sq mata 2.7a, 2.7b antðstoiqa. Kai ta dôo shmeða parakolouj jhkan e- pituq c mèqri thn eikìna 173 thc eikonoseir c kai Ðsque ìti to E (t) m» Th gia to qronikì di sthma t» 173. Sthn eikìna 174 tou bðnteo èna shmeðo (pou eðnai qrwmatismèno maôro sto sq ma) èqase to stìqo tou (sq ma 2.7d) to opoðo faðnetai kai apì thn tim tou E (t) m (E (t) m Th). Dedomènhc thc duskolðac na xèrei k poioc ek twn protèrwn to kat llhlo mègejoc gia thn perioq anaz thshc R (2.22), se aut thn Par - grafo proteðnetai h perioq anaz thshc R t na eðnai metablhtoô megèjouc. To mègejoc ja prèpei na eðnai kat llhlo ste na entopisteð h kalôterh dunat jèsh enìc qarakthristikoô shmeðou se duo diadoqikèc eikìnec. ArqÐzontac apì mia mikr se mègejoc perioq anaz thshc R t (p.q. 9 9 eikonostoiqeðwn), o algìrijmoc aux nei anadromik to mègejoc thc perioq c anaz thshc mèqri ènac orismènou orðou. H anadrom stamat ìtan h susqètish twn QDS enìc qarakthristikoô shmeðou se duo diadoqikèc eikìnec, xeper sei èna sugkekrimèno kat fli E o. O kajorismìc thc tim c tou katwflðou E o ègine me ton ex c trìpo. UpologÐsthkan oi timèc thc kanonikopoihmènhc susqètishc QDS twn qarakthristik n shmeðwn se diadoqikèc eikìnec gia diaforetik megèjh tou paramorf simou montèlou epif neiac se poikðlec eikonoseirèc. Ta peiramatik apotelèsmata èdei-

61 2.4. ParakoloÔjhsh ShmeÐwn 39 χρόνος σε εικόνες (a) χρόνος σε εικόνες (b) (g) (d) Sq ma 2.7: (a) H tim tou E (t) m se sqèsh me to qrìno (metrhmènoc se karè miac eikonoseir c) gia ènaqarakthristikì shmeðopou parakoloujeðtai apì ton algìrijmo (to spro stðgma). (b) H tim tou E (t) m se sqèsh me to qrìno (metrhmènoc se karè miac eikonoseir c) gia èna qarakthristikì shmeðo pou q nei to stìqo tou (to maôro stðgma). (g) Ta apotelèsmata parakoloôjhshc gia thn eikìna 173 apì thn upì exètash eikonoseir. (d) Ta apotelèsmata parakoloôjhshc gia thneikìna 174 apì thn upì exètash eikonoseir,ìpou to maôro qarakthristikì shmeðo q nei to stìqo tou kai sunep c qarakthrðzetai wc apotuqhmèno. xan ìti h tim tou E o pou mporeð na jewrhjeð asfal c, ste duo QDS

62 40 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn na jewrhjoôn pwc an koun sto Ðdio shmeðo eðnai Ðsh me 0:7. Parìmoiec mèjodoi gia thn anaz thsh katallhlìterou upoy fiou shmeðou èqoun qrhsimopoihjeð se pragmatikèc kai sunjetikèc eikìnec sto [38]. Stic efarmogèc pou o qrìnoc eðnai ènac polô shmantikìc par gontac, h ekten c anaz thsh tou upoy fiou shmeðou sthn perioq anaz thshc R t+1 mporeð na apofjeqjeð. H teqnik pou parousi sthke sthn prohgoômenh Par grafo (Par grafoc 2.3) kai qrhsimopoieð ton Canny aniqneut akm n, mporeð na uiojethjeð kai se aut n thn perðptwsh wc ex c. O algìrijmoc tou Canny aniqneut akm n efarmìzetai sthn perioq anaz thshc R t+1 kai anazht thn kalôterh pijan jèsh d (t) i tou shmeðou p (t) apì thn i eikìna I t sthn diadoqik thc I t+1, mìno se èna uposônolo thc perioq c R t+1. Autì to uposônolo orðzetai wc ta koin shmeða thc perioq c anaz thshc R t+1 kai thc exìdou tou Canny aniqneut akm n. Oi timèc pou anatðjentai sta kat flia tou Canny aniqneut akm n eðnai kat llhlec ste na paðrnoume san èxodo mia leptomer c katagraf twn akm n thc upì exètashc perioq c R t+1 thc eikìnac I t+1. Wstìso, prèpei na shmeiwjeð ìti se aut thn èkdosh tou algorðjmou ta apotelèsmata den eðnai tìso akrib ìso sthn gn sia pou perigr fhke. Autìc eðnai kai o basikìc lìgoc ìti se ìla ta peir mata pou anafèrontai sthn epìmenh Par grafo autoô tou KefalaÐou, qrhsimopoi jhke o algìrijmoc pou exet zei ìla ta shmeða sthn perioq anaz thshc. 2.5 Peiramatik Apotelèsmata H proteinìmenh mèjodoc parakoloôjhshc, h opoða ja apokaleðtai apì ed kai sto ex c mèjodoc idioqarakthristik n (MI), axiolog jhke efarmìzontac thn sta dedomèna miac b shc dedomènwn [39] pou perièqei eikonoseirèc. To ulikì aut c thc b shc apoteleðtai apì 100 GB eikonoseir n se full PAL an lush (25 fps, 4 : 2 : 2, , 24 bpp). Ta bðnteo perièqoun skhnèc me èna, dôo kai perissìtera toma pou kinoôntai

63 2.5. Peir mata 41 se mia prokajorismènh troqi k nontac tuqaðec kin seic. Oi perissìterec apì autèc tic skhnèc eðnai diajèsimec se dôo ekdìseic. H mða èkdosh eðnai me kanonikì fwtismì, ìpwc kajorðzontan apì touc teqnikoôc tou stoôntio kai h llh èkdosh me sunj kec upo-fwtismoô, dhlad o fwtismìc sthn skhn den tan omoiìmorfoc all up rqan shmeða me èntono fwtismì, shmeða me skièc, shmeða skotein k.o.k. Merik paradeðgmata eðnai diajèsima sto sq ma 2.8. H proteinìmenh mèjodoc axiolog jhke kai se llec eikonoseirèc pèra apì th b sh dedomènwn. Autèc oi eikonoseirèc perieðqan anjr pouc pou kinoôntan se eswterikoôc kai exwterikoôc q rouc, diagr fontac poikðlec troqièc kai k tw apì diaforetikèc sunj kec fwtismoô kai perib llontoc. Se ìla ta peir mata pou ulopoi jhkan se autì to Kef laio, h sklhrìthta twn elathrðwn k kai h m za twn kìmbwn m tou paramorf simou montèlou epifaneðac, tèjhkan Ðsa me th mon da. Ja prèpei na shmeiwjeð se autì to shmeðo, ìti skopìc thc èreunac se autì to Kef laio, den tan na anaptuqjeð èna prohgmèno sôsthma parakoloôjhshc anjr pwn, ikanì na qeirðzetai peript seic epik luyhc anjr pwn, na xekin apì thn arq thn parakoloôjhsh k poiou atìmou pou epan lje sto pedðo endiafèrontoc k.o.k. Stìqoc tou KefalaÐou eðnai na parousi sei mia kainotìmo kai apotelesmatik mèjodo epilog c kai parakoloôjhshc qarakthristik n shmeðwn se eikonoseirèc, h opoða metèpeita mporeð na efarmosteð se opoiod pote sônjeto sôsthma parakoloôjhshc antikeimènwn. Epiprìsjeta, mhqanismoð qeirismoô peript sewn poô to upì exètash antikeðmeno epikalôptetai apì k poio llo q netai apì thn skhn, mporoôn eôkola na epinohjoôn kai na enswmatwjoôn ston algìrijmo. 'Etsi, h apìdosh tou proteinìmenou MI algorðjmou èqei exetasjeð wc proc thn akrðbeia parakoloôjhshc tou upì exètash antikeimènou se perib llonta me diaforetikèc kin seic, enallagèc sto fwtismì kai qwrðc na lamb nontai upìyh peript seic pou xefeôgoun apì ta ìria thc sugkekrimènhc èreunac. Ta apotelèsmata tou MI algorðjmou parakoloôjhshc sugkrðjhkan me ta a-

64 42 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn ntðstoiqa tou Kanade-Lucas-Tomasi (KLT) algorðjmou parakoloôjhshc [27, 20] kai enìc sust matoc parakoloôjhshc pou basðzetai se SIFT shmeða [28] ston Harris algìrijmo epilog c qarakthristik n shmeðwn [19]. Ja prèpei na shmeiwjeð epðshc, ìti o arijmìc twn upì parakoloôjhsh shmeðwn se ìla ta peir mata, tan sqetik mikrìc gia treic lìgouc. Pr ton, stic perissìterec peript seic to mègejoc thc upì exètashc perioq c tan arket mikrì, deôteron, h diadikasða qeirwnaktik c exagwg c apotelesm twn parakoloôjhshc ste na sugkrijoôn me ta apotelèsmata twn algorðjmwn eðnai qronobìra kai epðponh diadikasða kai trðton, o mikrìc a- rijmìc qarakthristik n shmeðwn dieukolônei th sôgkrish apotelesm twn me gumnì m ti. Sthn pr th om da peiram twn o MI algìrijmoc parakoloôjhshc e- xet zetai se sqèsh me thn akrðbeia parakoloôjhshc xeqwrist n qarakthristik n shmeðwn. H mèjodoc epilog c qarakthristik n shmeðwn pou perigr fhke sthn Par grafo 2.3, qrhsimopoi jhke gia na epilegeð ènac sugkekrimènoc arijmìc qarakthristik n shmeðwn (M =9) se mia kajorismènh perioq miac eikìnac, p.q. se èna anjr pino kef li. H perioq thc eikìnac, kajorðzontan qeirokðnhta sthn pr th eikìna thc upì exètashc eikonoseir c. H mèjodoc parakoloôjhshc pou perigr fhke sthn Par - grafo 2.4 efarmìsthke se ìlec tic upìloipec eikìnec thc eikonoseir c. ParadeÐgmata apotelesm twn apeikonðzontai sto sq ma 2.8. EpÐshc, o KLT algìrijmoc parakoloôjhshc efarmìsthke sthn Ðdia eikonoseir kat ton Ðdio trìpo. Sunep c, o KLT epèlexe 9 qarakthristik shmeða sthn prokajorismènh perioq thc pr thc eikìnac apì to bðnteo sômfwna me th mèjodo pou perigr fetai sto [20]. Sto upìloipo thc eikonoseir c ta shmeða parakolouj jhkan apì ton KLT. To mègejoc tou paramorf simou montèlou epif neiac fwteinot twn sthn proteinìmenh mèjodo tèjhke Ðso me tic diast seic tou parajôrou R pou qrhsimopoieð o KLT gôrw apì k je qarakthristikì shmeðo pou epilègei gia parakoloôjhsh, dhlad tèjhke Ðso me 7 7 eikonostoiqeða. San mètro sôgkrishc twn dôo mejìdwn

65 2.5. Peir mata 43 (a) (b) (g) (d) (e) (st) Sq ma 2.8: Apotelèsmata parakoloôjhshc tou proteinìmenou algorðjmou MI se mia eikonoseir eikìnwn miac skhn c katagegrammènhc se stoôntio. Ta apotelèsmata pou apeikonðzontai eðnai se diast mata 120 eikìnwn. parakoloôjhshc qrhsimopoi jhke h susqètish twn perioq n kanonikopoihmènwn fwteinot twn metaxô thc arqik c perioq c parakoloôjhshc me

66 44 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn thn trèqousa. EpÐshc, upologðsthke kai h mèsh tim ìlwn twn parap nw tim n gia k je qarakthristikì shmeðo. 'Oso pio meg lh eðnai h tim thc susqètishc tìso pio akrib ja eðnai ta apotelèsmata parakoloôjhshc. Ta apotelèsmata parousi zontai ston PÐnaka 2.3. K poioc mporeð na parathr sei ìti mèsh tim thc susqètishc gia ìlh thn eikonoseir èinai arket megalôterh gia ton proteinìmeno MI algìrijmo se sqèsh me ton KLT.Epiprìsjeta, h apìklish thc mèshc tim c twn parap nw tim n eðnai mikrìterh gia ton proteinìmeno MI algìrijmo sugkritik me ton KLT.Autì upodhl nei ìtiomialgìrijmoc èqei ligìterec diakum nseic se sqèsh me ton KLT.Parìmoia peir mata apokt jhkan kai gia llec eikonoseirèc. PÐnakac 2.3: Mèsh tim thc kanonikopoihmènhc susqètishc (MKS) se perioqèc gôrw apì ta epilegmèna shmeða kai h apìklish twn parap nw tim n (AMKS) gia ton MI kai ton KLT algìrijmo parakoloôjhshc. ShmeÐa ShmeÐo 1 ShmeÐo 3 ShmeÐo 6 ShmeÐo 9 'Ola MKS (MI) MKS (KLT) AMKS (MI) AMKS (KLT) To deôtero sônolo peiram twn stoqeôei ston èlegqo thc dunatìthtac tou proteinìmenou algorðjmou na parakoloujeð swst qarakthristik shmeða gia ènan ikanopoihtikì arijmì diadoqik n eikìnwn. O MI kai o algìrijmoc KLT efarmìsthkan se di forec akoloujðec eikìnwn. Peiramatik apodeðqjhke ìti o algìrijmoc KLT adunateð na parakolouj sei ta qarakthristik shmeða gia meg lo qronikì di sthma sugkrinìmenoc me thn proteinìmenh mèjodo. Autì dieukrinðzetai ston PÐnaka 2.4 pou parèqei eikìnec gia th mèsh di rkeia zw c parakoloôjhshc (pou metriètai se arijmì eikìnwn) qarakthristik n shmeðwn kai gia touc dôo algorðjmouc,

67 2.5. Peir mata 45 gia diaforetik megèjh tou parajôrou R. To par juro R, eðnai to mègejoc tou montèlou gia ton algìrijmo MI kai to par juro gôrw apì k je qarakthristikì shmeðo pou qrhsimopoieðtai ston KLT.Ta shmeða pou q - noun to stìqo touc, aniqneôontai èpeita apì optik epije rhsh, dhlad, me thn epije rhsh twn apotelesm twn parakoloôjhshc prokeimènou na brejoôn ta qarakthristik shmeða pou parèkklinan se meg lo bajmì apì to stìqo touc. H anwterìthta thc mejìdou parakoloôjhshc MI mporeð epðshc na elegqjeð kai apì to sq ma 2.9, to opoðo apeikonðzei ton arijmì qarakthristik n shmeðwn upì parakoloôjhsh (epilegmèna sthn Ðdia perioq thc arqik c eikìnac thc Ðdiac eikonoseir c) se sqèsh me to qrìno (metrhmèno se eikìnec) kai gia touc dôo algorðjmouc, gia mia sugkekrimènh eikonoseir pou apeikonðzei èna tomo na kineðtai proc th k mera se mia zigk-zagk troqi. To mègejoc twn parajôrwn pou qrhsimopoi jhke tan Ðso me 7 7 eikonostoiqeða. EÐnai olof nero ìti h mèjodoc MI q nei ta ligìtera qarakthristik shmeða kaj c h parakoloôjhsh exelðssetai kai suneqðzei akìma kai ìtan o KLT èqei q sei ìla ta shmeða pou parakoloujoôse sthn eikìna 635, exaitðac miac apìtomhc kðnhshc tou atìmou sthn upì exètash eikonoseir. Parìmoia apotelèsmata epiteôqjhkan kai se llec akoloujðec eikìnwn. PÐnakac 2.4: H mèsh di rkeia zw c (se eikìnec) twn upì parakoloôjhsh qarakthristik n shmeðwn gia diaforetik megèjh tou montèlou/parajôrou. Mègejoc Montèlou/ParajÔrou MI KLT Epiplèon, prokeimènou na axiologhjeð h akrðbeia parakoloôjhshc, pa-

68 46 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn Sq ma 2.9: O arijmìc twn qarakthristik n shmeðwn pou parakoloôjhsan ton stìqo touc qwrðc apoklðseic gia k je eikìna miac akoloujðac kai gia touc duo algorðjmouc. r qjhsan qeirwnaktik oi pragmatikèc jèseic merik n qarakthristik n stoiqeðwn upì parakoloôjhsh gia di forec akoloujðec eikìnwn. Oi timèc autèc sugkrðjhkan me ta apotelèsmata twn dôo algorðjmwn. H diadikasða pou qrhsimopoi jhke se autì to peðrama tan h akìloujh: epitr phke kai stouc dôo algorðjmouc, ston KLT kai ston algìrijmo MI, na epilèxoun 9 qarakthristik shmeða sthn perioq pou apeikonðzei to prìswpo sthn pr th eikìna tou bðnteo, qrhsimopoi ntac o kajènac th dik tou diadikasða epilog c qarakthristik n shmeðwn. Katìpin, kai oi dôo algìrijmoi parakoloôjhsan ta epilegmèna qarakthristik shmeða gia to upìloipo thc eikonoseir c. To mègejoc tou parajôrou tèjhke Ðso me 7 7 eikonostoiqeða. Oi jèseic twn shmeðwn pou par qjhsan apì touc dôo algorðjmouc, sugkrðjhkan me tic jèseic pou par qjhsan apì anjr pinh epije rhsh, dhlad me tic pragmatikèc jèseic pou ja proèkuptan

69 2.5. Peir mata 47 an k poioc shmeðwne me to qèri th jèsh tou antikeimènou se k je qronik stigm. H eukleðdeia apìstash metaxô twn pragmatik n jèsewn kai twn jèsewn pou par qjhsan apì touc dôo algorðjmouc (dhlad to l joc jèshc parakoloôjhshc) qrhsimopoi jhke gia thn axiolìghsh twn apotelesm twn. 'Opwc mporeð na diapist sei k poioc sto sq ma 2.10 (gia mia akoloujða pou apeikonðzei par llhlh kðnhsh enìc atìmou proc thn k mera), o proteinìmenoc algìrijmoc MI eðnai akribèsteroc sthn parakoloôjhsh, dhlad, to l joc parakoloôjhshc eðnai suneq c mikrìtero. Pio sugkekrimèna, to l joc tou MI eðnai sqedìn treic forèc mikrìtero apì to antðstoiqo pou par getai apì ton KLT.Akìmh kai sthn perðptwsh enìc mh kat llhlou shmeðou (pou epilèqjhke epðthdec se mia omoiìmorfh perioq thc eikìnac) to mèso l joc parakoloôjhshc tou KLT eðnai uyhlìtero apì to antðstoiqo thc proteinìmenhc prosèggishc (sq ma 2.10b). O PÐnakac 2.5 parousi zei to mèso l joc jèshc parakoloôjhshc kai th diafor tou l jouc jèshc parakoloôjhshc gia olìklhrh thn eikonoseir, gia orismèna qarakthristik shmeða pou epilèqthkan kai parakolouj jhkan apì touc dôo algorðjmouc. H diafor l jouc jèshc parakoloôjhshc eðnai polô mikrìterh gia ton MI apì ìti gia ton KLT. Aut ta apotelèsmata deðqnoun ìti h proteinìmenh mèjodoc MI epitugq nei akribèsterh parakoloôjhsh apì ton KLT. To Ðdio peðrama epanal fjhke, all aut th for h epilog twn qarakthristik n shmeðwn basðsthke ston algìrijmo KLT. Ostìqoc autoô tou peir matoc eðnai na dieukrinisteð an o proteinìmenoc algìrijmoc parakoloôjhshc mporeð na prosfèrei ikanopoihtik apotelèsmata akìma kai sthn perðptwsh pou ta qarakthristik shmeða den èqoun epilegeð me th qrhsimopoðhsh thc mejìdou pou eis getai sthn Par grafo 2.3. Dhlad ìti h epituqða thc proteinìmenhc diadikasðac parakoloôjhshc ègkeitai ìqi mìno sthn mèjodo epilog c qarakthristik n shmeðwn all kai exaitðac tou dianôsmatoc qarakthristik n shmeðwn pou qrhsimopoieðtai sthn parakoloôjhsh. Se autì to peðrama, kai oi dôo algìrijmoi arqikopoi -

70 48 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn Απόσταση σε εικονοστοιχεία MI Απόσταση σε εικονοστοιχεία MI Χρόνος σε εικόνες (a) Χρόνος σε εικόνες (b) Sq ma 2.10: (a) EukleÐdeia apìstash (mèsh tim ìlwn twn upì parakoloôjhsh qarakthristik n shmeðwn) metaxô twn pragmatik n jèsewn kai twnantðstoiqwn pou par qjhsanapì touc KLT kai MI. (b) Apotelèsmata gia èna mh kat llhlo shmeðo, epilegmèno se mia omoiìmorfh perioq thc eikìnac. PÐnakac 2.5: Mèsh tim (MTL) kai apìklish (AL)thc eukleðdeiac apìstashc (l joc) se eikonostoiqeða, metaxô twn pragmatik n jèsewn twn qarakthristik n shmeðwn kai twn antðstoiqwn pou par qjhsan apì touc dôo algorðjmouc. K je algìrijmoc arqikopoi jhke me th dik tou mèjodo epilog c shmeðwn. ShmeÐa ShmeÐo 1 ShmeÐo 3 ShmeÐo 6 ShmeÐo 9 'Ola MTL (MI) MTL (KLT) AL (MI) AL (KLT) jhkan me ta qarakthristik shmeða pou epilèqthkan apì ton algìrijmo KLT.Sto upìloipo thc eikonoseir c, oi dôo algìrijmoi parakoloôjhsan ta shmeða basizìmenoi o kajènac sthn dik tou mèjodo parakoloôjhshc.

71 2.5. Peir mata 49 Ta apotelèsmata sugkrðjhkan (qrhsimopoi ntac thn eukleðdeia apìstash) me tic pragmatikèc jèseic twn shmeðwn pou par qjhsan qeironaktik. O PÐnakac 2.6 deðqnei ìti o proteinìmenoc algìrijmoc parakoloôjhshc den eðnai tìso akrib c ìso sthn prohgoômenh perðptwsh all eðnai kai p li akribèsteroc apì ton KLT algìrijmo. PÐnakac 2.6: Mèsh eukleðdeia apìstash (l joc) se eikonostoiqeða metaxô twn pragmatik n jèsewn twn qarakthristik n shmeðwn kai twn antðstoiqwn jèsewn pou par qjhsan apì touc duo algorðjmouc. Ta dedomèna stic grammèc 2 kai 3 apokt jhkan arqikopoi ntac kai touc dôo algorðjmouc me th mèjodo epilog c shmeðwn tou KLT. ShmeÐa ShmeÐo 1 ShmeÐo 3 ShmeÐo 6 ShmeÐo 9 'Ola MI MI -KLT KLT Sthn epìmenh om da peiram twn, o proteinìmenoc algìrijmoc epilog c qarakthristik n shmeðwn, pou parousi sthke sthn Par grafo 2.3, sugkrðjhke me duo gnwstoôc algorðjmouc sth bibliografða. Me ton SIFT algìrijmo epilog c shmeðwn [18] pou eðnai kat llhloc gia antistoðqhsh shmeðwn se eikìnec thc Ðdiac skhn c apì diaforetikèc k merec kai me ta qarakthristik shmeða pou par gontai apì ton algìrijmo Harris [19]. O proteinìmenoc algìrijmoc epilog c qarakthristik n shmeðwn, o SIFT algìrijmoc epilog c shmeðwn kai o aniqneut c Harris, efarmìsthkan sthn Ðdia, epilegmènh me to qèri, perioq sthn pr th eikìna miac eikonoseir c kai orismèna qarakthristik shmeða epilèqthkan gia k je algìrijmo. Ta epilegmèna qarakthristik shmeða parakolouj jhkan sto upìloipo thc akoloujðac me ton proteinìmeno algìrijmo parakoloôjhshc. San mètro sôgkrishc twn apotelesm twn qrhsimopoi jhke h kanonikopoihmènh su-

72 50 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn sqètish metaxô twn antðstoiqwn perioq n twn qarakthristik n shmeðwn (perioqèc eikìnac gôrw apì k je qarakthristikì shmeðo) thc arqik c eikìnac kai thc trèqousac gia ìla ta epilegmèna qarakthristik shmeða se ìlh thn eikonoseir. Ta apotelèsmata gia mia akoloujða 600 eikìnwn, pou parousi zontai ston PÐnaka 2.7 apodeiknôoun ìti o sunduasmìc tou proteinìmenou algorðjmou epilog c kai parakoloôjhshc qarakthristik n shmeðwn petuqaðnei thn kalôterh apìdosh. Se ìlh thn om da peiram twn, o arijmìc twn qarakthristik n shmeðwn kajorðsthke apì touc ek stote algìrijmouc epilog c shmeðwn SIFT kai Harris. PÐnakac 2.7: H mèsh tim thc kanonikopoihmènhc susqètishc (MKS) se perioqèc gôrw apì ta epilegmèna shmeða kai h apìklish twn parap nw tim n (AMKS) gia ta apotelèsmata parakoloôjhshc ìtan o SIFT, oh- arris kai o proteinìmenoc algìrijmoc epilog c shmeðwn qrhsimopoi jhkan gia thn arqikopoðhsh thc proteinìmenhc mejìdou parakoloôjhshc (trða qarakthristik shmeða. ShmeÐa ShmeÐo 1 ShmeÐo 2 ShmeÐo 3 'Ola MKS (MI) MKS (SIFT) MKS (Harris) AMKS (MI) AMKS (SIFT) AMKS (Harris) Se èna llo peðrama, h apìdosh parakoloôjhshc tou MI exet sthke se èna epðpedo, kampto antikeðmeno (èna ex fullo biblðou) prokeimènou na dieukrinisteð ìti o MI mporeð na epitôqei polô kal apotelèsmata parakoloôjhshc gia eudi krita shmeða. To upì exètash antikeðmeno parèmeine stajerì en h k mera kinoôntan kat tètoio trìpo ste na perilam-

73 Απόσταση σε εικονοστοιχεία 2.5. Peir mata 51 b nontai metatopðseic, klimak seic kai peristrofèc tou antikeimènou. Oi pragmatikèc jèseic twn pènte shmeðwn pou epilèqthkan sthn pr th eikìna thc akoloujðac, dhlad oi jèseic pou par gontai an h jèsh tou antikeimènou shmeiwjeð me to qèri, dhmiourg jhkan gia ìlh thn akoloujða. H eukleðdeia apìstash metaxô twn pragmatik n jèsewn kai twn jèsewn pou par qjhsan apì ton MI(upologÐsthke o mèsoc ìroc gia ìla ta shmeða), qrhsimopoi jhke wc krit rio apìdoshc. 'Opwc faðnetai sto sq ma 2.11, o algìrijmoc MI epitugq nei polô kal kai idiaðtera stajer apotelèsmata parakoloôjhshc, dedomènou ìti h mègisth mèsh apìstash apì tic pragmatikèc jèseic twn shmeðwn eðnai 1:5 eikonostoiqeða en h apìstash tou arijmhtikoô mèsou eðnai mìno 0:5 eikonostoiqeða. Ta apotelèsmata parakoloôjhshc gia th sugkekrimènh akoloujða apeikonðzontai sto sq ma Χρόνος σε εικόνες Sq ma 2.11: H eukleðdeia apìstash metaxô twn pragmatik n jèsewn kai twnjèsewnpouèdwsesanèxodo o proteinìmenoc algìrijmoc parakoloôjhshc MI (mèsh tim gia ta 5qarakthristik shmeða), gia thn eikonoseir pou apeikonðzetai sto sq ma To epìmeno sônolo peiram twn stoqeôei sthn axiolìghsh tou algo-

74 52 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn (a) (b) (g) (d) (e) (st) (z) (h) (j) Sq ma 2.12: Apotelèsmata parakoloôjhshc tou MI algorðjmou gia mia akoloujða 400 eikìnwn. To upì exètash antikeðmeno eðnai èna epðpedo antikeðmeno (ex fullo biblðou) ìpou ta qarakthristik shmeða eðnai eudi krita. Ta parap nw deðgmata eðnai se diast mata twn 50 eikìnwn. rðjmou parakoloôjhshc MI ìtan efarmìzetai se kin seic pou antimetwpðzontai suqn sthn parakoloôjhsh antikeimènwn, ìpwc h klim kwsh kai h peristrof tou upì exètash antikeimènou, dhlad tou anjr pinou pros pou. Se aut n thn perðptwsh, h apìdosh tou algorðjmou axiolog jhke se epðpedo antikeimènou, dhlad, elègqjhke an to upì exètash antikeðmeno

75 2.5. Peir mata 53 parakolouj jhke swst ìqi. Oi parak tw metrikèc qrhsimopoi jhkan, afoô pr ta ex game qeironaktik tic pragmatikèc jèseic tou pros pou stic upì exètash eikonoseirèc: ta alhj c jetik (AJ), ta yeud c jetik (YJ) kai ta yeud c arnhtik (YA). San AJ jewreðtai èna apotèlesma parakoloôjhshc ìtan autì to apotèlesma perikleðetai mèsa sthn perioq pou qarakthrðsthke san pragmatik tim. San YJ lamb netai to apotèlesma parakoloôjhshc pou perièqei kai epiplèon perioq apì to fìnto thc eikìnac en YA eðnai h perðptwsh pou o algìrijmoc parakoloôjhshc stamat na parakoloujeð to upì exètash antikeðmeno en den ja èprepe na eðqe sumbeð k ti tètoio. Me b sh autèc tic metrikèc, upologðsthke h akrðbeia (A = A A ) kai h an klhsh (AN = ). Ta apotelèsmata, gia pènte akoloujðec eikìnwn me diaforetik A +Ψ A +ΨA qarakthristik kðnhshc, sunoyðzontai ston PÐnaka 2.8. Se ìlec tic akoloujðec, to upì exètash antikeðmeno tan to kef li tou apeikonizìmenou pros pou. K - poioc mporeð na dei ìti o algìrijmoc parakoloôjhshc MI eðnai stajerìc se tètoiou eðdouc kin seic. Merik apotelèsmata parakoloôjhshc tou algorðjmou MI parousi zontai sta sq mata Sto sq ma 2.13, o hjopoiìc gèrnei to kef li tou se di forouc prosanatolismoôc. Sthn eikìna 2.14, o hjopoiìc peristrèfei to kef li tou 90 moðrec (par llhla sto epðpedo thc k merac) kai ètsi ta qarakthristik tou pros pou all zoun se meg lo bajmì. Mìno èna qarakthristikì shmeðo epilèqthke p nw sth môth tou atìmou, dedomènou ìti h môth eðnai to mìno mèroc tou pros pou pou paramènei oratì se ìlec tic eikìnec thc akoloujðac. MI katafèrnei na parakolouj sei to epilegmèno shmeðo se ìlh thn akoloujða. Epiplèon, k poioc mporeð na parathr sei sto sq ma 2.15, ènan njrwpo na peristrèfei to kef li tou mèqri 45 moðrec, ètsi ste ìla ta epilegmèna qarakthristik shmeða na paramènoun orat. Ta apotelèsmata parakoloôjhshc MI eðnai polô enjarruntik, dedomènou ìti ìla ta qarakthristik shmeða akoloujoôntai ikanopoihtik. Sto sq ma 2.16, o hjopoiìc perpat proc kai apì thc k merac. Kat sunèpeia, to mègejoc O

76 54 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn PÐnakac 2.8: H akrðbeia (A) kai h an klhsh (AN) parakoloôjhshc tou proteinìmenou algorðjmou gia 5 akoloujðec me diaforetikèc kin seic. KÐnhsh Eikìnec A AN EleÔjerh Metatìpish Klim kwsh KlÐsh Peristrof tou pros pou dieurônetai/elaqistopoieðtai entupwsiak kai se k poiec eikìnec thc akoloujðac ta qarakthristik gnwrðsmata tou pros pou eðnai sqedìn aìrata. EntoÔtoic, o MI parakoloujeð ta epilegmèna qarakthristik shmeða arket kal, eidik se epðpedo antikeimènou. Tèloc, h eikìna 2.17 deðqnei ìti o proteinìmenoc algìrijmoc eðnai stajerìc se skhnèc me allagèc fwtismoô kai se skhnèc pou upeisèrqontai skièc. 'Ena tètoio par deigma eðnai ìtan prokaloôntai sto prìswpo allagèc ston fwtismì, kaj c to tomo mpaðnei kai bgaðnei apì mia èntona fwtismènh perioq e- nìc dwmatðou. Parìmoia apotelèsmata me èntonec skièc sto prìswpo tou hjopoioô parousi zontai sto sq ma PÐnakac 2.9: H mèsh di rkeia zw c (se eikìnec) gia tic dôo ekdìseic tou SIFT algìrijmou (SIFT-I kai SIFT-II) kai tou MI algorðjmou gia di forec akoloujðec eikìnwn. Mèsh di rkeia zw c se eikìnec Eikìnec MI SIFT-I SIFT-II

77 2.5. Peir mata 55 (a) (b) (g) (d) (e) (st) (z) (h) (j) Sq ma 2.13: Apotelèsmata parakoloôjhshc tou MI algorðjmou gia mia a- koloujða eswterikoô q rou 400 eikìnwn. Ta deðgmata twn apotelesm twn eðnai se diast mata twn 50 eikìnwn. O hjopoiìc gèrnei to kef li tou. Sthn telik om da peiram twn, ènac prìsfatoc algìrijmoc parakoloôjhshc basismènoc sta qarakthristik shmeða SIFT [28], [18] exet sthke en ntia sthn proteinìmenh prosèggish epilog c kai parakoloôjhshc qarakthristik n shmeðwn. Sthn proanaferjeðsa ergasða [28], o Gordon kai o Lowe parousi zoun mia pl rh arqitektonik enìc sust matoc efarmìsimo sthn auxhmènh pragmatikìthta (augmented reality). Oi dia-

78 56 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn (a) (b) (g) (d) (e) (st) (z) (h) (j) (i) (k) (l) Sq ma 2.14: Apotelèsmata parakoloôjhshc tou MI algorðjmou gia mia akoloujða eswterikoô q rou 330 eikìnwn se di forec sunj kec fwtismoô. 'Enamìnoqarakthristikì shmeðo epilèqthke p nw sth môth tou hjopoioô, giatð tan to monadikì oratì se ìlh thn di rkeia thc akoloujðac. Ta deðgmata twn apotelesm twn eðnai se diast mata twn 30 eikìnwn. dikasðec epilog c kai parakoloôjhshc qarakthristik n shmeðwn autoô tou sust matoc anaptôqjhkan sta plaðsia autoô tou kefalaðou ste na

79 2.5. Peir mata 57 (a) (b) (g) (d) (e) (st) Sq ma 2.15: Apotelèsmata parakoloôjhshc tou MIalgorÐjmou giamia a- koloujða eswterikoô q rou 300 eikìnwn. O hjopoiìc peristrèfei to kef li tou mèqri 45 moðrec. Ta deðgmata twn apotelesm twn eðnai se diast mata twn 60 eikìnwn. sugkrijoôn me thn proteinìmenh mèjodo. DÔo diaforetikèc proseggðseic qrhsimopoi jhkan. Sthn pr th prosèggish (onom zetai SIFT-I) pou eðnai mesa sugkrðsimh me thn proteinìmenh mèjodo, ta qarakthristik shmeða SIFT upologðzontai sthn pr th kai deôterh eikìna kai brðskontai oi a- ntistoiqðec metaxô touc. Gia na to petôqoume autì, qrhsimopoieðtai èna di nusma 128 stoiqeðwn pou perigr fei k je qarakthristikì shmeðo kai h eukleðdeia apìstash metaxô twn dianusm twn dhl nei pìso ìmoia eðnai duo shmeða. Katìpin, ta shmeða pou èqoun antistoiqhjeð metaxô touc sto prohgoômeno b ma (dhlad aut pou perilamb nontai sthn 1 kai 2 eikìna) kai brðskontai mèsa sthn perioq tou pros pou, exet zontai an antistoiqoôntai kai sthn trðth eikìna. H diadikasða suneqðzetai èwc ìtou

80 58 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn (a) (b) (g) (d) (e) (st) Sq ma 2.16: Apotelèsmata parakoloôjhshc tou MI algorðjmou gia mia akoloujða eswterikoô q rou 500 eikìnwn. O hjopoiìc kineðtai apì kai proc thn k mera se apìstash 5 mètrwn. Ta deðgmata twn apotelesm twn eðnai sediast matatwn 100 eikìnwn. telei sei h akoloujða. Aut h diadikasða, den èdwse kal apotelèsmata apì thn poyh thc di rkeiac zw c twn shmeðwn. Sth deôterh prosèggish, (pou onom zetai SIFT-II), ta SIFT shmeða aniqneôjhkan an k je zeug ri diadoqik n eikìnwn (i kai i +1, i +1kai i +2) kai ta antðstoiqa 128-N dianôsmata qarakthristik n shmeðwn qrhsimopoi jhkan prokeimènou na brejoôn oi antistoiqðec metaxô touc. Aut h prosèggish par gage kalôtera apotelèsmata se sqèsh me ton SIFT-I, all kai p li den eðnai mesa sugkrðsima me ton proteinìmeno algìrijmo parakoloôjhshc dedomènou ìti sthn ousða den eðnai mia mèjodoc parakoloôjhshc qarakthristik n gnwrism twn (dhlad den akoloujeð èna shmeðo qarakthristik n gnwrism twn apì thn pr th eikìna kai met ) all tairi zei qarakthristik shmeða apì

81 2.5. Peir mata 59 (a) (b) (g) (d) (e) (st) (z) (h) (j) Sq ma 2.17: Apotelèsmata parakoloôjhshc tou MI algorðjmou gia mia akoloujða eswterikoô q rou 500 eikìnwn se diaforetikèc sunj kec fwtismoô. H Ôparxh èntonwn ski n den ephre zei thn diadikasða parakoloôjhshc. Ta deðgmata twn apotelesm twn eðnai se diast mata twn 62 eikìnwn. mða eikìna sthn epìmenh. Kai oi dôo proseggðseic par gagan kat tera apotelèsmata sesôgkrish me thn proteinìmenh mèjodo. Ta apotelèsmata (mèsh di rkeia zw c se eikìnec) gia tic dôo SIFT proseggðseic kai gia ton algìrijmo MI dðnontai ston PÐnaka 2.9. Merik apotelèsmata tou SIFT

82 60 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn (a) (b) (g) (d) (e) (st) (z) (h) (j) (i) (k) (l) Sq ma 2.18: Apotelèsmata parakoloôjhshc tou MI algorðjmou gia mia akoloujða eswterikoô q rou 1100 eikìnwn, se diaforetikèc sunj kec fwtismoô. H Ôparxh èntonwn ski n den ephre zei thn diadikasða parakoloôjhshc. Ta deðgmata twn apotelesm twn eðnai se diast mata twn 100 eikìnwn. kai MI algorðjmou parakoloôjhshc gia dôo akoloujðec parousi zontai sto sq ma H pr th apì tic dôo SIFT proseggðseic (SIFT-I), pou perigr fhke prohgoumènwc, qrhsimopoi jhke se aut n thn perðptwsh. 2.6 Sumper smata 'Enac nèoc algìrijmoc epilog c kai parakoloôjhshc 2D qarakthristik n shmeðwn pou basðzetai sth qr sh enìc 3D paramorf simou montèlou e- pifaneðac, prot jhke se autì to Kef laio. Se aut n thn prosèggish, h

83 2.6. Sumper smata 61 (a) (b) (g) (d) (e) (st) (z) (h) (j) (i) (k) (l) (m) (n) (x) (o) Sq ma 2.19: a-h: Apotelèsmata parakoloôjhshc gia thn pr th èkdosh tou SIFT algìrijmou (SIFT-I) gia dôo akoloujðec eikìnwn kai j-o: apotelèsmata tou MI algìrijmou stic antðstoiqec akoloujðec. epif neia fwteinìthtac thc eikìnac, antiproswpeôetai apì èna 3D paramorf simo montèlo epif neiac pou upìkeitai stouc nìmouc thc fusik c. Se autì to Kef laio perigr fhke leptomer c h diadikasða kat thn o- poða mporeð k poioc na prosarmìsei tic exis seic paramìrfwshc ste na epilèxei kai na parakolouj sei apotelesmatik qarakthristik shmeða p nw se mia akoloujða eikìnwn. 'Eqei apodeiqjeð ìti èna endi meso

84 62 Kef laio 2. Epilog kai ParakoloÔjhsh ShmeÐwn st dio aut n twn exis sewn eðnai ènac sunduasmìc di forwn mask n a- nðqneushc gramm n kai akm n. H proteinìmenh mèjodoc parakoloôjhshc shmeðwn sugkrðjhke me ton gnwstì algìrijmo parakoloôjhshc KLT kai me ènan algìrijmo parakoloôjhshc pou basðzetai se SIFT shmeða. Ta apotelèsmata deðqnoun ìti h proteinìmenh mèjodoc par gei an tera a- potelèsmata parakoloôjhshc, parèqei kalôterh akrðbeia kai akoloujeð ta qarakthristik shmeða gia megalôtero qronikì di sthma apì ton KLT kai ton SIFT. Epiplèon, o mhqanismìc epilog c qarakthristik n shmeðwn exet sthke en ntia sta SIFT kai Harris qarakthristik shmeða kai apodeðqjhke ìti èqei thn kalôterh apìdosh.

85 BibliografÐa [1] G. Stamou, M. Krinidis, E. Loutas, N. Nikolaidis, and I. Pitas, 2D and 3D motion tracking in digital video," in Handbook of Image and Video Processing, A. C. Bovik, Ed. Academic Press, [2] J. Wang and S. Singh, Video analysis of human dynamics - a survey," Real-Time Imaging, vol. 9, no. 5, pp , October [3] T. B. Moeslund, A. Hilton, and V. Krüger, A survey of advances in vision-based human motion capture and analysis," Computer Vision and Image Understanding, vol. 104, no. 2-3, pp , [4] D. M. Gavrila, The visual analysis of human movement: Asurvey," Computer Vision and Image Understanding, vol. 73, no. 1, pp , [5] J. K. Aggarwal and Q. Cai, Human motion analysis: A review," Computer Vision and Image Understanding, vol. 73, no. 3, pp , [6] M.Vezhnevets, Face and facial feature tracking for natural humancomputer interface," Proceedings in Graphicon, pp , September [7] H. Sidenbladh and M. Black, Learning the statistics of people in images and video," International Journal of Computer Vision,

86 64 BibliografÐa [8] L. Tsap, D. Goldgof, and S. Sarkar, Fusion of physically-based registration and deformation modeling for nonrigid motion analysis," IEEE Transactions on Image Processing, vol. 10, no. 11, pp , November [9] Y. Wang and S. Zhu, Analysis and synthesis of textured motion: Particles and waves," IEEE Transactions on Patern Analysis and Machine Intelligence, vol. 26, no. 10, pp , October [10] M. Kass, A. Witkin, and D. Terzopoulos, Snakes: Active contour models," International Journal of Computer Vision, vol. 1, no. 4, pp , [11] H. Chao, Y. F. Zheng, and S. C. Ahalt, Object tracking using the gabor wavelet transform and the golden section algorithm," IEEE Transactions on Multimedia, vol. 4, no. 4, pp , December [12] J. C. Nascimento and J. S. Marques, Robust shape tracking in the presence of cluttered background," IEEE Transactions on Multimedia, vol. 6, no. 6, pp , December [13] X. Tao and C. Debrunner, Stochastic car tracking with line- and color-based features," IEEE Transactions on Intelligent Transportation Systems, vol. 5, no. 4, pp , December [14] J. Verestoy and D. Chetverikov, Comprative performance evaluation of four feature point tracking techniques," in Proceedings of 22nd Workshop of the Austrian Pattern Recognition Group, Illmitz, Austria, 1998, pp [15] T. Tomassini, A. Fusiello, M. Trucco, and V. Roberto, Making good features track better," in Proceedings of International Conference on

87 BibliografÐa 65 Computer Vision and Pattern Recognition, Santa Barbara, 1998, pp [16] J. Bouguet, Pyramidal implementation of the lucas kanade feature tracker," Intel Corporation, Microprocessor Research Labs, OpenCV Documents, Tech. Rep., [17] J. Wieghardt, R. P. Wurtz, and C. Malsburg, Gabor-based feature point tracking with automatically learned constraints," in Dynamic Perception, September 2002, pp [18] D. Lowe, Distinctive image features from scale-invariant keypoints," International Journal of Computer Vision, vol. 60, no. 2, pp , November [19] C. Harris and M. Stephens, A combined corner and edge detector," in Proceedings of the Fourth Alvey Vision Conference, Manchester, March 1998, pp [20] J. Shi and C. Tomasi, Good features to track," in IEEE International Conference on Computer Vision and Pattern Recognition (CVPR94), Seattle, United States, June 1994, pp [21] R. T. Collins, L. Yanxi, and M. Leordeanu, Online selection of discriminative tracking features," IEEE Transactions on Patern A- nalysis and Machine Intelligence, vol. 27, no. 10, pp , October [22] C. Nastar and N. Ayache, Frequency-based nonrigid motion analysis: Application to four dimensional medical images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18, no. 11, pp , 1996.

88 66 BibliografÐa [23] C. Nikou, G. Bueno, F. Heitz, and J. Armspach, A joint physicsbased statistical deformable model for multimodal brain image a- nalysis," IEEE Transactions on Medical Imaging, vol. 20, no. 10, pp , [24] S. Krinidis, C. Nikou, and I. Pitas, Reconstruction of serially a- cquired slices using physics-based modelling," IEEE Transactions on Information Technology in Biomedicine, vol. 7, no. 4, pp , December [25] C. Nastar and N. Ayache, Fast segmentation, tracking, and analysis of deformable objects," in Proceedings of the Fourth International Conference on Computer Vision (ICCV'93), Berlin, Germany, May 1993, pp [26] A. Pentland and S. Sclaroff, Closed-form solutions for physicallybased shape modeling and recognition," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 7, pp , July [27] C. Tomasi and T. Kanade, Shape and motion from image streams: a factorization method, part 3, detection and tracking of point features," School of Computer Science Carnegie Mellon University Pittsburgh, Tech. Rep. CMU-CS , [28] I. Gordon and D. G. Lowe, Scene modelling, recognition and tracking with invariant image features," in Third IEEE and ACM I- nternational Symposium on Mixed and Augmented Reality (ISMAR 2004), November 2004, pp [29] B. Moghaddam, C. Nastar, and A. Pentland, A bayesian similarity measure for direct image matching," in International Conference on

89 BibliografÐa 67 Pattern Recognition (ICPR 1996), Vienna, Austria, August 1996, pp [30] G. Borgefors, On digital distance transforms in three dimensions," Computer Vision and Image Understanding, vol. 64, no. 3, pp , [31] P.-E. Danielsson, Euclidean distance transform," Computer Graphics and Image Processing, vol. 14, pp , [32] K. J. Bathe, Finite Element Procedure. New Jersey: Prentice Hall, Englewood Cliffs, [33] C. Nastar, Models physiques deformables et modes vibratoires pour l'analyse du mouvement non-rigide dans les images multidimensionnelles," Ph.D. Thesis, Ecole Nationale des Ponts et Chaussees, [34] A. Pentland and B. Horowitz, Recovery of non-rigid motion and structure," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 7, pp , July [35] R. Gonzalez and R. Woods, Digital Image Processing. Addison- Wesley Publishing Company, [36] W. Frei and C. Chen, Fast boundary detection: A generalization and a new algorithm," IEEE Transactions on Computers, vol. C-26, no. 10, pp , [37] J. Canny, A computational approach to edge detection," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 8, pp , [38] T. Kanade, A stereo matching algorithm with an adaptive window: Theory and experiment," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 9, Sep 1994.

90 68 BibliografÐa [39] M. Krinidis, G. Stamou, H. Teutsch, S. Spors, N. Nikolaidis, R. Rabenstein, and I. Pitas, An audio-visual database for evaluating person tracking algorithms," in Proceedings of IEEE International Conference onacoustics, Speech and Signal Processing (ICASSP 2005), Philadelphia, March 2005.

91 Kef laio 3 O Diakritìc Metasqhmatismìc Idioqarakthristik n kai h Efarmog tou se mia Teqnik SumpÐeshc Eikìnac me Ap leia PlhroforÐac 3.1 Eisagwg Entatik èreuna èqei diexaqjeð tic teleutaðec dekaetðec stouc metasqhmatismoôc shm twn. Autì to antikeðmeno exètashc suneqðzei na eðnai u- yhloô endiafèrontoc kai ìson afor tic jewrhtikèc ptuqèc tou all kai apì thn poyh twn efarmog n tou sthn perioq thc epexergasðac s matoc. 'Ena monodi stato s ma (1D) mporeð na aposuntejeð se èna sônolo suntelest n metasqhmatismoô me thn efarmog enìc monodi statou me- 69

92 70Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou tasqhmatismoô pou uiojeteð èna sônolo sunart sewn b shc. OmoÐwc, èna disdi stato s ma (2D), p.q. mia eikìna, mporeð na aposuntejeð qrhsimopoi ntac 2D sunart seic b shc, apokaloômenec suqn kai eikìnec b shc. Oi metasqhmatismoð eikìnac èqoun qrhsimopoihjeð se di forec efarmogèc, ìpwc h beltðwsh poiìthtac eikìnac [1], h apokat stash eikìnac [2], h perigraf eikìnac [3], to filtr risma [4], h sumpðesh [5], [6], h exagwg qarakthristik n shmeðwn [7], [8] kai pollèc llec. Di foroi metasqhmatismoð shm twn, ìpwc o diakritìc metasqhmatismìc Fourier (DFT), h o diakritìc metasqhmatismìc sunhmðtonou (DCT) [9] kai o metasqhmatismìc kum twn (wavelet) [10], èqoun protajeð kai efarmosteð sth bibliografða twn yhfiak n shm twn kai thc epexergasðac eikìnac. MetaxÔ twn proanaferjèntwn efarmog n, h sumpðesh eðnai Ðswc kai h pio exèqousa. H genik idèa pðsw apì thn sumpðesh pou basðzetai se k poion metasqhmatismì dedomènwn eðnai h ekmet lleush ènoc metasqhmatismoô pou aposusqetðzei to s ma eisagwg c kai sugkentr nei th sunolik tou e- nèrgei se ènan mikrì arijmì suntelest n. Den up rqei k poioc bèltistoc metasqhmatismìc gia autì ton skopì [6], wstìso o metasqhmatismìc Karhunen-Lo eve (KLT) mporeð na jewrhjeð bèltistoc upì orismènec sunj kec. 'Opwc, se mia gkaoussian phg gia opoiesd pote posostì duadik n yhfðwn kai strathgik dèsmeushc [11]. Wstìso, o upologismìc tou KLT eðnai qronobìroc, dedomènou ìti den up rqei k poioc genikìc tôpoc gia thn exagwg tou kai epiplèon eðnai kai exart menoc apì to s ma. Sthn ergasða [12], oi suggrafeðc katadeiknôoun tic apotuqðec kai tic epituqðec tou KLT. 'Alloi metasqhmatismoð, ìpwc o DCT [13]-[15], o DFT [16], o Hadamard [17], o Slant [18] eðnai upologistik grhgorìteroi apì ton KLT, petuqaðnontac ìmwc elafr c qeirìterh apìdosh apì aut tou KLT kai ìson afor thn energeiak sumpðesh all kai thn aposusqètish tou s matoc. MetaxÔ twn parap nw, o DCT eðnai o pio eurôtata qrhsimopoihmènoc metasqhmatismìc sth sumpðesh eikìnac. Pr gmati, o DCT enswmat jhke se di fora prìtupa sumpðeshc, ìpwc o JPEG [13],

93 3.1. Eisagwg 71 o MPEG 1/2 [19], o H.261 [20] kai o H.263 [21]. Se autì to Kef laio, parousi zetai ènac nèoc metasqhmatismìc, e- falt rio tou opoðou up rxe oi teqnikèc pou parousi sthkan stic [22]-[24] kai diapragmateôontan thn an lush kðnhshc eôkamptwn antikeimènwn, thn eujugr mmish seiriak epðkthtwn tom n kai thn polômorfh an lush i- atrik n eikìnwn, antðstoiqa. Sthn ergasða [22], oi dunamikèc paramorf seic tou antikeimènou proseggðsthkan me èna paramorf simo montèlo pou upìkeitai stouc nìmouc thc fusik c. Me b sh thn Ðdia arq, se aut thn diatrib, upojètoume ìti èna 2D s ma (oi fwteinìthtec thc eikìnac) mporoôn na antiproswpeujoôn apì mia 3D epif neia, dhlad thn epif neia fwteinot twn thc eikìnac. H basik idèa eðnai na proseggisteð h epif neia fwteinot twn miac eikìnac apì èna paramorf simo montèlo epif neiac. 'Epeita, èna endi meso b ma thc diadikasðac paramìrfwshc qrhsimopoieðtai, to opoðo apodeiknôetai pwc eðnai ènac 2D diakritìc metasqhmatismìc pou mporeð na aposunjèsei thn eikìna se mia kathgorða eikìnwn b shc. Kat parìmoio trìpo, me thn ekmet lleush miac paramorf simhc anoikt c kampôlhc (alusðda), k poioc mporeð na sqhmatðsei ènan 1D diakritì metasqhmatismì prokeimènou na anaparast sei èna 1D s ma apì èna sônolo 1D sunart sewn b shc. Oproteinìmenoc metasqhmatismìc, pou onom zetai diakritìc metasqhmatismìc idioqarakthristik n (Discrete Modal Transform (DMT)), apodeiknôetai pwc eðnai mia genðkeush tou DCT, an kai an kei sthn kathgorða twn mh-diaqwrðsimwn kai mh-orjokanonik n metasqhmatism n. Sunep c, merikèc apì tic idiìthtec twn diaqwrðsimwn metasqhmatism n den isqôoun. To gegonìc ìti o DCT mporeð na proèljei apì èna paramorf simo montèlo pou prospajeð na proseggðsei thn epif neia fwteinot twn miac eikìnac eðnai mia shmantik èkbash aut c thc melèthc. 'Ena polô shmantikì qarakthristikì tou DMT eðnai ìti mporeð na antimetwpisjeð wc o DCT klimakwmènoc apì ènan kainotìmo, analutikì pðnaka kb nthshc pou enswmat nei mia fusik par metro gia ton èlegqo twn epipèdwn sugkè-

94 72Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou ntrwshc/sumpðeshc. O proteinìmenoc metasqhmatismìc efarmìzetai se mia teqnik sumpðeshc me ap leia plhroforðac kai ta apotelèsmata deðqnoun ìti mporeð na apotelèsei èna qr simo ergaleðo sthn perioq sumpðeshc eikìnac. Sugkrinìmenoc me ton DCT (o opoðoc sundu zetai me touc pðnakec kb nthshc tou JPEG), o proteinìmenoc metasqhmatismìc mporeð na epitôqei sugkrðsimh poiìthta eikìnac se qamhlèc analogðec sumpðeshc kai kalôterh poiìthta sumpiesmènhc eikìnac se uyhlèc analogðec sumpðeshc. Epiplèon, èqei tic polô kalèc idiìthtec thc sugkèntrwshc enèrgeiac kai thc aposusqètishc tou s matoc. To upìloipo tou KefalaÐou organ netai wc ex c. To paramorf simo montèlo epif neiac pou upìkeitai stouc nìmouc thc fusik c perigr fetai sthn Par grafo 3.2 en sthn Par grafo 3.3 eis getai o proteinìmenoc 1D kai 2D diakritìc metasqhmatismìc. Oi idiìthtec tou proteinìmenou diakritoô metasqhmatismoô perigr fontai sthn Par grafo 3.4. Sthn Par grafo 3.5 exet zontai h ikanìthta sugkèntrwshc enèrgeiac kai hi- kanìthta aposusqètishc tou DMT. Sthn Par grafo 3.6 parousi zetai mia efarmog sumpðeshc eikìnac me ap leiec plhroforðac pou basðzetai sth filosofða tou JPEG kai qrhsimopoieð ton DMT kai sugkrðnetai me èna parìmoio algìrijmo sumpðeshc pou basðzetai ston DCT. Ta telik sumper smata sun gontai sthn Par grafo Trisdi stato Paramorf simo Montèlo Epif neiac pou Upìkeitai stouc Nìmouc thc Fusik c Se aut thn Par grafo perigr fetai èna paramorf simo montèlo epif - neiac pou upìkeitai stouc nìmouc kai tic idiìthtec thc fusik c kai eis - getai sta [22] kai [25]. H perigraf thc leitourgðac kai twn periorism n tou montèlou jewreðtai anagkaða ste na katasteð autì to Kef laio a-

95 3.2. Paramorf simo Montèlo Epif neiac 73 (a) (b) Sq ma 3.1: (a) Eikìna enìc pros pou, (b) epif neia fwteinot twn pou anaparist thn eikìna. nex rthto. Up rqoun dôo sqhmatismoð tou montèlou, ènac gia èna 3D paramorf simo montèlo epif neiac kai ènac gia èna 2D paramorf simo montèlo kampul n. Epilègoume na analôsoume to 3D montèlo dedomènou ìti eðnai pio perðploko kai sugqrìnwc, oi upojèseic kai h diadikasða paramìrfwshc eðnai oi Ðdiec kai gia touc duo sqhmatismoôc montèlwn. To 2D paramorf simo montèlo kampul n pou upìkeitai stouc nìmouc thc fusik c perigr fetai en suntomða, sto tèloc aut c thc Paragr fou, lìgw thc omoiìtht c tou me thn 3D perðptwsh. H fwteinìthta thc eikìnac I(x; y) mporeð na jewrhjeð ìti kajorðzei mia epif neia p nw apì thn perioq thc eikìnac, pou ja kaleðtai apì e- d kai sto ex c epif neia fwteinot twn (x; y; I(x; y)) ston apokaloômeno XYI q ro [26] (sq ma 3.1). 'Ena 3D paramorf simo montèlo epif neiac pou upìkeitai stouc nìmouc thc fusik c mporeð na qrhsimopoihjeð gia na proseggðsei thn epif neia fwteinìthtac. To paramorf simo montèlo e- pif neiac apoteleðtai apì èna omoiìmorfo plègma N = N h N w kìmbwn,

96 74Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou ìpwc dieukrinðzetai kai sto sq ma 3.2a. Se aut thn Par grafo, upojètoume ìti ta N h kai N w eðnai Ðsa me to Ôyoc kai to pl toc thc eikìnac antðstoiqa, dhlad, ìti k je eikonostoiqeðo thc eikìnac antistoiqeð se è- nan kìmbo tou plègmatoc. Oi suntetagmènec twn kìmbwn tou upì exètash montèlou apojhkeôontai se èna N-di stato di nusma sthl n, ta stoiqeða tou opoðou eðnai 3-di stata dianôsmata seir n: v (t) = = h x (t) 11;:::;x (t) ; 1 Nw 21;:::;x x(t) (t) jj0;:::;x (t) NhNw h i T x (t) 1 ;:::;x (t) i ;:::;x (t) N ; (3.1) i T ìpou x (t) i = [x (t) i ; y (t) i ; z (t) i ] = [x (t) i ;y (t) i ;I (t) (x Model i;y i )] kai t dhl nei th t- st qronik stigm paramìrfwshc. Gia to prìblhma autì kajeautì, k je kìmboc tou paramorf simou montèlou epif neiac mporeð na kinhjeð mìno kat m koc tou z xona, dhlad mìno ston xona fwteinot twn, kat sunèpeia x (t) i = x i kai y (t) i = y i. K je kìmboc tou montèlou jewreðtai ìti èqei m za m kai sundèetai me tèsseric geðtonèc tou, me idanik elat ria sklhrìthtac μ k, fusikoô m kouc l 0 kai suntelest apìsbeshc c (sq ma 3.2b). Oi stajerèc μ k kai m perigr foun ta fusik qarakthristik tou paramorf simou montèlou kai kajorðzoun th sumperifor tou. K tw apì thn epðdrash twn eswterik n kai exwterik n dun mewn, to sôsthma m - zac elathrðwn paramorf netai kai teðnei na proseggðsei thn 3D epif neia fwteinot twn thc eikìnac. JewroÔme pwc mìno elastikèc paramorf seic up rqoun, dhlad mìlic afairoôntai ìlec oi efarmosmènec dun meic pou prokaloôn thn paramìrfwsh, to montèlo anakteð thn arqik morf tou. 'Otan to k μ k aux netai /kai to m mei netai, h analogða μ aux netai kai m to montèlo epif neiac teðnei na sumperiferjeð wc kampto. Autì shmaðnei sthn pr xh, ìti to montèlo epif neiac fwteinot twn mporeð met bðac na paramorf jei. Se aut n thn perðptwsh, oi dun meic pou efarmìzontai stouc kìmbouc èqoun epipt seic se geitonièc kìmbwn (e n ìqi se olìklh- k ro to plègma), an loga me thn akrib tim thc analogðac μ. En, ìtan m

97 3.2. Paramorf simo Montèlo Epif neiac 75 to m aux netai /kai to k μ k mei netai, h analogða μ mei netai kai to montèlo epif neiac fwteinot twn teðnei na eðnai pl rwc paramorf simo, m pou shmaðnei ìti k je dônamh, ousiastik, èqei epipt seic mìno ston kìmbo (m za), ìpou efarmìzetai. To upì exètash montèlo, pou upìkeitai stouc nìmouc kai tic idiìthtec thc fusik c, kubern tai apì th jemeli dh exðswsh dunamik c: f el (x (t) i )+f d (x (t) i )+f ext (x (t) i )=m i ẍ (t) i, i =1; 2;:::;N; (3.2) ìpou ẍ (t) i eðnai h epit qunsh tou i-stoô kìmbou. H exwterik dônamh f ext ( ) pou efarmìzetai se k je kìmbo, kajorðzetai apì thn èlxh tou montèlou ìtan efarmìzontai se autì dun meic an logec me tic fwteinìthtec thc eikìnac (dhlad ìntac an logec proc thn eukleðdeia apìstash metaxô twn suntetagmènwn twn kìmbwn kai tou antðstoiqou eikonostoiqeðou thc eikìnac, tou opoðou h anapar stash ston XY I q ro eðnai (x i ;y i ;I(x i ;y i )) [27], [28]). H elastik dônamh, f el ( ) ston i-stì kìmbo orðzetai wc: f el (x (t) i )= μ k X j2 T (i) b (t) ij l 0 X j2 T (i) (t) bij kb (t) ij k 1 A ; (3.3) ìpou to T (i) dhl nei to sônolo twn tess rwn geitonik n kìmbwn pou sundèontai me ton i kìmbo kai b ij = x (t) i x (t) j, j 2 T (i) eðnai h dianusmatik diafor twn dôo kìmbwn. H dônamh apìsbeshc f d ( ) eðnai an logh proc thn taqôthta _x (t) i twn kìmbwn: f d (x (t) i )= c _x (t) i ; (3.4) ìpou c eðnai h stajer apìsbeshc. H parap nw exðswsh diakubèrnhshc (3.2) isqôei gia ìlouc touc N kìmbouc tou montèlou kai odhgeð se èna mh grammikì sôsthma periplegmènwn diaforik n exis sewn, dedomènou ìti h metatìpish enìc kìmbou exart tai apì th metatìpish twn geitonik n tou pou èqei epipt seic ston ìro f el ( ).

98 76Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou (a) y z c m c k c c m c k F 12 c m c c k c m y f 14 c f z 14 F 14 f x 14 x l o k k k k c m c k c c m c k c c m c k c c m F 24 l o (b) Sq ma 3.2: (a) Tetr pleuro montèlo epif neiac, (b) Par deigma 3D montèlou epifaneðac apoteloômeno apì 8 kìmbouc m zac m, pou sundèontai metaxô touc me idanik elat ria sklhrìthtac k μ kai suntelest apìsbeshc c. Treic dun meic energoôn p nw sto montèlo kai odhgoôn sthn paramìrfwsh tou.

99 3.2. Paramorf simo Montèlo Epif neiac 77 Prokeimènou na lujeð autì to sôsthma twn periplegmènwn diaforik n exis sewn, k poioc mporeð na jèsei to fusikì m koc twn elathrðwn Ðso me mhdèn, l 0 =0kai na prosjèsei mia stajer dônamh isorropðac f eq = f el sthn arister pleur thc exðswshc (3.2) [22]. Me autìn ton trìpo, h fusik kat stash tou montèlou eðnai h arqik diamìrfws tou (sq ma 3.2a). Aut h upìjesh èqei to kôrio pleonèkthma ìti to montèlo mporeð na exetasteð sta plaðsia thc grammik c elastikìthtac, dhlad, h exðswsh (3.2) metasqhmatðzetai se èna sônolo grammik n diaforik n exis sewn me tic metatopðseic twn kìmbwn na aposundèontai se k je suntetagmènh, anex rthta apì to mègejoc twn metatopðsewn. To paramorf simo montèlo epif neiac, genik, kuberniètai apì thn akìloujh lagkrasian ( Lagrangian) exðswsh pin kwn: Mü (t) + C _u (t) + Ku (t) = f (t) ; (3.5) ìpou u (t) = [u (t) 1 u (t) 2 ::: u (t) N ]T eðnai to N-di stato di nusma me tic kombikèc metatopðseic u (t) = v (t) v (t0), ta stoiqeða u (t) i tou opoðou eðnai 3- di stata dianôsmata seir n. Oi M, C, kai K eðnai, antðstoiqa oi N N pðnakec m zac, apìsbeshc, kai sklhrìthtac tou montèlou, twn opoðwn h akrib c diatôpwsh dðnetai analutik sto [25] kai f (t) =[f (t) 1 f (t) 2 ::: f (t) N ]T eðnai to N-di stato di nusma ta stoiqeða tou opoðou eðnai ta exwterik dianôsmata dônamhc pou efarmìzontai sto montèlo. twn exwterik n dianusm twn dun mewn f (t) K je stoiqeðo f (t) i mporeð na jewrhjeð wc èna eikonikì elat rio fusikoô m kouc mhdèn kai sklhrìthtac g, pou en nei k je kìmbo tou montèlou epif neiac me to antðstoiqo eikonostoiqeðo sthn eikìna (kai pio sugkekrimèna to antðstoiqo shmeðo sthn epif neia fwteinot twn thc eikìnac). H exðswsh (3.5) eðnai mia peperasmènh diatôpwsh twn stoiqeðwn thc diadikasðac paramìrfwshc tou montèlou. AntÐ na lujeð mesa h exðswsh isorropðac (3.5), k poioc mporeð na qrhsimopoi sei thn an lush idioqarakthristik n [25] kai na th metasqhmatðsei me mia allag b shc [30] ston apokaloômeno q ro idioqarakthri-

100 78Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou stik n: u (t) = Ψ~u (t) ; (3.6) ìpou Ψ eðnai ènac tetragwnikìc antistrèyimoc pðnakac metasqhmatismoô, di stashc N N kai t xewc N (pou prèpei na kajoristeð) kai ~u (t) = [~u (t) 1 ~u (t) 2 ::: ~u (t) N ]T anafèretai wc to genikeumèno di nusma metatopðsewn. 'Enac apotelesmatikìc trìpoc epilog c tou Ψ eðnai na tejeð Ðso me ènan pðnaka Φ =[ffi 1 ;:::;ffi N ], oi st lec ffi i tou opoðou eðnai ta idiodianôsmata tou genikeumènou idioprobl matoc: Kffi i =! 2 i Mffi i ; i =1;:::;N; (3.7) u (t) = Φ~u (t) = NX i=1 ffi i ~u (t) i ; (3.8) ìpou K kai M eðnai oi pðnakec sklhrìthtac kai m zac tou montèlou. H exðswsh (3.8) anafèretai kai wc exðswsh idioqarakthristik n. To i- stì idiodi nusma ffi i dhlad, h i-st st lh tou Φ kaleðtai epðshc i-stì idiodi nusma tal ntwshc. To ~u (t) i eðnai to i-stì stoiqeðo tou ~u (t) kai to! i eðnai h antðstoiqh idiotim (apokaloômenh kai wc suqnìthta tal ntwshc). E n o pðnakac ~C = Φ T CΦ eðnai diag nioc (h upìjesh aut onom zetai wc upìjesh Rayleigh sto [22]), h exðswsh diakubèrnhshc (3.5) se morf pin kwn analôetai se 3N bajmwtèc exis seic (N exis seic gia touc x, y, z xonec) sto q ro idioqarakthristik n: ìpou i =1;:::;N, ~u (t) i tou ~C kai ~f (t) i =[ ~ f (t) i;x ; ~ f (t) ~u (t) i;x +~c i _ ~u (t) i;x +!2 i ~u (t) i;x = ~ f (t) i;x (3.9) ~u (t) i;y +~c i _ ~u (t) i;y +!2 i ~u (t) i;y = ~ f (t) i;y ; (3.10) ~u (t) i;z +~c i _ ~u (t) i;z +! 2 i ~u (t) i;z = ~ f (t) i;z ; (3.11) =[~u (t) i;x; ~u (t) i;y; ~u (t) i;z], ~c i eðnai to i-stì diag nio stoiqeðo ; ~ i;y f (t) i;z ] to i-stì stoiqeðo tou metasqhmatismènou dianôsmatoc exwterik n dun mewn ~ f (t), ìpou ~ f (t) = Φ T f (t), f (t) eðnai to

101 3.2. Paramorf simo Montèlo Epif neiac 79 di nusma exwterik n dun mewn. H epðlush aut n twn exis sewn sthn fi-st epan lhyh odhgeð sto ~u (t) i kai epomènwc sto ~u (t). To di nusma metatopðsewn u (t) twn kìmbwn tou montèlou lamb netai apì thn exðswsh idioqarakthristik n (3.8). 'Ena shmantikì pleonèkthma twn diatup sewn pou perigr fhkan mèqri t ra, eðnai ìti ta dianôsmata tal ntwshc (idiodianôsmata): ffi i =[ffi i (1);:::;ffi i (N)]; (3.12) kai oi suqnìthtec tal ntwshc (idiotimèc)! i miac epðpedhc topologðac (ìpwc aut tou sq matoc 3.2a) èqoun mia rht diatôpwsh [22] kai den eðnai aparaðthto na upologistoôn qrhsimopoi ntac teqnikèc idio-aposônjeshc:! 2 (j; j 0 )=! 2 jnw+j0 = 4μ k m» sin 2 ßj 2N h + sin 2 ßj 0 2N w ; (3.13) ffi n;n 0(j; j 0 )=ffi jn w+j0(n N w + n 0 ) = cos ßj(2n 1) N h cos ßj0 (2n 0 1) N w ; (3.14) ìpou j = 0; 1;:::;N h 1, j 0 = 0; 1;:::;N w 1, n = 1; 2;:::;N h kai n 0 =1; 2;:::;N w. Sthn perðptws mac, ìpou h arqik kai h telik (epijumht ) kat - stash tou paramorf simou montèlou epif neiac, dhlad h arqik epðpedh diamìrfwsh tou montèlou kai h epif neia fwteinot twn thc eikìnac, eðnai gnwst, mporoôme na upojèsoume ìti èna stajerì fortðo dônamhc f efarmìzetai sto montèlo epif neiac. Ta stoiqeða twn dun mewn sto f, kat m koc twn axìnwn x kai y lamb nontai Ðsa me mhdèn, dhlad f i;x = f i;y =0. Ta stoiqeða aut n twn dun mewn kat m koc tou z xona ( xonac fwteinot twn) lamb nontai Ðsa me thn eukleðdeia apìstash metaxô tou shmeðou (x; y; I(x; y)) thc epif neiac fwteinot twn kai thc jèshc tou antðstoiqou kìmbou sthn arqik diamìrfws tou montèlou (x; y; 0), dhlad, Ðso me th

102 80Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou fwteinìthta I(x; y) tou eikonostoiqeðou (x; y): f (x 1)N w +y;z = f(x; y) =I(x; y); x =1;:::;N h ; y =1;:::;N w (3.15) 'Opou f (x 1)N w+y;z eðnai to stoiqeðo f (x 1)N w +y tou dianôsmatoc f kat m koc tou z xona. Upì aut thn kat stash, to montèlo paramorf netai mìno kat m koc tou z xona, pou ephre zetai apì stajerèc dun meic. Kat sunèpeia, h exðswsh (3.5) aplopoieðtai sthn akìloujh exðswsh diakubèrnhshc isorropðac pou antistoiqeð sto statikì prìblhma: Ku = f; (3.16) stoq roidioqarakthristik n: ~K~u = ~ f; (3.17) ìpou ~K = Φ T KΦ kai ~ f = Φ T f, f eðnai to di nusma exwterik n dun mewn. SÔmfwna me tic parap nw allagèc, h exðswsh (3.17) aplopoieðtai se 3N bajmwtèc exis seic:! 2 i ~u i;x = f ~ i;x ;! 2 i ~u i;y = f ~ i;y =0;! 2 i ~u i;z = f ~ i;z =0; (3.20) ìpou i =1;:::;N. Kat sunèpeia, antð tou upologismoô tou dianôsmatoc metatìpishc u apì thn (3.16), k poioc mporeð na upologðsei ta! 2 i kai ta ffi i apì thn (3.13) kai thn (3.14) antðstoiqa, to ~u apì thn (3.20) kai telik na upologðsei to u qrhsimopoi ntac thn (3.8). Apì th qrhsimopoðhsh thc (3.8) kai thc (3.20), mporeð na diapistwjeð ìti oi paramorf seic u xy enìc kìmbou tou paramorf simou montèlou kat m koc tou xona fwteinot twn pou antistoiqeð sto eikonostoiqeðo (x; y), sômfwna me thn an lush idioqarakthristik n gia mia epðpedh topologða kai me exwterikèc dun meic twn opoðwn h z sunist sa dðnetai apì thn

103 3.2. Paramorf simo Montèlo Epif neiac 81 (a) y m c k c m c k c m c k c m c k c m F 3 y f 5 f x 5 F 5 x (b) Sq ma 3.3: (a) 'Ena 2D anoiqtì montèlo kampôlhc, (b) Par deigma enìc 2D montèlou kampôlhc apoteloômeno apì 5 kìmbouc m zac m pou sundèontai me idanik elat ria sklhrìthtac k μ kai me suntelest apìsbeshc c. DÔo dun meic energoôn sto montèlo kai to odhgoôn se paramìrfwsh. exðswsh (3.15) en oi llec dôo eðnai mhdèn, mporoôn na perigrafoôn apì: u xy = Nh 1 X i=0 Nw 1 X j=0 P N P h N w n=1 (1 +! 2 (i; j)) P Nh n=1 P N w n0 =1 ffi 2 n;n0(i; j) ffi x;y(i; j); (3.21) n0 =1 I(n; n 0 )ffi n;n 0(i; j) ìpou u xy eðnai h z sunist sa tou stoiqeðou u (x 1)N w +y tou dianôsmatoc u (oi llec duo sunist sec eðnai mhdenikèc) kai I(n; n 0 ) eðnai h fwteinìthta thc eikìnac tou eikonostoiqeðou (n; n 0 ). H parap nw exðswsh ekfr zei to telikì apotèlesma thc proanaferjeðsac mejodologðac gia thn paramìrfwsh enìc montèlou epif neiac, basizìmenoi sthn an lush idioqarakthristik n. K poioc mporeð na dei ìti oi paramorf seic sqetðzontai mesa me tic idiotimèc! 2 (i; j) kai ta idiodianôsmata ffi 2 (i; j) tou montèlou, pou upologðzetai apì tic exis seic (3.13) kai (3.14) antðstoiqa. OmoÐwc me ta 2D s mata, èna 1D s ma mporeð na anaparastajeð qrhsimopoi ntac èna 2D paramorf simo montèlo pou upìkeitai stouc nìmouc

104 82Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou thc fusik c. 'Ena 1D diakritì s ma s(x) (me x = 1; 2;:::;N) mporeð na jewrhjeð wc mia 2D kampôlh (x; s(x)). O sqhmatismìc enìc tètoiou 1D s matoc mporeð na epiteuqjeð me th qrhsimopoðhsh miac anoikt c topologðac alusðdwn N eikonik n maz n (sq ma 3.3) pou proseggðzei to s ma. Oi upojèseic gia to paramorf simo montèlo kampul n eðnai oi Ðdiec me ekeðnec tou paramorf simou montèlou epif neiac. Oi dun meic pou energoôn stouc kìmbouc jewroôntai pwc èqoun mìno mia sunist sa di forh tou mhdenìc, kat m koc tou s(x) xona. To mègejoc aut c thc sunist sac eðnai Ðso me thn antðstoiqh tim tou s matoc s(x). Ta dianôsmata tal ntwshc (idiodianôsmata) ffi i kai oi suqnìthtec tal ntwshc (idiotimèc)! i twn anoikt n kampul n èqoun thn akìloujh rht diatôpwsh [22]:! 2 (i) = 4μ k ßi m sin2 ; (3.22) 2N ßi(2n 1) ffi n (i) = cos ; (3.23) 2N ìpou ffi n (i) eðnai to n-stì stoiqeðo tou idiodianôsmatoc ffi(i), n 2 f1; 2;:::;Ng kai i 2 f0; 1;:::;N 1g. Mèsw miac an lushc parìmoiac me aut n pou parousi zetai gia to montèlo epif neiac, mporeð k poioc na katal xei eôkola stic paramorf seic enìc kìmbou tou 2D paramorf simou montèlou kampul n pou antistoiqeð sto deðgma s(x) tou s matoc gia mia anoikt kampôlh (topologða alusðdwn). Oi paramorf seic dðnontai apì thn parak tw exðswsh: NX P N n=1 u x = s(n)ffi P n(i) (1 +! 2 N (i)) n=1 ffi2 n(i) ffi x(i): (3.24) i=0 3.3 O Diakritìc Metasqhmatismìc Idioqarakthristik n (DMT) Se aut thn Par grafo, eis getai o 1D kai 2D diakritìc metasqhmatismìc idioqarakthristik n (DMT).O proteinìmenoc metasqhmatismìc eðnai

105 3.3. Diakritìc Metasqhmatismìc Idioqarakthristik n 83 èna endi meso apotèlesma thc diadikasðac paramìrfwshc pou perigr fetai sthn Par grafo 3.2. Sthn perðptwsh twn 2D shm twn, dhlad stic eikìnec, qrhsimopoieðtai èna 3D paramorf simo montèlo epif neiac, pou upìkeitai stouc nìmouc thc fusik c kai perigr fhke sthn Par grafo 3.2, gia na proseggðsei thn epif neia thc eikìnac. 'Opwc anafèrjhke dh, to Ôyoc kai to pl toc (se kìmbouc) tou paramorf simou montèlou eðnai Ðso me to Ôyoc kai to pl toc (se eikonostoiqeða) thc eikìnac kai upotðjetai, ìti to montèlo epif neiac mporeð na paramorfwjeð mìno kat m koc tou z xona. Kat sunèpeia, oi paramorf seic u tou 3D paramorf simou montèlou epif neiac pou efarmìzetai se mia eikìna I, dðnontai apì thn exðswsh (3.21) pou mporeð na xanagrafeð ìpwc: u xy = Nh 1 X k=0 Nw 1 X l=0 F(k; l) q PN h i=1 ffi x;y (k; l) P ; N w j=1 ffi2 i;j(k; l) x =1;:::;N h ; y =1;:::;N w ; (3.25) ìpou F(k; l) = P N P h N w i=1 (1 +! 2 (k; l))q PN h i=1 I(i; j)ffi j=1 i;j(k; l) P N w j=1 ffi2 i;j(k; l) : (3.26) H exðswsh (3.25) efarmìzetai xeqwrist se k je kìmbo tou paramorf simou montèlou epifaneðac. O ìroc thc exðswshc paramìrfwshc pou perigr fetai sthn exðswsh (3.26) eðnai ènac pðnakac diast sewn N h N w. Apì th stigm poô h exðswsh (3.26) perilamb nei thn upì exètash eikìna, o ìroc F(k; l) mporeð na jewrhjeð ìti antiproswpeôei touc suntelestèc enìc 2D metasqhmatismoô eikìnac. AutoÐ oi suntelestèc mporoôn na qrhsimopoihjoôn gia na aposunjèsoun mia eikìna se eikìnec b shc oi opoðec èqoun endiafèrousec idiìthtec. O ìroc kanonikopoðhshc P N h i=1 P N w j=1 ffi2 i;j(k; l) ston paronomast thc

106 84Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou exðswshc (3.26) mporeð na aplopoihjeð peraitèrw [31] wc ex c: ìpou a(k) = ( XNh Nw i=1 X j=1 ffi 2 i;j(k; l) =a(k)a(l); (3.27) N; k =0 N ; k 6= 0 ; k 2 f0; 1;:::;N 1g: (3.28) 2 'Epeita, qrhsimopoi ntac tic exis seic (3.13), (3.14), (3.26), (3.27) kai (3.28), to F(k; l) mporeð na ekfrasteð wc: F(k; l) = Nh 1 X i=0 Nw 1 X j=0 I(i; j)v k;l (i; j); (3.29) v k;l (i; j) = h 1+ hsin 2 cos ßk(2i+1) cos ßl(2j+1) 2Nh 2Nw ßk 2Nh + sin 2 ßl 2Nw iip a(k)a(l) ; (3.30) k ìpou k = 0; 1;:::;N h 1, l = 0; 1;:::;N w 1, = 4 μ. Oi exis seic m (3.29) kai (3.30) orðzoun ton proteinìmeno 2D diakritì metasqhmatismì idioqarakthristik n, ìpou F(k; l) eðnai oi suntelestèc tou metasqhmatismoô. Apì th suz thsh sthn Par grafo 3.2 eðnai profanèc ìti h par - metroc tou metasqhmatismoô elègqei thn elastikìthta tou antðstoiqou paramorf simou montèlou. O 2D DMT susqetðzetai mesa me ton DCT, o opoðoc orðzetai wc ex c [9]: C(k; l) =b(k)b(l) ìpou b(k) = Nh 1 X i=0 8 < : Nw 1 X q j=0 I(j; j) cos 1 q ; k =0 N ßk(2i +1) ßl(2j +1) cos ; (3.31) 2N h 2N w 2 ; k 6= 0 ; k 2 f0; 1;:::;N 1g: (3.32) N

107 3.3. Diakritìc Metasqhmatismìc Idioqarakthristik n 85 PÐnakac 3.1: Oi eikìnec b shc tou 2D DMT gia mègejoc montèlou N h =3, N w =3kai = W 11 W 12 W :3333 0:3333 0:3333 0: :3266 0:1347 0:2694 0: :3333 0:3333 0: : : :1347 0:2694 0:1347 0:3333 0:3333 0:3333 0: :3266 0:1347 0:2694 0:1347 W 21 W 22 W :3266 0:3266 0:3266 0: :3333 0:1443 0:2887 0: :3266 0:3266 0:3266 0: :3333 0:1443 0:2887 0:1443 W 31 W 32 W :1347 0:1347 0:1347 0: :1443 0:0667 0:1333 0: :2694 0:2694 0: : : :1333 0:2667 0:1333 0:1347 0:1347 0:1347 0: :1443 0:0667 0:1333 0: SugkrÐnontac tic exis seic (3.28), (3.29), (3.30) me (3.31), (3.32) eðnai eôkolo na exaqjeð to sumpèrasma ìti oi suntelestèc F tou DMT susqetðzontai me touc suntelestèc tou DCT wc ex c: F(k; l) = h 1+ sin 2 ßk 2Nh 1 + sin 2 ßl 2Nw i C(k; l) = C(k; l) Z(k; l) : (3.33) K poioc mporeð eôkola na parathr sei ìti ìtan to =0,tìte F(k; l) = C(k; l). Kat sunèpeia, mporoôme na isquristoôme, ìti o proteinìmenoc metasqhmatismìc eðnai mia genðkeush tou DCT, to opoðo enisqôetai kai apì to gegonìc ìti èqoun parìmoiec idiìthtec, ìpwc faðnetai parak tw sthn Par grafo 3.4. Ousiastik, oi suntelestèc tou DMT eðnai klimakwmènec ekdìseic twn suntelest n tou DCT, ìpou o par gontac klim kwshc eðnai o paronomast c Z(k; l) sthn exðswsh (3.33). Mia apeikìnish twn suntelest n klim kwshc gia N h = N w =8kai =1parousi zetai sto sq ma 3.4. O par gontac klim kwshc perilamb nei thn par metro, h opoða, ìpwc ja apodeiqjeð stic Paragr fouc 3.5 kai 3.6, elègqei tic idiìthtec sugkèntrwshc enèrgeiac tou metasqhmatismoô. To Z(k; l) diadramatðzei ènan rìlo parìmoio me autìn tou pðnaka kb nthshc pou qrhsimopoieðtai gia ton DCT sthn kwdikopoðhsh JPEG.Kat sunèpeia, o DMT mporeð na

108 86Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou Z(k,l) l k Sq ma 3.4: O paranomast c thc exðswshc (3.33) gia N h = N w = 8 kai =1. jewrhjeð wc o DCT sunduasmènoc me èna nèo, analutik upologismèno pðnaka kb nthshc. PÐnakac 3.2: Oi eikìnec b shc tou 2D DCT gia mègejoc eikìnac N h =3 kai N w = W W W 13 0:3333 0:3333 0:3333 0: :4082 0:2357 0:4714 0: :3333 0:3333 0: : : :2357 0:4714 0:2357 0:3333 0:3333 0:3333 0: :4082 0:2357 0:4714 0:2357 W 21 W 22 W :4082 0:4082 0:4082 0:5 0 0:5 0:2887 0:5774 0: :4082 0:4082 0:4082 0:5 0 0:5 0:2887 0:5774 0:2887 W 31 W 32 W :2357 0:2357 0:2357 0: :2887 0:1667 0:3333 0: :4714 0:4714 0: : : :3333 0:6667 0:3333 0:2357 0:2357 0:2357 0: :2887 0:1667 0:3333 0: O antðstrofoc metasqhmatismìc DMT dðnetai apì th sqèsh: I(i; j) = XNh Nw X k=1 l=1 F(k; l)w k;l (i; j); (3.34)

109 3.3. Diakritìc Metasqhmatismìc Idioqarakthristik n 87 ìpou i =0; 1;:::;N h 1, j =0; 1;:::;N w 1 kai w k;l (i; j) eðnai Ðsa me: w k;l (i; j) = cos ßk(2i +1) ßl(2j +1) 1+ cos 2N h 2N w hsin 2 ßk 2Nh + sin 2 ßl 2Nw i p a(k)a(l) : (3.35) Ta w k;l (i; j) apoteloôn tic sunart seic b shc tou 2D diakritoô metasqhmatismoô DMT. H apìdeixh gia ton 2D antðstrofo metasqhmatismì DMT perilamb netai sto Par rthma A. Oi eikìnec b shc tou proteinìmenou metasqhmatismoô apeikonðzontai ston PÐnaka 3.1 gia mègejoc eikìnac N h =3, N w =3kai =1. Ston pðnaka 3.2, parousi zontai oi antðstoiqec eikìnec b shc tou DCT gia mègejoc eikìnac 3 3. EÐnai olof nero pwc oi eikìnec b shc twn dôo metasqhmatism n èqoun parìmoia dom. Sthn perðptwsh twn 1D shm twn, èna 2D paramorf simo montèlo kampul n qrhsimopoieðtai gia na antiproswpeôsei to s ma. To m koc tou montèlou eðnai Ðso me to mègejoc tou s matoc kai upotðjetai ìti to montèlo kampul n mporeð na paramorfwjeð mìno kat m koc tou y xona. Qrhsimopoi ntac parìmoia mejodologða me aut n pou parousi zetai parap nw gia th 2D perðptwsh, to zeug ri (eujôc kai antðstrofoc) tou 1D metasqhmatismoô idioqarakthristik n gia èna s ma s(i) dðnetai apì touc tôpouc: s(i) = F(k) = N 1 X k=0 " N 1 X i=0 s(i) F(k)cos cos ßk(2i+1) 2N ΛΛp ; (3.36) 1+ sin 2 ßk a(k) ßk(2i +1) 2N 2N # 2N p a(k) 1+ sin 2 ßk : (3.37) Ta dianôsmata b shc gia ton proteinìmeno 1D metasqhmatismì (me = 1) kai gia to 1D DCT apeikonðzontai sto sq ma 3.5 gia mègejoc s matoc 3.

110 88Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou W 1 W 2 W 3 W 4 W 5 W 6 W 7 W 8 Sq ma 3.5: Ta dianôsmata b shc gia mègejoc s matoc 8 tou 1D DMT (me =1)kaitou DCT.

111 3.4. Idiìthtec MetasqhmatismoÔ Idiìthtec tou DiakritoÔ MetasqhmatismoÔ DMT Se aut thn Par grafo, parousi zontai oi idiìthtec tou 2D DMT kai epishmaðnontai oi omoiìthtèc tou me ekeðnec tou DCT.Oi idiìthtec tou 1D proteinìmenou metasqhmatismoô, eðnai parìmoiec me tou 2D metasqhmatismoô kai ètsi, den ja parousiastoôn se aut thn Par grafo. O DMT eðnai ènac grammikìc kai pragmatikìc metasqhmatismìc. Epiplèon, o DMT kai o antðstrofoc DMT diamorf noun èna orjokanonikì zeug ri metasqhmatismoô, dhlad : N 1 N 1 X X i=0 j=0 v k;l (i; j)w k 0 ;l 0(i; j) =ffi(k k 0 ;l l 0 ); (3.38) ìpou ffi eðnai h monadiaða sun rthsh. H apìdeixh ìti to zeug ri DMT kai IDMT (antðstrofoc DMT) eðnai orjog nio kai orjokanonikì, perilamb netai sto Par rthma B. Epiplèon, antðjeta apì ton DCT, oi eikìnec b shc tou DMT w k;l (i; j) eðnai orjog niec all ìqi orjokanonikèc (Par rthma B ), dhlad N 1 N 1 X X i=0 j=0 w k;l (i; j)w k 0 ;l 0(i; j) = ( g 6= 1; k = k 0 kai l = l 0 0; alli c : (3.39) 'Etsi, o DMT den eðnai ènac orjokanonikìc (monadiaðoc) metasqhmatismìc kai h enèrgeia tou sto pedðo twn suqnot twn den diathreðtai. Epiplèon, antðjeta apì ton DCT, o DMT eðnai mh-diaqwrðsimoc, ìpwc faðnetai sthn exðswsh (3.33). Dedomènou ìti o DMT eðnai mh-diaqwrðsimoc metasqhmatismìc, h u- pologistik poluplokìtht tou gia mia N N eikìna eðnai thc t xewc O(N 4 ). EntoÔtoic, dedomènou ìti o 2D DMT mporeð na upologisteð qrhsimopoi ntac apeujeðac ton DCT (3.33), h poluplokìtht tou mporeð na

112 90Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou (a) (b) Sq ma 3.6: (a) Mia eikìna exwterikoô q rou, (b) oi suntelestèc tou DMT gia =1. meiwjeð se O(N 2 log 2 N), e n qrhsimopoihjoôn gr gorec efarmogèc upologismoô tou DCT [32]. Oi sunart seic b shc tou DMT antistoiqoôn se gnwstoôc telestèc epexergasðac eikìnac, dhlad se aniqneutèc gramm n kai akm n pollaplasiasmènouc me ènan suntelest pou exart tai apì to. Gia thn a- ploôsterh perðptwsh, ìpou to N h = N w = 3 (PÐnakac 3.1), oi eikìnec b shc W 12 kai 21 eðnai oi Prewitt telestèc [33] pou aniqneôoun akmèc se k jetec kai orizìntiec kateujônseic. Epiplèon, oi eikìnec b shc W 13 kai W 31 eðnai aniqneutèc k jetwn kai orizìntiwn gramm n [33]. Epiprìsjeta, oi W 23 kai W 32 eðnai aniqneutèc akm n [34] kai h W 33 eðnai h Laplacian m ska anðqneushc gramm n. Oi m skec kai gia llec timèc twn N h kai N w antistoiqoôn epðshc se telestèc anðqneushc gramm n kai akm n. O DMT èqei tic ristec idiìthtec energeiak c sumpðeshc, parìmoiec me autèc tou DCT. Ta sq mata 3.6 kai 3.7 epexhgoôn thn energeiak sumpðesh sto pedðo suqnot twn gia dôo eikìnec, qrhsimopoi ntac ton DMT (me = 1). EÐnai profanèc, ìti h enèrgeia kai gia tic dôo eikìnec

113 3.5. Sugkèntrwsh Enèrgeiac kai Ikanìthta Aposusqètishc 91 (a) (b) Sq ma 3.7: (a) 'Ena anjr pino prìswpo, (b) oi suntelestèc DMT gia =1. sugkentr netai sthn perioq qamhl c suqnìthtac, dhlad, sthn p nw arister perioq. Aut h idiìthta ja ereunhjeð peraitèrw sthn epìmenh Par grafo. 3.5 Sugkèntrwsh Enèrgeiac kai Ikanìthta Aposusqètishc tou DMT Se aut thn Par grafo exet zontai h ikanìthta sugkèntrwshc enèrgeiac kai h apodotikìthta aposusqètishc tou DMT qrhsimopoi ntac dokimastikèc eikìnec kaj c epðshc kai èna stoqastikì montèlo eikìnac. Sto pr to sônolo peiram twn, o DMT efarmìsthke se di forec eikìnec kai metr jhke to posostì thc enèrgeiac pou sugkentr netai sto 3% twn suntelest n metasqhmatismoô pou brðskontai sth perioq qamhl c suqnìthtac dhlad, sto p nw aristerì tetarthmìrio tou pedðou suqnìthtac (sq ma 3.8). Me lla lìgia, upologðsthke to posostì thc enèrgeiac twn suntelest n pou brðskontai sthn sprh perioq tou sq matoc 3.8

114 92Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou proc th sunolik enèrgeia. O PÐnakac 3.3 parousi zei th sugkèntrwsh enèrgeiac tou DMT sthn perioq pou parousi zetai sto sq ma 3.8, gia di forec eikìnec kai gia di forec timèc thc paramètrou. To mègejoc tou parajôrou pou qrhsimopoi jhke gia na upologistoôn oi metasqhmatismènec eikìnec tan to pragmatikì mègejoc thc eikìnac. Ta apotelèsmata deðqnoun ìti o proteinìmenoc metasqhmatismìc sumpièzei thn enèrgeia se merikoôc suntelestèc sthn perioq qamhl c suqnìthtac. Pio sugkekrimèna, kaj c to aux netai, o DMT sugkentr nei ìlo kai perissìterh enèrgeia sthn perioq qamhl c suqnìthtac. Kat sunèpeia, o DMT perilamb nei ènan èmfuto trìpo sugkèntrwshc enèrgeiac, mèsw thc paramètrou. Autì eðnai èna polô shmantikì qarakthristikì, dedomènou ìti to sundèetai mesa me to paramorf simo montèlo mèsw tou opoðou o DMT eis qjhke kai eðnai h par metroc pou elègqei thn elastikìthta tou montèlou. Mia meg lh tim tou odhgeð se èna kampto paramorf simo montèlo pou mporeð met bðac na paramorfwjeð kai kat sunèpeia lamb - noume mia qondroeid prosèggish thc epif neiac fwteinot twn thc eikìnac h opoða exoudeter nei ta tm mata uyhl c suqnìthtac thc eikìnac. Apì th stigm pou oi suntelestèc tou DMT exart ntai apì thn eikìna pou qrhsimopoieðtai gia na paramorfwjeð to montèlo (deðte thn exðswsh (3.25) ), h enèrgeia sugkentr netai sthn perioq qamhl c suqnìthtac. Apì thn llh, mia mikr tim tou odhgeð se èna idiaðtera elastikì paramorf simo montèlo pou paramorf netai gia na paraqjeð mia leptomer c prosèggish thc epif neiac fwteinot twn thc eikìnac. Kat sunèpeia diathroôntai perissìtera tm mata uyhl c suqnìthtac. Autì èqei san apotèlesma h enèrgeia na eðnai di sparth sthn perioq twn metasqhmatismènwn suntelest n tou DMT. Sto akìloujo sônolo peiram twn, axiolog jhke h apìdosh tou proteinìmenou metasqhmatismoô qrhsimopoi ntac dôo metrikèc apìdoshc metasqhmatism n, dhlad th dunatìthta aposusqètishc tou s matoc kai thn dunatìthta sugkèntrwshc enèrgeiac, parìmoiec me autèc pou qrhsi-

115 3.5. Sugkèntrwsh Enèrgeiac kai Ikanìthta Aposusqètishc 93 Sq ma 3.8: To posostì thc enèrgeiac upologðzetai mìno gia thn sprh perioq. Aut h perioq antistoiqeð sto 3% twn suntelest n tou pedðou suqnìthtac. PÐnakac 3.3: Posostì thc sunolik c enèrgeiac to opoðo brðsketai sto 3% thc qamhlì-suqnotik c perioq c ( sprh perioq tou sq matoc 3.8) gia ton DMT kai di forec timèc tou. Exetazìmenec Eikìnec DMT =1 =10 =20 Lèna MpampouÐnoc exwterikìc q roc eswterikìc q roc Anjr pino prìswpo stoôntio mèsh tim

116 94Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou mopoi jhkan sta [35] kai [36]. Autèc oi metrikèc upologðsthkan qrhsimopoi ntac èna montèlo summetablhtìthtac gia thn upì exètash eikìna kai axiolog ntac tic sunart seic summetablhtìthtac twn suntelest n metasqhmatismoô. H eikìna eisagwg c diamorf jhke wc mia 2D markobian akoloujða monadiaðac apìklishc kai mhdenik c mèshc tim c me mia ekjetik, isotropik, mh-diaqwrðsimh sun rthsh metablhtìthtac kai suntelest susqètishc ρ, to opoðo eðnai èna suqn qrhsimopoihmèno montèlo sthn e- pexergasða eikìnac [32]. O pðnakac summetablhtìthtac gia mia M N eikìna pou tairi zei se autì to montèlo dðnetai apì th sqèsh: p Cov(i; j; i 0 ;j 0 )=E[I(i; j)i(i 0 ;j 0 (i i0 )] = ρ ) 2 +(j j0 ) 2 ; (3.40) 'Opou E[ ] dhl nei ton telest prosdokðac (expectation). Lamb nontac upìyh èna metasqhmatismì eikìnac me eikìnec b shc v kl (i; j) kai k; i 2 f0; 1;:::;N 1g, l; j 2 f0; 1;:::;M 1g, o pðnakac summetablhtìthtac Cov T (k; l; k 0 ;l 0 ) twn suntelest n tou metasqhmatismoô F(k; l) mporeð na upologisteð wc ex c: Cov T (k; l; k 0 ;l 0 ) = E[F(k; l)f(k 0 ;l 0 )] = E[ = = " N 1 M 1 X X i=0 j=0 " N 1 M 1 X X i0 =0 I(i; j)v kl (i; j) j0 =0 I(i 0 ;j 0 )v k 0 l 0(i 0 ;j 0 ) X X X X N 1 M 1 N 1 M 1 i=0 j=0 i0 =0 X X X X N 1 M 1 N 1 M 1 i=0 j=0 i0 =0 # # ] j0 =0 E[I(i; j)i(i 0 ;j 0 )]v kl (i; j)v k 0 l 0(i 0 ;j 0 ) j0 =0 Cov(i; j; i 0 ;j 0 )v kl (i; j)v k 0 l 0(i 0 ;j 0 ): (3.41) Se autì to peðrama, oi metrikèc thc ikanìthtac sugkèntrwshc enèrgeiac kai thc aposusqètishc s matoc gia 1D s mata kai metasqhmati-

117 3.5. Sugkèntrwsh Enèrgeiac kai Ikanìthta Aposusqètishc 95 smoôc pou parousi zontai sta [35], [36], epekt jhkan sth 2D perðptwsh. Wc ek toôtou, h ikanìthta aposusqètishc enìc 2D metasqhmatismoô mporeð na ekfrasteð wc: DE = P N 1 i=0 P N 1 i=0 P M 1 j=0 P M 1 P N 1 i0 =0 P M 1 j0 =0 jcov T (i; j; i 0 ;j 0 )j : (3.42) j=0 jcov T (i; j; i; j)j 'Enac apodotikìc metasqhmatismìc prèpei na dðnei suntelestèc metasqhmatismoô pou eðnai ìso to dunatìn pio asusqètistoi, dhlad sthn idanik perðptwsh to E[F(k; l)f(k 0 ;l 0 )] = Cov T (k; l; k 0 ;l 0 ) prèpei na eðnai Ðso me to mhdèn gia k 6= k 0 l 6= l 0. Se aut n thn perðptwsh, isqôei ìti DE = 1. Genik, meg lec timèc tou DE (dhlad timèc kont sto 1) upodeiknôoun kalèc idiìthtec aposusqètishc. H dunatìthta sugkèntrwshc enèrgeiac upologðzetai apì th sqèsh: EPA( ) = P i=0 P N 1 i=0 P jcov j=0 T (i; j; i; j)j P M 1 jcov j=0 T (i; j; i; j)j ; (3.43) ìpou eðnai to posostì twn suntelest n pou diathroôntai. H dunatìthta sugkèntrwshc enèrgeiac metr, sto pedðo tou metasqhmatismoô, thn analogða thc enèrgeiac pou perilamb netai stouc suntelestèc pou brðskontai sthn perioq qamhl c suqnìthtac proc thn enèrgeia ìlwn twn suntelest n. Uyhlèc timèc tou EPA (dhlad timèc kont sto 1) deðqnoun uyhl energeiak sugkèntrwsh. Prèpei na shmeiwjeð ìti gia è- nan mh-orjokanonikì metasqhmatismì, ìpwc o DMT, hsunolik enèrgeia sthn perioq metasqhmatismoô eðnai diaforetik apì aut n sto qwrikì pedðo. EntoÔtoic, dedomènou ìti to EPA ekfr zetai wc energeiak analogða (sto pedðo metasqhmatismoô), eðnai mia ègkurh metrik apodotikìthtac kai sthn upì exètash perðptwsh. Sto sq ma 3.9 faðnontai apeikonðseic thc ikanìthtac aposusqètishc tou DMT gia timèc thc paramètrou Ðsec me 1 (DMT 1 ), 10 (DMT 10 ) kai 30 (DMT 30 ). O suntelest c susqètishc ρ (exðswsh (3.40) paðrnei timèc

118 Ικανότητα αποσυσχέτισης 96Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou συντελεστής συσχετισμού ρ Sq ma 3.9: Ikanìthta aposusqètishc (DE) sesqèsh me to ρ. KampÔlec par qjhsan gia (a) DMT, =1(DMT 1 ), (b) DMT, =10(DMT 10 ), (g) DMT, = 30 (DMT 30 ), (d) DCT, (DCT), (e) DCT kbantismèno me ton PÐnaka 3.4 (DCT QT ). apì 0:75 èwc 0:98 (dhlad gia uyhl susqetismèna s mata, to opoðo eðnai qarakthristik perðptwsh stic eikìnec). Sto sq ma 3.9 apeikonðzetai to DE se sqèsh me tic timèc tou ρ gia ton DCT (onom zetai DCT) kai gia ton DCT klimakwmèno me ta stoiqeða tou pðnaka kb nthshc (PÐnakac 3.4) pou brðsketai sto par rthma tou protôpou tou JPEG (onom zetai DCT QT ). To mègejoc tou metasqhmatismoô tan 8 8, dhlad N = M = 8tìso gia ton DCT ìso kai gia ton DMT.Sta sq mata 3.10 kai 3.11 parousi zontai oi kampôlec ikanìthtac energeiak c sugkèntrwshc (EPA) se sqèsh me to suntelest susqètishc ρ kai gia touc duo algorðjmouc, me = 2 kai 3 (dhlad gia 4 kai 9 suntelestèc qamhl c suqnìthtac) antðstoiqa. Aut ta sq mata deðqnoun ìti o DMT èqei polô kalèc idiìthtec sugkèntrwshc enèrgeiac kai aposusqètishc tou s matoc, pou aux nontai ìso aux netai kai to. Prèpei na shmeiwjeð entoôtoic, ìti h polô kal apìdosh tou DMT den proèrqetai apì ton Ðdio to metasqhmatismì

119 3.6. Efarmog se SumpÐesh Eikìnac 97 PÐnakac 3.4: OpÐnakac kb nthshc fwteinìthtac tou DCT autì kajeautì, dedomènou ìti o DMT eðnai ousiastik o DCT klimakwmènoc me k poiouc suntelestèc. Dedomènou ìti to aux netai, autoð oi par gontec klim kwshc teðnoun na euno soun touc suntelestèc qamhl c suqnìthtac, aux nontac kat sunèpeia to EPA tou algorðjmou. Wc ek toôtou, asfalèstera sumper smata sqetik me thn apìdosh tou algorðjmou ìson afor to DCT mporoôn na lhfjoôn k tw apì to prðsma enìc algìrijmou sumpðeshc eikìnac, ìpou kai ja ektejeð leptomer c sthn e- pìmenh Par grafo. Shmei ste epðshc ìti, ìpwc eðnai profanèc apì tic exis seic (3.41), (3.42) kai (3.43), h efarmog enìc suntelest klim - kwshc Q ston pðnaka kb nthshc tou DCT, den all zei th morf twn kampul n thc sugkèntrwshc enèrgeiac kai ikanìthtac aposusqètishc gia ton DCT (dhlad tic kampôlec DCT QT sta sq mata ). 3.6 Efarmog tou DMT se SumpÐesh Eikìnac me Ap leia PlhroforÐac An kai h kôria sumbol autoô tou KefalaÐou, eðnai heisagwg tou metasqhmatismoô DMT, se aut thn Par grafo parousi zetai mia efarmog

120 Ικανότητα συγκέντρωσης ενέργειας (η=3) Ικανότητα συγκέντρωσης ενέργειας (η=2) 98Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou συντελεστής συσχετισμού ρ Sq ma 3.10: Ikanìthta sugkèntrwshc enèrgeiac EPA( ) se sqèsh me to ρ gia =2. Oi kampôlec par qjhsan gia (a) DMT, =1(DMT 1 ), (b) DMT, =10(DMT 10 ), (g) DMT, =30(DMT 30 ), (d) DCT, (DCT), (e) DCT kbantismèno me ton PÐnaka 3.4 (DCT QT ). συντελεστής συσχετισμού ρ Sq ma 3.11: Ikanìthta sugkèntrwshc enèrgeiac EPA( ) se sqèsh me to ρ gia =3. Oi kampôlec par qjhsan gia (a) DMT, =1(DMT 1 ), (b) DMT, =10(DMT 10 ), (g) DMT, =30(DMT 30 ), (d) DCT, (DCT), (e) DCT kbantismèno me ton PÐnaka 3.4 (DCT QT ).

121 3.6. Efarmog se SumpÐesh Eikìnac 99 tou DMT se èna sôsthma sumpðeshc eikìnac me ap leiec plhroforðac. O proteinìmenoc metasqhmatismìc sugkrðnetai me ton DCT se ikanìthta sumpðeshc kai poiìthtac thc sumpiesmènhc eikìnac. Epilèxame na qrhsimopoi soume ton DCT gia na sugkrðnoume ton proteinìmeno metasqhmatismì, lìgw twn omoiot twn metaxô touc. 'Alloc ènac lìgoc eðnai ìti o DCT eðnai o eurôtata qrhsimopoihmènoc metasqhmatismìc se poll prìtupa sumpðeshc eikìnac, p.q. ston JPEG. To pr to sônolo peiram twn diapragmateôthke thn axiolìghsh thc poiìthtac twn sumpiesmènwn eikìnwn ìtan efarmìzontai o DMT kai o DCT stic upì exètash eikìnec. Gia na epiteuqjeð h sumpðesh eikìnac, h Ðdia diadikasða qrhsimopoi jhke kai gia touc dôo metasqhmatismoôc. Kai oi dôo 2D metasqhmatismoð efarmìzontai se mia eikìna, qrhsimopoi ntac èna 8 8 par juro. Prokeimènou na aporrifjoôn oi uyhlèc suqnìthtec kai na epiteuqjeð sumpðesh, o DCT prèpei na kbantisteð. Se autì to peðrama, qrhsimopoi jhke o tupopoihmènoc pðnakac kb nthshc pou eis qjhke sto par rthma tou JPEG [15] (PÐnakac 3.4). Gia na epiteuqjeð pollapl sumpðesh, o parap nw pðnakac pollaplasi sthke me èna suntelest klim kwshc Q kai efarmìsthke se ìlec tic perioqèc thc eikìnac. Gia ton DMT den qrhsimopoi jhke kanènac pðnakac kb nthshc, afoô o suntelest c ston paronomast thc exðswshc (3.33) leitourgeð san pðnakac kb nthshc. 'Oloi oi suntelestèc suqnìthtac tou DCT diairèjhkan me tic timèc tou pðnaka kb nthshc, kai èpeita oimetasqhmatismènoi suntelestèc tou DMT kai tou DCT stroggulopoi jhkan stouc pio kontinoôc akèraiouc arijmoôc touc. Oi suntelestèc suqnìthtac pou èqoun eðte mikr tim eðte meg lo diairèth ston pðnaka kb nthshc, stroggulopoioôntai pijan c sto mhdèn. Taxinom ntac touc suntelestèc suqnìthtac se fjðnousa seir (p.q. me ton algìrijmo zig-zagk), k poioc ja katal xei se èna di nusma suntelest n, to opoðo sto tèloc tou ja apoteleðtai apì mhdenik. Prokeimènou na apokthjeð h sumpiesmènh eikìna, pr ta, oi stroggulopoihmènoi suntelestèc tou DCT pollaplasi zontai me ton pð-

122 100Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou naka kb nthshc kai èpeita, oi antðstrofoi metasqhmatismoð efarmìzontai sta dianôsmata suntelest n, kai gia touc dôo metasqhmatismoôc. Oi metrikèc pou qrhsimopoi jhkan gia th sôgkrish twn apotelesm - twn ìson afor thn poiìthta thc sumpiesmènhc eikìnac tan oi ex c: to mègisto l joc jorôbou tou s matoc (PSNR) metaxô thc arqik c kai thc sumpiesmènhc eikìnac, to stajmismèno mègisto l joc jorôbou tou s matoc (WPSNR) [37] kai to sunolikì antilhptikì l joc (TPE) pou ekfr - zetai apì th metrik tou Watson [38]. Oi sqèseic pou qrhsimopoioôntai gia to PSNR kai to WPSNR dðnontai apì tic exis seic: r PNh i=1 P Nw PSNR =20log WPSNR = 20 log 10 j=1(ioriginal(i;j) Icompressed(i;j)) 2 NhNw max(i original (i; j)) ; (3.44) r PNh i=1 P Nw j=1(nv Fij (Ioriginal(i;j) Icompressed(i;j))) 2 NhNw (3.45) 1 NVF ij = ; (3.46) 1+ff 2 ij ìpou NVF ij eðnai h sun rthsh diaf neiac jorôbou (noise visibility function) kai ff 2 ij eðnai h topik apìklish enìc parajôrou miac eikìnac I kentrarismèno sto eikonostoiqeðo me suntetagmènec (i; j). ; Parìlo pou to WPSNR kai h Watson metrik eðnai pio filosofhmènec kai apodotikèc metrikèc apì to PSNR ston èlegqo poiìthtac miac eikìnac, den apoteloôn kai ton kalôtero trìpo sôgkrishc twn duo algorðjmwn. O kôrioc lìgoc eðnai ìti o pðnakac kb nthshc tou DCT de sqedi sthke me thn prooptik apìdoshc miac antikeimenik c poiìthtac all me skopì thn aôxhsh thc upokeimenik c epðdoshc tou algorðjmou. Wstìso, protim jhkan apì ton upokeimenikì èlegqo thc poiìthtac twn eikìnwn, giatð aut h diadikasða eðnai exairetik qronobìra kai epðponh. Prokeimènou na sugkrijoôn ta apotelèsmata sumpðeshc twn dôo metasqhmatism n, o DMT kai o DCT efarmìsthkan se eikìnec diaforeti-

123 3.6. Efarmog se SumpÐesh Eikìnac Percentage (%) of non zero coefficients DMT/PSNR DCT/PSNR DMT/WPSNR DCT/WPSNR Percentage (%) of non zero coefficients DMT/PSNR DCT/PSNR DMT/WPSNR DCT/WPSNR PSNR / WPSNR (a) PSNR / WPSNR (b) Percentage (%) of non zero coefficients DMT/PSNR DCT/PSNR DMT/WPSNR DCT/WPSNR Percentage (%) of non zero coefficients DMT/PSNR DCT/PSNR DMT/WPSNR DCT/WPSNR PSNR / WPSNR (g) PSNR / WPSNR (d) Percentage (%) of non zero coefficients DMT/PSNR DCT/PSNR DMT/WPSNR DCT/WPSNR Percentage (%) of non zero coefficients DMT/PSNR DCT/PSNR DMT/WPSNR DCT/WPSNR PSNR / WPSNR (e) PSNR / WPSNR (st) Sq ma 3.12: To PSNR kai to WPSNR metaxô thc arqik c kai thc sumpiesmènhc eikìnac se sqèsh me to posostì twn mh mhdenik n suntelest n suqnìthtac (percentage of non zero coefficients) gia di forec timèc tou kai tou Q tìso gia ton DMT ìso kai gia ton DCT antðstoiqa, gia di forec eikìnec: (a) Lèna, (b) MpampouÐnoc (M ntril), (g) mia eikìna exwterikoô q rou, (d) mia eikìna eswterikoô q rou, (e) èna anjr pino prìswpo kai (st) mia eikìna se stoôntio.

124 102Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou Percentage (%) of non zero coefficients DMT DCT Percentage (%) of non zero coefficients DMT DCT Total Perceptual Error (a) Total Perceptual Error (b) 16 DMT DCT 8 DMT DCT Percentage (%) of non zero coefficients Percentage (%) of non zero coefficients Total Perceptual Error Total Perceptual Error (g) (d) Percentage (%) of non zero coefficients DMT DCT Percentage (%) of non zero coefficients DMT DCT Total Perceptual Error (e) Total Perceptual Error (st) Sq ma 3.13: To sunolikì antilhptì l joc (Total Perceptual Error (TPE)), pou ekfr zetai apì th Watson metrik, metaxô thc arqik c kai thc sumpiesmènhc eikìnac se sqèsh me to posostì twn mh mhdenik n suntelest n suqnìthtac (percentage of non zero coefficients) gia di forec timèc tou kai tou Q tìso gia ton DMT ìso kai gia ton DCT antðstoiqa, gia di forec eikìnec: (a) Lèna, (b) MpampouÐnoc (M ntril), (g) mia eikìna exwterikoô q rou, (d) mia eikìna eswterikoô q rou, (e) èna anjr pino prìswpo kai (st) mia eikìna se stoôntio.

125 3.6. Efarmog se SumpÐesh Eikìnac 103 k n megej n kai perieqomènou, ìpwc eikìnec pros pwn, eikìnec stoôntio, eikìnec pou apeikonðzoun anjr pouc, eswterikèc kai upaðjriec skhnèc. All zontac timèc sta kai Q gia ton DMT kai ton DCT antðstoiqa, epiteôqjhkan di fora epðpeda sumpðeshc. Se aut ta peir mata, h sumpðesh metr jhke wc to posostì twn suntelest n suqnìthtac pou eðnai di foro apì to mhdèn (percentage of non zero coefficients). Oi kampôlec thc poiìthtac eikìnac (dhlad to PSNR, to WPSNR kai h TPE Watson metrik ) se sqèsh me to posostì twn suntelest n suqnìthtac pou eðnai di fora apì to mhdèn gia merikèc apì tic dokimastikèc eikìnec, dðnontai sta sq mata 3.12 kai Ta apotelèsmata apodeiknôoun ìti o DMT mporeð na epitôqei perðpou thn Ðdia kalôterh poiìthta eikìnac sta Ð- dia epðpeda sumpðeshc. Genik, ston parap nw algìrijmo sumpðeshc, o DMT epitugq nei kalôterh poiìthta eikìnac apì ton DCT gia uyhl e- pðpeda sumpðeshc (mikrì posostì suntelest n suqnìthtac di foro apì to mhdèn). ParadeÐgmatoc q rin, ìtan mìno to 3% twn suntelest n eðnai di foro tou mhdenìc, o DMT epitugq nei mia beltðwsh tou WPSNR se sqèsh me ton DCT thc t xhc tou 1:6db gia mia eikìna eswterikoô q rou kai thc t xhc tou 1:8db gia mia eikìna pou apeikonðzei èna anjr pino prìswpo (sq ma 3.1a). Oi antðstoiqec belti seic sthn TPE metrik tou Watson eðnai 0:016 kai 0:019db antðstoiqa. Se qamhl epðpeda sumpðeshc, oi dôo algìrijmoi epitugq noun sqedìn thn Ðdia apìdosh. Merikèc apì tic dokimastikèc eikìnec parousi zontai sto sq ma Parìmoia a- potelèsmata epiteôqjhkan se ìlec tic eikìnec pou qrhsimopoi jhkan sta peir mat mac kai den eðnai dunatìn na parajèsoume se autì to Kef laio. H deôterh om da peiram twn asqol jhke me thn axiolìghsh thc sumpðeshc kai thc poiìthtac eikìnac tou DMT kai tou DCT ìtan efarmìzontai se èna prìtupo sumpðeshc pou basðzetai ston JPEG. Se aut n thn perðptwsh, h akìloujh diadikasða efarmìzetai kai stouc dôo metasqhmatismoôc. Kai oi dôo metasqhmatismoð efarmìzontai se mia eikìna, qrhsimopoi ntac èna 8 8 par juro. Katìpin, o tupopoihmènoc pðnakac

126 104Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou (a) (b) (g) (d) (e) (st) (z) (h) (j) Sq ma 3.14: Efarmog tou DMT kai DCT se sumpðesh eikìnac me a- p leia plhroforðac. Oi par metroi Q kai epilèqthkan ètsi ste oi duo algìrijmoi na epitôqoun sqedìn to Ðdio epðpedo sumpðeshc gia k je eikìna. (a), (b), (g): Oi arqikèc eikìnec. Oi sumpiesmènec eikìnec qrhsimopoi ntac ton DMT: (d) = 250, posostì suntelest n suqnìthtac di foro tou mhdenìc =6%kai PSNR =42:80, (e) =250, posostì suntelest n suqnìthtac di foro tou mhdenìc = 10% kai PSNR = 36:59, (st): = 25, posostì suntelest n suqnìthtac di foro tou mhdenìc = 14:5% kai PSNR = 40:27. Oi sumpiesmènec eikìnec qrhsimopoi ntac ton DCT: (z) Q = 2, posostì suntelest n suqnìthtac di foro tou mhdenìc = 6% kai PSNR = 42:77, (h) Q = 2, posostì suntelest n suqnìthtac di foro tou mhdenìc = 10% kai PSNR = 36:45, (j) Q = 2, posostì suntelest n suqnìthtac di foro tou mhdenìc = 14:5% kai PSNR =40:11.

127 3.6. Efarmog se SumpÐesh Eikìnac 105 kb nthshc pou up rqei sto par rthma tou JPEG [15] (PÐnakac 3.4), pollaplasi sthke me mia par metro klim kwshc Q ste na epiteuqjeð pollapl sumpðesh. Gia ton DMT den qrhsimopoi jhke pðnakac kb nthshc, afoô ìpwc anafèrjhke dh, h par metroc klim kwshc ston paronomast thc exðswshc (3.33) energeð ousiastik wc pðnakac kb nthshc. Oi suntelestèc tou metasqhmatismoô tou DMT kai tou DCT stroggulopoi jhkan stouc pio kontinoôc akèraiouc arijmoôc. Oi mh mhdenikoð suntelestèc a- niqneôjhkan me ton algìrijmo taxinìmhshc zigk-zagk kai upobl jhkan se kwdikopoðhsh entropðac (entropy coding). 'Ena sônolo eikìnwn, diaforetikì apì autì pou qrhsimopoi jhke sto prohgoômeno peðrama, qrhsimopoi jhke se aut n thn perðptwsh. All - zontac timèc stic paramètrouc kai Q epiteôqjhkan di fora epðpeda sumpðeshc gia ton DMT kai ton DCT antðstoiqa. Se aut thn om da peiram twn, h sumpðesh metr jhke se sqèsh me to epðpedo sumpðeshc, dhlad wc o arijmìc twn temaqðwn sthn arqik eikìna pou diaireðtai me ton a- rijmì twn temaqðwn sth sumpiesmènh eikìna, met apì thn kb nthsh kai thn kwdikopoðhsh entropðac. Sta sq mata 3.15 kai 3.16 apeikonðzontai oi kampôlec thc poiìthtac thc eikìnac (PSNR, WPSNR kai TPE Watson metrik ) se sqèsh me to epðpedo sumpðeshc (compression ratio) gia èna uposônolo twn eikìnwn dokim c pou qrhsimopoioôntai se aut ta peir - mata. K poioc mporeð na parathr sei, ìti o DMT epitugq nei sqedìn se ìlec tic peript seic, kalôterh poiìthta eikìnac apì ton DCT.ParadeÐgmatoc q rin, oi belti seic tou WPSNR gia ton DMT se sqèsh me ton DCT eðnai thc t xhc tou 1:1db gia epðpeda sumpðeshc 1 : 20 sto sq ma 3.15b kai thc t xhc tou 0:6db gia epðpeda sumpðeshc 1 : 15 sthn eikìna 3.15d. Oi antðstoiqec belti seic gia th metrik TPE Watson eðnai 0:009 kai 0:008db antðstoiqa. Parìmoia apotelèsmata epiteôqjhkan se ìlec tic eikìnec pou qrhsimopoi jhkan sta peir mat mac. Sto teleutaðo sônolo peiram twn, antð na qrhsimopoihjoôn tupopoihmènoi pin kec kb nthshc pou basðzontai se peir mata pou èginan gia ta

128 106Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou 1:35 1:30 DMT/PSNR DCT/PSNR DMT/WPSNR DCT/WPSNR 1:45 1:40 1:35 DMT/PSNR DCT/PSNR DMT/WPSNR DCT/WPSNR Compression Ratio 1:25 1:20 1:15 1:10 Compression Ratio 1:30 1:25 1:20 1:15 1:10 1:5 1: PSNR / WPSNR PSNR / WPSNR (a) (b) 1:35 1:30 DMT/PSNR DCT/PSNR DMT/WPSNR DCT/WPSNR 1:45 1:40 1:35 DMT/PSNR DCT/PSNR DMT/WPSNR DCT/WPSNR Compression Ratio 1:25 1:20 1:15 1:10 Compression Ratio 1:30 1:25 1:20 1:15 1:10 1:5 1: PSNR / WPSNR PSNR / WPSNR (g) (d) 1:30 1:25 DMT/PSNR DCT/PSNR DMT/WPSNR DCT/WPSNR 1:45 1:40 1:35 DMT/PSNR DCT/PSNR DMT/WPSNR DCT/WPSNR Compression Ratio 1:20 1:15 1:10 Compression Ratio 1:30 1:25 1:20 1:15 1:10 1:5 1: PSNR / WPSNR PSNR / WPSNR (e) (st) Sq ma 3.15: KampÔlec Epipèdou sumpðeshc-paramìrfwshc (Compression Ratio) gia touc dôo metasqhmatismoôc DMT kai DCT, gia di forec dokimastikèc eikìnec: (a) mia eikìna pouapeikonðzei mia lðmnh, (b) mia eikìna pou apeikonðzei èna spðti, (g) mia eikìna meèna z o, (d) mia eikìna meèna paidð, (e) mia eikìna meènalouloôdi kai (st) èna portraðto. Hparamìr- fwsh thc eikìnac axiolog jhke me tic metrikèc PSNR kai WPSNR.

129 3.6. Efarmog se SumpÐesh Eikìnac 107 1:35 1:30 DMT DCT 1:40 1:35 DMT DCT 1:30 Compression Ratio 1:25 1:20 1:15 Compression Ratio 1:25 1:20 1:15 1:10 1:10 1: Total Perceptual Error 1: Total Perceptual Error (a) (b) 1:35 1:30 DMT DCT 1:45 1:40 DMT DCT 1:25 1:35 Compression Ratio 1:20 1:15 Compression Ratio 1:30 1:25 1:10 1:20 1:5 1: Total Perceptual Error (g) 1: Total Perceptual Error (d) 1:30 1:25 DMT DCT 1:40 1:35 DMT DCT 1:30 Compression Ratio 1:20 1:15 1:10 Compression Ratio 1:25 1:20 1:15 1:5 1: Total Perceptual Error 1: Total Perceptual Error (e) (st) Sq ma 3.16: KampÔlec Epipèdou sumpðeshc-paramìrfwshc (Compression Ratio) giatouc dôo metasqhmatismoôc DMT kai DCT, gia di forec dokimastikèc eikìnec: (a) mia eikìna pouapeikonðzei mia lðmnh, (b) mia eikìna pou apeikonðzei èna spðti, (g) mia eikìna me èna z o, (d) mia eikìna me èna paidð, (e) mia eikìna meènalouloôdi kai (st) èna portraðto. H paramìrfwsh thc eikìnac axiolog jhke me th metrik Total Perceptual Error (TPE) Watson.

130 108Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou 1:35 1:30 DMT/PSNR DCT/PSNR DMT/WPSNR DCT/WPSNR 1:25 1:20 DMT/PSNR DCT/PSNR DMT/WPSNR DCT/WPSNR 1:25 Compression Ratio 1:20 1:15 Compression Ratio 1:15 1:10 1:10 1:5 1: PSNR / WPSNR PSNR / WPSNR (a) (b) 1:35 1:30 DMT/PSNR DCT/PSNR DMT/WPSNR DCT/WPSNR 1:45 1:40 1:35 DMT/PSNR DCT/PSNR DMT/WPSNR DCT/WPSNR Compression Ratio 1:25 1:20 1:15 1:10 Compression Ratio 1:30 1:25 1:20 1:15 1:10 1:5 1: PSNR / WPSNR PSNR / WPSNR (g) (d) 1:40 1:35 DMT/PSNR DCT/PSNR DMT/WPSNR DCT/WPSNR 1:35 1:30 DMT/PSNR DCT/PSNR DMT/WPSNR DCT/WPSNR 1:30 Compression Ratio 1:25 1:20 1:15 Compression Ratio 1:25 1:20 1:15 1:10 1:10 1:5 1: PSNR / WPSNR PSNR / WPSNR (e) (st) Sq ma 3.17: KampÔlec epipèdou sumpðeshc-paramìrfwshc (Compression ratio-distortion) gia ton DMT kai ton DCT, gia di forec eikìnec pou apeikonðzoun: (a) ènan k po, (b) èna kal ji, (g) j lassa, (d) mia gunaðka, (e) èna anjr pino prìswpo kai (st) èna d soc. H paramìrfwsh axiolog jhke me tic metrikèc PSNR kai WPSNR.

131 3.6. Efarmog se SumpÐesh Eikìnac 109 1:35 1:30 DMT DCT 1:25 DMT DCT 1:20 1:25 Compression Ratio 1:20 1:15 Compression Ratio 1:15 1:10 1:10 1:5 1: Total Perceptual Error Total Perceptual Error (a) (b) 1:35 1:30 DMT DCT 1:45 1:40 DMT DCT 1:25 1:35 Compression Ratio 1:20 1:15 Compression Ratio 1:30 1:25 1:20 1:10 1:15 1:5 1: Total Perceptual Error 1: Total Perceptual Error (g) (d) 1:40 1:35 DMT DCT 1:30 1:25 DMT DCT 1:30 Compression Ratio 1:25 1:20 1:15 Compression Ratio 1:20 1:15 1:10 1:10 1:5 1: Total Perceptual Error Total Perceptual Error (e) (st) Sq ma 3.18: KampÔlec epipèdou sumpðeshc-paramìrfwshc (Compression ratio-distortion) gia ton DMT kai ton DCT, gia di forec eikìnec pou apeikonðzoun: (a) ènan k po, (b) èna kal ji, (g) j lassa, (d) mia gunaðka, (e) èna anjr pino prìswpo kai (st) èna d soc. H paramìrfwsh axiolog jhke me th metrik Total Perceptual Error (TPE) tou Watson.

132 110Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou prìtupa sumpðeshc tou DCT, ekmetalleut kame mia teqnik pou basðzetai ston èlegqo tou posostoô twn temaqðwn (bit). Pio sugkekrimèna, efarmìsthke mia bèltisth diadikasða katanom c temaqðwn, pou exet sthke sto [39] kai basðzetai stic statistikèc idiìthtec miac eikìnac. H eikìna qwrðsthke se 8 8 par jura kai oi dôo metasqhmatismoð efarmìsthkan se k je par juro. H èxodoc tou DCT klimak jhke apì touc suntelestèc kb nthshc pou pro ljan apì tic statistikèc idiìthtec thc eikìnac qrhsimopoi ntac th diadikasða katanom c temaqðwn tou [39] kai to epilegmèno posostì temaqðwn. Kanènac suntelest c kb nthshc den efarmìsthke ston DMT lìgw tou èmfutou elègqou sumpðeshc pou parèqei o paronomast c thc exðswshc (3.33). 'Epeita, oi suntelestèc tou DMT kai tou DCT stroggulopoi jhkan ston plhsièstero akèraio arijmì kai ektelèsjhke h kwdikopoðhsh entropðac [39]. Kat th di rkeia thc kwdikopoðhshc entropðac, oi suntelestèc tou DCT taxinom jhkan me th qrhsimopoðhsh tou algorðjmou taxinìmhshc zigk-zagk, en oi suntelestèc tou DMT taxinom jhkan se aôxousa seir basismènoi stouc suntelestèc tou paronomast (3.33): Z(k; l) =1+» sin 2 ßk 2N h + sin 2 ßl 2N w ; (3.47) ìpou N h, N w eðnai oi diast seic tou 2D metasqhmatismoô. Oi suntelestèc tou DMT diairoôntai me autìn ton ìro, epomènwc, h parap nw taxinìmhsh upodhl nei ìti oi suntelestèc pou diairoôntai me mikrèc timèc tou Z diathroôn megalôterh plhroforða kai prèpei na krathjoôn en oi suntelestèc pou diairoôntai me meg lec timèc tou Z mporoôn na aporrifjoôn. Sta sq mata 3.17 kai 3.18, apeikonðzontai oi kampôlec epipèdou sumpðeshc-paramìrfwshc (compression ratio-distortion) gia èna uposônolo twn eikìnwn dokim c pou qrhsimopoioôntai sta peir mat mac. Sthn perðptwsh tou DMT, h pollapl sumpðesh epiteôqjhke all zontac to. OmoÐwc me to prohgoômeno peðrama, to epðpedo sumpðeshc metr jhke wc o arijmìc twn temaqðwn sthn arqik eikìna pou diairèjhke me ton a-

133 3.7. Sumper smata 111 rijmì twn temaqðwn sth sumpiesmènh eikìna, met apì thn kb nthsh kai thn kwdikopoðhsh entropðac. En h paramìrfwsh axiolog jhke qrhsimopoi ntac tic metrikèc PSNR, WPSNR (sq ma 3.17), kaj c epðshc kai to TPE tou Watson (sq ma 3.18). K poioc mporeð na parathr sei, ì- ti o DMT epitugq nei stic perissìterec peript seic, kalôterh poiìthta eikìnac apì ton DCT gia ta uyhl epðpeda sumpðeshc. ParadeÐgmatoc q rin, oi belti seic sto WPSNR ènanti tou DCT eðnai 0:6db gia mia a- nalogða sumpðeshc 1 : 15 (sq ma 3.17a), 1:1db gia analogða sumpðeshc 1:35gia thn eikìna pros pou (sq ma 3.1a) kai 0:5db gia analogða sumpðeshc 1:35(sq ma 3.17d). Oi antðstoiqec belti seic sth metrik TPE tou Watson eðnai 0:004, 0:007 kai 0:006db antðstoiqa. Stic qamhlìterec analogðec sumpðeshc, oi dôo metasqhmatismoð èqoun sqedìn thn Ðdia apìdosh. Parìmoia apotelèsmata epiteôqjhkan se ìlec tic eikìnec pou qrhsimopoi jhkan sta peir mat mac. 3.7 Sumper smata Oi tôpoi tou eujô kai antðstrofou 1D kai 2D diakritoô, mh diaqwrðsimou metasqhmatismoô s matoc idioqarakthristik n, eis qjhsan se autì to Kef laio. Oi proteinìmenoi 1D kai 2D metasqhmatismoð eðnai èna endi - meso st dio thc diadikasðac paramìrfwshc enìc 2D kai 3D paramorf simou montèlou antðstoiqa, pou upìkeitai stouc nìmouc kai tic idiìthtec thc fusik c. O proteinìmenoc metasqhmatismìc èqei parìmoia dom me ton DCT afoô ton perilamb nei kai san eidik perðptwsh kai èqei sunep c parìmoiec idiìthtec me ton DCT. To gegonìc ìti o DCT mporeð na paraqjeð qrhsimopoi ntac wc afethrða èna paramorf simo montèlo pou prospajeð na proseggðsei thn epif neia fwteinìthtac miac eikìnac, eðnai mia shmantik èkbash aut c thc melèthc. Ousiastik, oi suntelestèc ( isodônama, oi eikìnec b shc) tou proteinìmenou metasqhmatismoô eðnai klimakwmènec ekdìseic twn suntelest n tou DCT ( twn eikìnwn b shc

134 112Kef laio3. Metasqhmatismìc Idioqarakthristik n DiakritoÔ Qrìnou tou) kai ètsi o metasqhmatismìc mporeð na antimetwpisjeð epðshc wc è- nac nèoc, kainotìmoc pðnakac kb nthshc gia ton DCT. Kat sunèpeia, o proteinìmenoc metasqhmatismìc perilamb nei ènan èmfuto kai shmantikì mhqanismì epilog c epipèdwn sumpðeshc pou epitrèpei to kajorismì tou epipèdou sumpðeshc qwrðc opoiad pote idiaðterh diadikasða kb nthshc. E- farmìsame ton proteinìmeno metasqhmatismì se èna montèlo sumpðeshc me ap leiec plhroforðac kai ton sugkrðname me ton DCT, dedomènou ìti o teleutaðoc qrhsimopoieðtai eurèwc sth sumpðesh eikìnac. Ta apotelèsmata deðqnoun ìti o proteinìmenoc metasqhmatismìc mporeð na epitôqei polô kal energeiak sugkèntrwsh kai aposusqètish tou s matoc, sugkrðsimh poiìthta eikìnac me ton DCT se qamhl epðpeda sumpðeshc kai stic perissìterec peript seic, kalôterh poiìthta eikìnac gia uyhl epðpeda sumpðeshc. Ta mellontik sqèdia ìson afor ton proteinìmeno metasqhmatismì, perilamb noun thn ektèlesh upokeimenik n sugkrðsewn metaxô tou DCT kai tou DMT. Dhlad, th qrhsimopoðhsh miac epitrop c jeat n pou ja sugkrðnoun ta apotelèsmata. Stìqoc eðnai epðshc kai h prosp jeia na parasqejeð ènac pðnakac kb nthshc pou perilamb netai ston DMT kai apodðdei kalôtera apotelèsmata apì autìn pou qrhsimopoieðtai sta prìtupa tou JPEG.Mia tètoia èreuna ja stoqeôsei sthn ex ghsh thc dom c kai twn idiot twn tou anjr pinou optikoô sust matoc.

135 BibliografÐa [1] S. S. Agaian, K. Panetta, and A. M. Grigoryan. Transform-based image enhancement algorithms with performance measure. IEEE Transactions on Image Processing, 10(3): , Mar [2] M. S. Brown and W. B. Seales. Image restoration of arbitrarily warped documents. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(10): , Oct [3] C. Wufan, Z. Jie, S. Yuhua, C. Jianjun, and L. Xianqing. Description of medical images in characteristic subspace and vector quantization coding based on wavelet transformation. In IEEE International Conference on Image Processing, volume 1, pages , Seattle, United States, Sept [4] B. Chiptrasert and K. R. Rao. Discrete Cosine Transform filtering. Signal Processing, 19(3): , Mar [5] D. L. Donoho, M. Vetterli, R. A. DeVore, and I. Daubechies. Data compression and harmonic analysis. IEEE Transactions on Information Theory, 44(6): , Oct [6] H. Feng and M. Effros. On the rate-distortion performance and computational efficiency of the Karhunen Loeve transform for 113

136 114 BibliografÐa lossy data compression. IEEE Transactions on Image Processing, 11(2): , Feb [7] D. Nandy and J. Ben-Arie. Generalized feature extraction u- sing expansion matching. IEEE Transactions on Image Processing, 8(1):22 32, Jan [8] J. T. Chien and C. C. Wu. Discriminant waveletfaces and nearest feature classifiers for face recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(12): , Dec [9] N. Ahmed, T. Natarajan, and K. Rao. Discrete cosine transform. IEEE Computers, C-23:90 93, Jan [10] M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechiess. Image coding using wavelet transform. IEEE Transactions on Image Processing, 1(2): , Apr [11] V. K. Goyal. Theoretical foundations of transform coding. IEEE Signal Processing Magazine, 18(5):9 21, Sep [12] M. Effros, H. Feng, and K. Zeger. Suboptimality ofthekarhunen Loeve Transform for transform coding. IEEE Transactions on Information Theory, 50(8): , Aug [13] G. K. Wallace. The jpeg still picture compression standard. Communications of the ACM, 34(4):30 44, Apr [14] J. K. Li, J. Li, and C. C. J. Kuo. Layered DCT still image compression. CirSysVideo, 7(2): , Apr [15] W. B. Pennebaker and J. L. Mitchell. JPEG: Still Image Data Compression Standard. Van Nostrand Reinhold, New York, 1993.

137 BibliografÐa 115 [16] Y. Yusong, S. Guangda, W. Chunmei, and S. Qingyun. Invertible integer fft applied on lossless image compression. In IEEE International Conference on Robotics, Intelligent Systems and Signal Processing, volume 2, pages , 8-13 Oct [17] I. Valova and Y. Kosugi. Hadamard-based image decomposition and compression. IEEE Transactions on Information Technology in Biomedicine, 4: , Dec [18] Z.-X. Hou, N.-N. Xu, H. Chen, and X.-L. Li. Fast slant transform with sequency increment and its application in image compression. In Proceedings of 2004 International Conference on Machine Learning and Cybernetics, volume 7, pages , Aug [19] Didier Le Gall. Mpeg: A video compression standard for multimedia applications. Communications of the ACM, 34(4):46 58, Apr [20] Video Codec for Audiovisual Services at p 64 kbit=s ITU-T Recommendation H.261. Version 1: ITU-T, ITU-T Recommendation H.261, [21] ITU Telecom. Standardization Sector of ITU. Video coding for low bitrate communication. ITU-T Recommendation H.263, Mar [22] C. Nastar and N. Ayache. Frequency-based nonrigid motion analysis: Application to four dimensional medical images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(11): , [23] C. Nikou, G. Bueno, F. Heitz, and J.P. Armspach. A joint physicsbased statistical deformable model for multimodal brain image a- nalysis. IEEE Transactions on Medical Imaging, 20(10): , 2001.

138 116 BibliografÐa [24] S. Krinidis, C. Nikou, and I. Pitas. Reconstruction of serially a- cquired slices using physics-based modelling. IEEE Transactions on Information Technology in Biomedicine, 7(4): , December [25] A. Pentland and S. Sclaroff. Closed-form solutions for physicallybased shape modeling and recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(7): , Jul [26] B. Moghaddam, C. Nastar, and A. Pentland. A bayesian similarity measure for direct image matching. In International Conference on Pattern Recognition (ICPR 1996), pages , Vienna, Austria, August [27] G. Borgefors. On digital distance transforms in three dimensions. Computer Vision and Image Understanding, 64(3): , [28] P.-E. Danielsson. Euclidean distance transform. Computer Graphics and Image Processing, 14:227 28, [29] K. J. Bathe. Finite Element Procedure. Prentice Hall, Englewood Cliffs, New Jersey, [30] A. Pentland and B. Horowitz. Recovery of non-rigid motion and structure. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(7): , July [31] M. R. Spiegel. Mathematical Formulas. McGraw-Hill, New York, [32] A. K. Jain. Fundamentals of Digital Image Processing. Prentice Hall, Englewood Cliffs, New Jersey, 1989.

139 BibliografÐa 117 [33] R. Gonzalez and R. Woods. Digital Image Processing. Addison- Wesley Publishing Company, [34] W. Frei and C.C. Chen. Fast boundary detection: A generalization and a new algorithm. IEEE Transactions on Computers, C- 26(10): , [35] W. K. Cham and R. J. Clarke. Application of the principle of dyadic symmetry to the generation of orthogonal transforms. IEE Proceedings, Pt. F, 133(3): , June [36] R. J. Clarke. Digital Compression of Still Images and Video. Academic Press, London, [37] A. Netravali and B. Haskell. Digital Pictures Representation and Compression. Plenum Press, New York, [38] A. Mayache, T. Eude, and H. Cherifi. A comparison of image quality models and metrics based on human visual sensitivity. InProceedings of the International Conference on Image Processing (ICIP 1998), volume 3, pages , Chicago, IL, USA, October [39] V. Bhaskaran and K. Konstantinides. Image and Video Compression Standards. Kluwer Academic Publishers, London, 1995.

140 118 BibliografÐa

141 Kef laio 4 EktÐmhsh Trisdi statou ProsanatolismoÔ Anjr pinou KefalioÔ se Eikonoseirèc me Qr sh Paramorf simwn Montèlwn kai Aktinik n Sunart sewn B sewn 4.1 Eisagwg Htrisdi stath ektðmhsh prosanatolismoô anjr pinwn pros pwn se eikonoseirèc eðnai èna antikeðmeno pou sunantiètai suqn se pollèc efarmogèc thc teqnht c ìrashc. Sthn parakoloôjhsh antikeimènwn se eikonoseirèc [1], h kateôjunsh tou kefalioô se sunduasmì me thn progenèsterh gn - 119

142 120 Kef laio 4. EktÐmhsh Trisdi statou ProsanatolismoÔ Pros pou sh gia ton kìsmo, epitrèpei thn an lush thc kðnhshc twn pros pwn kai tic projèseic touc. H kateôjunsh tou kefalioô eðnai epðshc endeiktik gia thn anagn rish thc estðash thc prosoq twn anjr pwn, èna gegonìc pou eðnai polô shmantikì stic efarmogèc allhlepðdrashc anjr pouupologist [2]. H trisdi stath kateôjunsh tou kefalioô mporeð epiplèon na qrhsimopoihjeð sth exereônhsh twn trisdi statwn paiqnidi n [3], stic optikèc epikoinwnðec [4], sthn trisdi stath anadhmiourgða tou pros pou [5] kai se pollèc llec efarmogèc. H trisdi stath kateôjunsh tou kefalioô qrhsimopoieðtai epðshc kai san b ma proepexergasðac, sthn anðqneush pros pou [6], sthn anagn rish pros pou [7] kai sthn an lush twn anjr pinwn ekfr sewn [8], dedomènou ìti autèc oi diadikasðec eðnai polô euaðsjhtec akìmh kai se mikrèc peristrofèc tou kefalioô. Kat sunèpeia, h akrib c gn sh thc kateôjunshc tou pros pou eðnai èna ousiastikì prìblhma pou mporeð na sumb lei sthn aôxhsh thc apìdoshc tètoiwn efarmog n. 'Enac arijmìc algorðjmwn ektðmhshc prosanatolismoô tou kefalioô leitourgeð se stereoskopikèc akoloujðec [9, 10]. Wstìso, oi stereoskopikèc plhroforðec mporeð na mhn eðnai diajèsimec stic proanaferjeðsec efarmogèc. Kat sunèpeia, h èreuna gia thn ektðmhsh tou prosanatolismoô anjr pinou kefalioô kat th di rkeia twn teleutaðwn et n èqei epikentrwjeð se mh stereoskopikèc akoloujðec. H basik prìklhsh sthn ektðmhsh prosanatolismoô tou anjr pinou kefalioô se disdi statec eikonoseirèc eðnai h an ptuxh gr gorwn algorðjmwn pou den apaitoôn ekten proepexergasða thc eikonoseir c. Eikìnec qamhl c-an lushc, eikìnec me jìrubo, epikalôyeic tmhm twn thc skhn c, aprosdiìristec kin seic, allagèc sto fwtismì kai to sônjeto upìbajro miac skhn c eðnai merik apì ta probl mata sthn diadikasða ektðmhshc prosanatolismoô tou anjr pinou kefalioô. An loga me ton trìpo pou to prìswpo antimetwpðzetai, oi up rqousec mèjodoi mporoôn na diairejoôn se treic kathgorðec:

143 4.1. Eisagwg 121 ffl mèjodoi basizìmenec se qarakthristik shmeða tou pros pou, ffl mèjodoi basizìmenec se montèla, ffl kai mèjodoi basizìmenec ston trìpo anapar stashc tou pros pou. Mia sôgkrish twn uparqìntwn algorðjmwn ektðmhshc kateôjunshc pros pwn dðnetai sta [11, 12, 13]. H ekmet lleush thc qwrik c jèshc qarakthristik n gnwrism twn tou pros pou gia thn ektðmhsh thc kateôjunshc tou pros pou èqei ereunhjeð apì polloôc epist monec [14, 15, 16, 17]. Se autèc tic proseggðseic, h trisdi stath dom tou pros pou axiopoieðtai mazð me tic dedomènec anjrwpometrikèc plhroforðec prokeimènou na kajoristeð h kateôjunsh tou pros pou. H elleiptik morf tou pros pou kai h analogða twn prwteuìntwn kai deutereuìntwn axìnwn aut c thc èlleiyhc, h gewmetrðac thc perioq c gôrw apì to stìma kai th môth, h gramm pou sundèei ta kèntra twn mati n, h gramm pou sundèei tic stomatikèc gwnðec kai h summetrða tou anjr pinou pros pou eðnai merik apì ta gewmetrik qarakthristik gnwrðsmata pou qrhsimopoioôntai gia na ektimhjeð h trisdi stath kateôjunsh tou anjr pinou kefalioô. Sthn ergasða [17], pènte qarakthristik gnwrðsmata tou anjr pinou pros pou, dhlad, ta kèntra twn mati n, oi krec tou stìmatoc kai h môth entopðzontai mèsa sthn aniqneumènh perioq tou pros pou. Mia strathgik st jmishc efarmìzetai met apì thn anðqneush twn qarakthristik n gnwrism twn tou pros pou, ste na upologisteð akribèstera h telik jèsh twn pènte gnwrism twn. H kateôjunsh tou pros pou upologðzetai me thn ekmet lleush miac metrik c pou basðzetai sth sôgkrish thc jèshc twn epðkthtwn qarakthristik n gnwrism twn tou pros pou me tic antðstoiqec jèseic se èna prìswpou me mhdenik peristrof kai stouc treic xonec. Sthn ergasða [14], h jèsh twn qarakthristik n gnwrism twn tou pros pou sundu zetai me tic plhroforðec qr matoc prokeimènou na upologisteð h 3D kateôjunsh tou

144 122 Kef laio 4. EktÐmhsh Trisdi statou ProsanatolismoÔ Pros pou pros pou. To dèrma kai h perioq twn malli n tou pros pou ex gontai basismènoi se èna aisjhtik omoiìmorfo sôsthma qr matoc. H anðqneush qarakthristik n gnwrism twn sto prìswpo ekteleðtai sthn perioq pou dhl jhke san prìswpo apì ton antðstoiqo aniqneut kai oriojetoôntai oi perioqèc twn mati n, twn frudi n, tou stìmatoc kai thc môthc. Katìpin, stic parap nw perioqèc efarmìzetai anðqneush gwni n. H pio arister kai dexi gwnða epilègontai wc qarakthristik shmeða tou pros pou. H 3D kateôjunsh tou kefalioô prokôptei apì to sunduasmì twn qarakthristik n gnwrðsmata, thn perioq dèrmatoc tou pros pou kai twn malli n. Aut h kathgorða algorðjmwn èqei èna shmantikì meionèkthma: h apìdos touc exart tai apì thn epituq anðqneush twn qarakthristik n gnwrism twn tou pros pou pou paramènei èna dôskolo prìblhma, eidik sta mh-metwpik prìswpa. Sta teleutaða èth pollèc prosp jeiec èqoun diexaqjeð se algorðjmouc ektðmhshc trisdi stathc kateôjunshc kefalioô [18, 19, 20]. Hbasik idè- a se aut n thn kathgorða mejìdwn eðnai na qrhsimopoihjeð èna dedomèno 3D prìtupo pros pou pou qartografeðtai ep nw stic 2D eikìnec eisìdou. Mìlic brejoôn oi antistoiqðec 2D-3D metaxô twn dedomènwn eisìdou kai tou protôpou pros pou, sumbatikèc teqnikèc ektðmhshc prosanatolismoô kefalioô axiopoioôntai ste na apokthjeð h 3D kateôjunsh tou pros pou. To kôrio prìblhma se autoôc touc algorðjmouc eðnai na brejoôn me ènan eôrwsto trìpo ta qarakthristik tou pros pou pou mporoôn na qrhsimopoihjoôn gia na kajorðsoun thn kalôterh qartogr fhsh tou 3D protôpou stic 2D eikìnec eisìdou. Sthn ergasða [20], to 3D prìtupo eðnai èna trigwnikì plègma uf c. H omoiìthta metaxô tou (proballìmenou) protôpou kai thc tou pros pou eikìnac eisagwg c axiologeðtai mèsw miac kat llhlhc metrik c. O prosanatolismìc tou protôpou pou dðnei thn kalôterh antistoiqða eðnai kai h kat' ektðmhsh kateôjunsh tou kefalioô. Sthn ergasða [19], èna sugkekrimèno kubikì polu numo qrhsimopoieðtai gia na morfopoi sei èna 3D genikì prìswpo se mia sugkekrimènh dom

145 4.1. Eisagwg 123 pros pou qrhsimopoi ntac san eðsodo pollapl siec apìyeic pros pwn. H ektðmhsh tou prosanatolismoô epitugq netai mèsw thc epanalhptik c elaqistopoðhshc miac metrik c basismènh sto q rth apìstashc (pou kataskeu zetai me th qrhsimopoðhsh miac dianusmatik c EukleÐdeiac sun rthshc apìstashc). Oi teqnikèc pou basðzontai sthn trìpo anapar stashc tou pros pou [21, 22, 23], epitugq noun ikanopoihtik apotelèsmata akìmh kai me eikìnec eisìdou qamhl c an lushc. Se autèc tic proseggðseic, antð thc qrhsimopoðhshc qarakthristik n shmeðwn tou pros pou montèlwn pros pou, qrhsimopoieðtai olìklhrh h eikìna gia thn ektðmhsh tou prosanatolismoô tou kefalioô. Sthn teqnik pou parousi zetai sto [23], qrhsimopoieðtai èna neurwnikì dðktuo me eðsodo eikìnec pros pou pou katagr fontai apì mia panoramik fwtografik mhqan me skopì thn ektðmhsh thc kateôjunshc tou pros pou. 'Ena poluepðpedo dðktuo ekpaideôetai gia k je mia gwnða (peristrof kai klðsh) me proepexergasmènec eikìnec pros pwn pou proèrqontai apì ènan algìrijmo anðqneushc pros pou. H proepexergasða apoteleðtai eðte apì kanonikopoðhsh istogr mmatoc eðte apì anðqneush akm n. Stic ergasðec [12, 21], ènac algìrijmoc sundèei thn parakoloôjhsh tou kefalioô me ton prosanatolismì tou se èna miktì fðltro swmatidðwn (particle filter). H mèjodoc sthrðzetai se mia Bayesian morfopoðhsh tou probl matoc pou stìqoc eðnai na upologðsei to prosanatolismì tou kefalioô mèsw thc ekm jhshc diakrit n prosanatolism n apì di fora sônola ekpaðdeushc. Qarakthristik shmeða uf c kai qr matoc twn perioq n pros pou qrhsimopoi jhkan wc eisagwg sto fðltro swmatidðwn. DÔo diaforetikèc parallagèc exet sthkan sthn ergasða [12]. H pr th parakoloujeð to kef li se mia eikonoseir kai èpeita u- pologðzei to prosanatolismì tou en h deôterh parakoloujeð to kef li kai ektim ton prosanatolismì tou apì koinoô. Palindrom seic edraðwn dianusm twn (AED) (Support Vector Regression) [24], dhlad, mhqanèc edraðwn dianusm twn (MED) (Support Vector Machines) ìpou h èxodoc

146 124 Kef laio 4. EktÐmhsh Trisdi statou ProsanatolismoÔ Pros pou touc perièqei suneqeðc pragmatikèc timèc èqoun epðshc qrhsimopoihjeð stic mejìdouc ektðmhshc prosanatolismoô kefalioô pou basðzontai ston trìpo anapar stashc tou pros pou. Stouc algorðjmouc pou prot jhkan sta [25, 26], dôo m skec Sobel (orizìntiec kai k jetec) qrhsimopoi jhkan gia na proepexergastoôn tic eikìnec ekpaðdeushc kai oi dôo filtrarismènec eikìnec sundu sthkan apì koinoô. H An lush prwteuìntwn sunistws n (APS) ( Principal Component Analysis) efarmìzetai sth filtrarismènh eikìna prokeimènou na meiwjeð h di stash twn eikìnwn ekpaðdeushc (eikìnec pros pwn me gnwstì prosanatolismì). H mèjodoc MED qrhsimopoi jhke prokeimènou na kataskeuastoôn dôo ektimhtèc gia ton prosanatolismì tou kefalioô, ènac gia thn klðsh kai ènac gia thn peristrof tou kefalioô. H eðsodoc stic MED tan ta dianôsmata pou proèkuyan apì thn APS kai h èxodoc touc tan h ektðmhsh thc gwnðac tou pros pou. Dedomènou ìti o telikìc stìqoc thc sugkekrimènhc ergasðac tan h anðqneush pros pou apì diaforetikèc optikèc gwnðec, oi ektimhmènec gwnðec qrhsimopoi jhkan sth sunèqeia gia thn epilog tou kat llhlou aniqneut pros pou metaxô enìc sunìlou aniqneut n pou leitourgoôn gia diaforetikì di sthma prosanatolismoô tou kefalioô o kajènac. Sth mèjodo pou prot jhke sto [27], h AED qrhsimopoieðtai gia na upologðsei to prosanatolismì tou kefalioô apì trisdi statec eikìnec. 'Enac diakritìc metasqhmatismìc kum twn tri n epipèdwn efarmìzetai se ìlec tic 3D eikìnec ekpaðdeushc kai h upoz nh LL (pou anadeiknôei leptomèreiec gia ton prosanatolismì tou kefalioô, katastèllontac memonwmènec leptomèreiec tou pros pou, kai paramènontac sqetik amet blhth stic ekfr seic tou pros pou) qrhsimopoieðtai san eðsodoc se dôo MED pou ekpaideôontai qrhsimopoi ntac gnwst paradeðgmata ste sth sunèqeia na upologðsoun thn klðsh kai thn peristrof tou kefalioô gia kainoôrgiec eikìnec. H mèjodoc ektðmhshc prosanatolismoô tou kefalioô apì disdi statec eikonoseirèc pou proteðnetai se autì to kef laio an kei stic mejìdouc

147 4.1. Eisagwg 125 basismènec ston trìpo anapar stashc tou kefalioô. H proteinìmenh mèjodoc qrhsimopoieð èna paramorf simo montèlo pou proseggðzei thn epif neiac (fwteinìthta) thc eikìnac to opoðo prot jhke sta [28, 29] gia taðriasma eikìnwn. SÔmfwna me thn prosèggis touc, mia eikìna antiproswpeôetai san mia 3D epif neia ston apokaloômeno XYI-q ro, o opoðoc sundu zei tic qwrikèc sunist sec XY me th fwteinìthta thc eikìnac I. 'Ena paramorf simo montèlo epif neiac, tou opoðou h exðswsh paramìrfwshc lônetai mèsw thc teqnik an lushc idioqarakthristik n (Modal Analysis), qrhsimopoieðtai sth sunèqeia gia na proseggðsei aut n thn epif neia. H teqnik an lushc idioqarakthristik n eðnai mia tupopoihmènh teqnik pou efarmìzetai sth mhqanik kai èqei eisaqjeð ston tomèa thc teqnht c ìrashc kai thc an lush eikìnwn sthn ergasða [30]. H teqnik an lushc idioqarakthristik n epitrèpei apotelesmatikoôc upologismoôc kai èqei qrhsimopoihjeð se poikðlec efarmogèc gia thn epðlush paramorf sewn montèlwn, ìpwc gia thn an lush thc kðnhshc mh strer n antikeimènwn [31], gia thn eujugr mmish seiriak n tom n apì trisdi statouc ìgkouc [32], gia polutropik an lush eikìnwn egkef lou [33], gia thn kat tmhsh 2D antikeimènwn [34], gia sumpðesh eikìnac [35] kai gia 2D parakoloôjhsh antikeimènwn [36]. Sthn perðptws mac, to paramorf simo montèlo epif neiac qrhsimopoieðtai gia na proseggðsei, sto XY I q ro, tic perioqèc eikìnac pou apeikonðzoun prìswpa. To genikeumèno di nusma metatopðsewn, pou eðnai èna endi meso b ma thc diadikasðac paramìrfwshc, qrhsimopoieðtai sth sunèqeia me ènan kainotìmo trìpo dhlad, gia thn parakoloôjhsh kai thn ektðmhsh tou prosanatolismoô tou kefalioô se eikonoseirèc. Parìmoia me to Kef laio 2, h diadikasða parakoloôjhshc basðzetai sth mètrhsh kai to taðriasma apì eikìna se eikìna tou genikeumènou dianôsmatoc metatopðsewn enìc paramorf simou montèlou topojethmèno sto prìswpo. To genikeumèno di nusma metatopðsewn qrhsimopoieðtai epðshc gia na ekpaideôsei trða dðktua parembol c aktinik n sunart sewn b shc

148 126 Kef laio 4. EktÐmhsh Trisdi statou ProsanatolismoÔ Pros pou (ASB) upologðzontac tic treic gwnðec tou kefalioô (peristrof, klðsh kai kôlish), se sqèsh me to epðpedo thc k merac. H klðsh kai h peristrof antiproswpeôoun thn kðnhsh ston katakìrufo kai ton orizìntio xona tou pros pou, en h kôlish antiproswpeôei thn peristrof tou kefalioô se sqèsh me to epðpedo thc k merac (sq ma 4.1). Oproteinìmenoc algìrijmoc exet sthke sth b sh dedomènwn IDIAP [12] pou apoteleðtai apì eikonoseirèc pou apokt jhkan se fusik perib llonta kai perièqoun meg lec peristrofèc tou pros pou. H b sh dedomènwn perilamb nei epðshc to prosanatolismì tou kefalioô gia k je mia eikìna. Ta apotelèsmata deðqnoun ìti o proteinìmenoc algìrijmoc mporeð na upologðsei to 3D di - nusma prosanatolismoô tou pros pou me èna mèso l joc thc t xewc twn 4 bajm n. Περιστροφή Κλίση Κύλιση Sq ma 4.1: Peristrof, klðsh kai kôlish tou anjr pinou kefalioô. To upìloipo tou KefalaÐou organ netai wc ex c. Sthn Par grafo 4.2, parousi zetai mia sôntomh perigraf thc diadikasða paramìrfwshc ston XY I-q ro. O algìrijmoc parakoloôjhshc kai h apìkthsh tou dianôsmatoc shmeðwn pou qrhsimopoieðtai gia thn ektðmhsh tou prosanatolismoô tou kefalioô eis gontai sthn Par grafo 4.3. Sthn Par grafo 4.4, perigr fetai to dðktuo parembol c aktinik n sunart sewn b shc kai epishmaðnetai h qr sh tou gia thn ektðmhsh tou trisdi statou prosanato-

149 4.2. Paramorf simo Montèlo Epif neiac 127 lismoô tou kefalioô. H apìdosh thc proteinìmenhc teqnik c exet zetai sthn Par grafo 4.5. Ta telik sumper smata sun gontai sthn Par - grafo Paramorf simo Montèlo Anjr pinou KefalioÔ Se aut thn Par grafo, ja perigrafoôn en suntomða to paramorf simo montèlo kai h teqnik an lushc idioqarakthristik n pou qrhsimopoioôntai gia thn prosèggish eikìnwn oi opoðec apeikonðzoun prìswpa ston XY I-q ro. 'Opwc èqei dh anaferjeð sthn eisagwg 4.1, aut h prosèggish èqei protajeð stic ergasðec [28, 29] kai èqei qrhsimopoihjeð sthn proteinìmenh perðptws me k poiec tropopoi seic, pou perigr fontai sth sunèqeia. H kainotomða thc prosèggis c mac, brðsketai sth qrhsimopoðhsh tou apokaloômenou genikeumènou dianôsmatoc metatopðsewn, pou perilamb netai teqnik an lushc idioqarakthristik n, gia thn parakoloôjhsh kai thn ektðmhsh prosanatolismoô tou pros pou, ìpwc ja perigrafeð sthn Par grafo 4.3. SÔmfwna me tic teqnikèc pou parousi sthkan sta [28, 29], mia eikìna mporeð na anaparastajeð wc mia epif neia fwteinìthtac (x; y; I(x; y)), sundu zontac th fwteinìthta thc eikìnac I(x; y) tic qwrikèc thc sunist sec (x; y) (sq ma 4.2). OantÐstoiqoc q roc apokaleðtai XY I q roc kai to paramorf simo montèlo qrhsimopoieðtai gia na proseggðsei aut n thn epif neia. H teqnik thc an lushc idioqarakthristik n [30], qrhsimopoieðtai gia na lôsei tic exis seic paramìrfwsewn. To paramorf simo montèlo epif neiac apoteleðtai apì èna omoiìmorfo tetr pleuro plègma N = N h N w kìmbwn, ìpwc faðnetai sto sq ma 2.1. Se aut thn Par grafo, upojètoume ìti ta N h, N w eðnai Ðsa me to Ôyoc kai to pl toc thc eikìnac (se eikonostoiqeða) antðstoiqa, ètsi ste

150 128 Kef laio 4. EktÐmhsh Trisdi statou ProsanatolismoÔ Pros pou (a) (b) (g) (d) Sq ma 4.2: (a) Mia eikìna pros pou, (b) h fwteinìthta thc eikìnac san mia epif neia, (g) to paramorfwmèno montèlo pou proseggðzei thn epif neia thc eikìnac, (d) to paramorfwmèno montèlo pou proseggðzei thn epif neia thc eikìnac (mìno to 25 % twn suntelest n qrhsimopoi jhkan sthn paramìrfwsh tou montèlou). k je eikonostoiqeðo thc eikìnac na antistoiqeð se ènan kìmbo plègmatoc. K je kìmboc upotðjetai ìti èqei m za m kai sundèetai me touc geitonikoôc tou kìmbouc me tèleia elat ria sklhrìthtac k, fusikoô m kouc l 0 kai suntelest apìsbeshc c. Upì thn ep reia eswterik n kai oi exwterik n dun mewn, to sôsthma m zac-elathrðwn paramorf netai se èna 3D plègma anaparist ntac thn epif neia fwteinìthtac thc eikìnac, ìpwc mporeð na dei k poioc sto Sq ma 4.2g. Sthn perðptws mac, oi arqikèc kai telikèc katast seic twn paramor-

151 4.2. Paramorf simo Montèlo Epif neiac 129 f simwn montèlwn epif neiac eðnai gnwstèc. H arqik kat stash eðnai h arqik (epðpedh) diamìrfwsh tou montèlou kai h telik kat stash eðnai h epif neia èntashc thc eikìnac, ìpwc parousi zetai sto sq ma 4.2b. E- pomènwc, mporeð na jewrhjeð ìti mia stajer dônamh f efarmìzetai sto montèlo epif neiac [33]. Dedomènou ìti den endiaferìmaste gia thn dunamik twn paramorf sewn, mporoôme na epikentrwjoôme sth diatôpwsh tou statikoô probl matoc wc ex c: Ku = f: (4.1) ìpoo K eðnai o N N pðnakac sklhrìthtac, f = [f 1 ;:::;f N ] T eðnai èna N 3 di nusma pou ta N stoiqeða tou eðnai 3D dianôsmata exwterik n dun mewn pou efarmìzontai sto montèlo kai u eðnai to N 3 di nusma metatopðsewn twn kìmbwn pou dðnetai apì th sqèsh: u =[u 1 ;:::;u i ;:::;u N ] T ; (4.2) ìpou u i =[u i;x ; u i;y ; u i;z ] eðnai h metatìpish tou i-stoô kìmbou. AntÐ na brejeð mesa h kat stash isorropðac tou sust matoc (4.1), k poioc mporeð na qrhsimopoi sei allag b shc [30]: u = Φ~u = N =NhNw X i=1 ffi i ~u i ; (4.3) ìpou ~u anafèretai san to genikeumèno di nusma metatopðsewn (generalized displacement vector), ~u i eðnai h i-st sunist sa tou ~u kai Φ eðnai ènac pðnakac thc t xewc tou N, pou oi st lec touc eðnai ta idiodianôsmata ffi i tou genikeumènou idioprobl matoc: Kffi i =! 2 i Mffi i ; (4.4) ìpou M eðnai o pðnakac m zac tou montèlou. To i-stì idiodi nusma ffi i, dhlad, h i-st st lh tou Φ apokaleðtai kai i-stì idiodi nusma tal ntwshc kai to! i eðnai h antðstoiqh idiotim (pou apokaleðtai kai suqnìthta

152 130 Kef laio 4. EktÐmhsh Trisdi statou ProsanatolismoÔ Pros pou tal ntwshc). H exðswsh (4.3) eðnai gnwst wc exðswsh epallhlðac twn idioqarakthristik n tou montèlou. Sthn pr xh, prospajoôme na proseggðsoume tic metatopðseic twn kìmbwn u qrhsimopoi ntac to ^u pou eðnai to elattwmèno jroisma twn N 0 qamhlì-suqnotik n sunistws n, ìpou N 0 <N: u ß ^u = N X 0 i=1 ffi i ~u i : (4.5) Ta idiodianôsmata ffi i, i =1;:::;N 0, diamorf noun ton apokaloômeno e- lattwmèno q ro idioqarakthristik n tou sust matoc. Autì eðnai kai to shmantikìtero pleonèkthma thc teqnik c an lushc idioqarakthristik n: ìti lônetai se ènan upoq ro pou antistoiqeð stic N 0 qamhlì-suqnotikèc sunist sec thc dom c tou montèlou [30, 31, 33]. Oarijmìc twn N 0 sunistws n pou qrhsimopoioôntai gia thn perigraf thc epif neiac montèlou, epilègetai ètsi ste na apokthjeð mia sumpag c kai epark c akrib c paramorf simh antipros peush thc epif neiac. 'Enac qarakthristikìc a- rijmìc gia ton ìro N 0 pou kalôptei polloôc tôpouc paramorf simwn montèlwn, eðnai Ðsoc me to èna tètarto tou sunolikoô arijmoô twn sunistws n. 'Ena shmantikì pleonèkthma twn diatup sewn pou perigr fhkan mèqri t ra, tìso sto sunolikì ìso kai ston elattwmèno q ro twn idioqarakthristik n, eðnai ìti ta dianôsmata tal ntwshc (idiodianôsmata), ffi i kai oi suqnìthtec tal ntwshc (idiotimèc)! i miac epðpedhc topologðac èqoun mia rht diatôpwsh [31] kai den eðnai aparaðthto na upologistoôn qrhsimopoi ntac teqnikèc idioaposônjeshc:! 2 (j; j 0 )= 4k m ffi n;n 0(j; j 0 ) = cos» sin 2 ßj 2N h + sin 2 ßj 0 2N w ; (4.6) ßj(2n 1) N h cos ßj0 (2n 0 1) N w ; (4.7)

153 4.2. Paramorf simo Montèlo Epif neiac 131 ìpou j = 0; 1;:::;N h 1, j 0 = 0; 1;:::;N w 1, n = 1; 2;:::;N h, n 0 = 1; 2;:::;N w,! 2 (j; j 0 ) =! jnw+j0, 2 ffi n;n 0(j; j 0 ) eðnai to (n; n 0 )-stì stoiqeðo tou pðnaka ffi(j; j 0 ), ìpou ffi(j; j 0 )=ffi jn w+j0. Sto q ro thc tropik c an lushc idioqarakthristik n h exðswsh (4.1) mporeð na xanagrafeð wc ex c: ~K~u = ~ f; (4.8) ìpou ~K = Φ T KΦ kai ~ f = Φ T f, f apoteleð to exwterikì di nusma dun - mewn. Wc ek toôtou, qrhsimopoi ntac tic exis seic (4.3), (4.6) kai (4.7), h sqèsh (4.8) aplopoieðtai se 3N bajmwtèc exis seic:! 2 i ~u i;j = ~ f i;j ; (4.9) ìpou j = x; y; z kai ~u i;j eðnai to j-sto stoiqeðo tou i-stoô dianôsmatoc ~u. Sthn perðptws mac, ta stoiqeða twn dun mewn sto di nusma f kat m koc twn axìnwn x kai y lamb nontai na eðnai Ðsa me mhdèn, dhlad, f i;x = f i;y = 0. Apì thn llh meri, ta stoiqeða twn dun mewn kat m koc tou z xona (èntashc) lamb nontai na eðnai an loga proc thn EukleÐdeia apìstash metaxô tou shmeðou (x; y; I(x; y)) kai thc jèshc tou antðstoiqou kìmbou tou montèlou sthn arqik tou diamìrfwsh (x; y; 0), dhlad, Ðso me th fwteinìthta I(x; y) tou eikonostoiqeðou (x; y): f (x 1)N w +y;z = f(x; y) =I(x; y), ìpou f (x 1)N w +y;z eðnai h sunist sa tou z xona tou (x 1)N w + y-stoô stoiqeðou f (x 1)N w +y tou dianôsmatoc f. Epiplèon, to paramorf simo montèlo den epitrèpetai na paramorfwjeð kat m koc tou Q kai U xona, dhlad isqôei ìti ~u i;x = ~u i;y = 0. Wc ek toôtou, to N 3 genikeumèno di nusma metatopðsewn mporeð na aplopoihjeð se èna N-di stato di nusma pou perièqei mìno tic z sunist sec: ~u = [~u 1 ;:::;~u i ;:::;~u N hnw] T = [~u 1;z ;:::;~u i;z ;:::;~u N hnw;z] T. Qrhsimopoi ntac tic exis seic (4.3), (4.6), (4.7) kai (4.9) mazð me tic proanafer-

154 132 Kef laio 4. EktÐmhsh Trisdi statou ProsanatolismoÔ Pros pou jeðsec timèc twn dun mewn, k poioc mporeð na upologðsei to ~u k wc ex c: ~u (i 1)N w+j = P N h n=1 P N w (1 +! 2 (i; j))q PN h n=1 n0 =1 I(n; n 0 )ffi n;n 0(i; j) P N w n0 =1 ffi 2 n;n0(i; j) : (4.10) Prèpei na shmeiwjeð ìti to paramorf simo montèlo epitugq nei na prosomoi sei mìno mia prosèggish thc epif neiac èntashc thc upì exètashc eikìnac. Gia to prìblhma tou prosanatolismoô tou anjr pinou kefalioô, oi eikìnec pros pou miac eikonoseir c anaparistoôntai me èna paramorf simo montèlo. To sq ma 4.2 perigr fei thn prosèggish thc epif neiac èntashc (sq ma 4.2b) miac eikìnac pros pou (pou apeikonðzetai sto sq ma 4.2a) apì èna paramorf simo montèlo epif neiac (sq mata 4.2 b, g). To mègejoc tou montèlou (se kìmbouc) pou qrhsimopoi jhke gia na proseggðsei thn epif neia thc eikìnac tan Ðsoc me to mègejoc thc eikìnac (se eikonostoiqeða). To genikeumèno di nusma metatopðsewn ~u twn exis sewn (4.8), (4.10) qrhsimopoieðtai, ìpwc ja parousiasteð stic parak tw Paragr fouc, prokeimènou na parakoloujhjoôn perioqèc 2D pros pwn se eikìnec kai gia na ektimhjeð o 3D prosanatolismìc tou kefalioô. 'Ena di gramma ro c tou proteinìmenou algorðjmou parousi zetai sto sq ma 4.3. Oi leptomèreiec tou algorðjmou ja parasqejoôn stic epìmenec Paragr fouc. 4.3 ParakoloÔjhsh Anjr pinou Pros pou kai DhmiourgÐa tou QarakthristikoÔ DianÔsmatoc ProsanatolismoÔ 'Enac algìrijmoc anðqneushc metwpik n pros pwn se pragmatikì qrìno [37] efarmìzetai sthn pr th eikìna miac eikonoseir c prokeimènou na

155 4.3. DhmiourgÐa DianÔsmatoc ProsanatolismoÔ 133 Εικόνα Εισόδου Παρακολούθηση Προσώπου Πρώτη Εικόνα Οχι Ναι Ανίχνευση Μετωπικών Προσώπων Ανίχνευση Προσώπων Υπολογίζεται το CFV για όλες τις θέσεις μέσα στην περιοχή αναζήτησης Εύρεση της θεσης με το CFV που ταιριάζει στο CFV του παραθύρου στην προηγούμενη εικόνα Ικανοποιητική Ποιότητα Ταιριάσματος Ναι Οχι Αυξάνεται το μέγεθος της περιοχής αναζήτησης Είναι το μέγεθος της περιοχής αναζήτησης μικρότερο από το κατώφλι; Ναι Νέα θέση του προσώπου στη τρέχουσα εικόνα Οχι Το πρόσωπο θεωρείται χαμένο Εκτίμηση Προσανατολισμού Ανθρώπινου Προσώπου Στο CFV της νέας θέσης προστίθεται η γωνία της προηγούμενης εικόνας 3 εκπαιδευμένα δίκτυα RBFs τροφοδοτούνται με το προσαυξημένο CFV Προσανατολισμός προσώπου για την τρέχουσα εικόνα Sq ma 4.3: To di gramma ro c tou proteinìmenou algorðjmou ektðmhshc prosanatolismoô anjr pinou kefalioô. arqikopoi sei th diadikasða parakoloôjhshc kai ektðmhshc prosanatolismoô tou anjr pinou kefalioô. O algìrijmoc anðqneushc pros pou basðzetai se apl qarakthristik gnwrðsmata pou prokôptoun apì tic Haar sunart seic b seic, ìpwc anafèretai sto [38]. Aut ta qarakthristik gnwrðsmata epekt jhkan sthn teqnik pou perigr fetai sto [37], gia na mei soun peraitèrw ton arijmì twn lanjasmènwn ektim sewn. To apotèlesma thc diadikasðac anðqneushc pros pou eðnai èna par juro gô-

156 134 Kef laio 4. EktÐmhsh Trisdi statou ProsanatolismoÔ Pros pou rw apì to kèntro pros pou, dhlad, gôrw apì th môth, h opoða eswkleðei thn perioq tou pros pou. Sth sunèqeia, mia teqnik parakoloôjhshc pros pou parìmoia me aut n pou perigr fetai sthn ergasða [36] kai h opoða perigr fetai analutik kai sto Kef laio 2, qrhsimopoieðtai gia na parakolouj sei ton kentrik perioq tou pros pou. H kôria diafor metaxô tou algorðjmou katadðwxhc pou qrhsimopoieðtai ed kai thc mejìdou pou perigr fhke sto Kef laio 2,eÐnai ìti h teleutaða stoqeôei sthn parakoloôjhsh qarakthristik n gnwrism twn (qrhsimopoi ntac plhroforðec apì thn perib llousa perioq ), en o proteinìmenoc algìrijmoc eðnai prosarmosmènoc se olìklhrec perioqèc. Prìsjetec plhroforðec gia ton algìrijmo parakoloôjhshc mazð me polu rijma peiramatik apotelèsmata mporeð na brei k poioc sto Kef laio 2 kai sthn ergasða [36]. Oi akìloujec upojèseic uiojetoôntai ston proteinìmeno algìrijmo: ffl To par juro pros pou (h perioq tou anjr pinou kefalioô pou parakoloujeðtai) eðnai stajeroô megèjouc, dhlad, to prìswpo den kineðtai shmantik proc makri thc k merac. Autì eðnai mia realistik upìjesh gia tic perissìterec efarmogèc pou qrhsimopoioôn ton prosanatolismì tou kefalioô (p.q. allhlepðdrash anjr pouupologist, anagn rish pros pou, ektðmhsh blèmmatoc). ffl 'Ena mèroc tou anjr pinou pros pou eðnai p nta oratì (oi eikìnec pou apeikonðzoun to pðsw mèroc tou kefalioô den mac apasqoloôn) kai den emfanðzontai epikalôyeic tou pros pou me lla antikeðmena. Kai oi dôo autèc upojèseic eðnai epðshc realistikèc gia tic perissìterec efarmogèc. E n krijeð anagkaðo, o proteinìmenoc algìrijmoc parakoloôjhshc mporeð na emploutisteð me mhqanismoôc diaqeðrishc epikalôyewn tou pros pou. O algìrijmoc parakoloôjhshc pros pou ulopoieðtai me thn efarmog tou paramorf simou montèlou (pou perigr fhke en suntomða sthn

157 4.3. DhmiourgÐa DianÔsmatoc ProsanatolismoÔ 135 Par grafo 4.2) se èna mikrì parajôrou W (p.q. diast sewn eikonostoiqeðwn) gôrw apì to kèntro tou pros pou p t =(x; y) kai dðnontac tim sto genikeumèno di nusma metatopðsewn ~u t (x; y) thc exðswshc (4.8) gia autì to par juro: ~u t (x; y) =[~u t 1(x; y); ~u t 2(x; y);:::;~u t NHNW (x; y)]t ; (4.11) ìpou t dhl nei th qronik stigm kai N H, N W eðnai to Ôyoc kai pl toc tou paramorf simou montèlou epif neiac (Ðso se diast seic me to par juro). Apì ed kai sto ex c ja kaloôme to di nusma ~u t (x; y) san di nusma qarakthristik n gnwrism twn (characteristic feature vector (CFV)). 'Eqei apodeiqjeð sthn ergasða [36] ìti autì to di nusma eðnai ènac sunduasmìc di forwn mask n anðqneushc gramm n kai akm n pou efarmìzontai sto par juro parakoloôjhshc. Kat sunèpeia, parakolouj ntac to prìswpo kai tairi zontac to CFV se diadoqikèc eikìnec eðnai mia stajer mèjodoc apènanti stic allagèc fwtismoô. Prokeimènou na brejeð h jèsh p t+1 =(x 0 ;y 0 ) tou kèntrou tou N H N W parajôrou W sthn epìmenh eikìna I t+1 thc eikonoseir c, o algìrijmoc upologðzei to CFV ~u t+1 gia ìla ta par jura twn opoðwn to kèntro (k; l) brðsketai mèsa se mia perioq anaz thshc R me Ôyoc N Hreg kai pl toc N Wreg, kentrarismènh stic suntetagmènec (x; y) thc eikìnac I t+1. H nèa jèsh tou kèntrou W brðsketai sth jèsh (x 0 ;y 0 ) thc perioq c anaz thshc thc opoðac to CFV tairi zei pio polô me to CFV tou p t. Pio sugkekrimèna: p t+1 =(x 0 ;y 0 )! arg min(k~u t+1 (k; l) ~u t (x; y)k); (4.12) kl ìpou k k ekfr zei thn EukleÐdeia apìstash, k 2 fx N Hreg 1 ;:::;x;:::;x+ 2 NHreg 1 g kai l 2 fy N Wreg 1 ;:::;y;:::;y+ N Wreg 1 g H epilog thc EukleÐdeiac apìstashc basðsthke se èna sônolo peiram twn pou exètasan thn apìdosh tou proteinìmenou algorðjmou parakoloôjhshc qrhsimopoi ntac diaforetik mètra prokeimènou na epileqteð h

158 136 Kef laio 4. EktÐmhsh Trisdi statou ProsanatolismoÔ Pros pou epìmenh jèsh tou pros pou. H EukleÐdeia apìstash èdwse ta kalôtera apotelèsmata sugkrinìmenh me thn kanonikopoihmènh susqètish kai me th metrik js t x;y S t+1 k;l j, ìpou S t x;y S t x;y = dðnetai apì th sqèsh: NH XNW i=1 fi fi ~u t i(x; y) fi fi : (4.13) To peðrama perigr fetai leptomer c sthn Par grafo 4.5. Dedomènou ìti oi kin seic tou pros pou pou parakoloujeðtai mporeð na all xoun me thn p rodo tou qrìnou, dhlad, to prìswpo mporeð na epitaqônei na epibradônei se orismèna tm mata thc eikonoseir c, o algìrijmoc qrhsimopoieð mia perioq anaz thshc R metablhtoô megèjouc. Gia k je eikìna thc akoloujðac, o algìrijmoc prospajeð na entopðsei to nèo kèntro tou parajôrou W (pou eswkleðei to prìswpo) qrhsimopoi ntac arqik mia mikr perioq anaz thshc (p.q. 7 7). Wstìso, e n to kalôtero taðriasma thc eukleðdeiac apìstashc (4.12) eðnai p nw apì èna prokajorismèno ìrio, o algìrijmoc aux nei to mègejoc thc perioq c anaz thshc, prospaj ntac na breð mia kalôterh antistoiqða (mia antistoiqða pou petuqaðnei eukleðdeia apìstash k tw apì to prokajorismèno ìrio) sth megalôterh perioq anaz thshc. E n autì den eðnai p li efiktì, h aôxhsh tou megèjouc thc perioq c anaz thshc suneqðzetai mèqri èna orismèno mègisto mègejoc perioq n (R = 23). Merik apotelèsmata parakoloôjhshc gia th b sh dedomènwn IDIAP parousi zontai sto sq ma 4.4. Ektìc apì th qr sh tou gia thn parakoloôjhsh pros pou, to CFV tou parajôrou W qrhsimopoieðtai kai gia thn ektðmhsh tou prosanatolismoô tou pros pou. To CFV perièqei plhroforðec gia thn kentrik orat perioq tou pros pou, dhlad, thn perioq gôrw apì th môth stic metwpikèc eikìnec to m goulo sta peristremmèna prìswpa (sq ma 4.4), dedomènou ìti ta stoiqeða tou perièqoun plhroforðec sqetikèc me tic metatopðseic tou paramorf simou montèlou epif neiac pou proseggðzei thn

159 4.3. DhmiourgÐa DianÔsmatoc ProsanatolismoÔ 137 Sq ma 4.4: Apotelèsmata parakoloôjhshc pros pou pou apokt jhkan se eikonoseirèc pou perièqoun hjopoioôc me poikðlouc prosanatolismoôc pros pou. epif neia èntashc sthn upì exètash perioq. 'Oso o prosanatolismìc tou pros pou all zei sto 3D q ro, h probol tou sthn eikìna (2D q roc) all zei epðshc. Kat sunèpeia, to par juro stajeroô megèjouc W perilamb nei to kentrikì mèroc tou pros pou se di forec ìyeic (sq ma 4.4). Wc ek toôtou, autèc oi plhroforðec mporoôn na qrhsimopoihjoôn gia na ektimhjeð o prosanatolismìc tou pros pou. Ta qarakthristik tou paramorf simou montèlou epif neiac pou qrhsimopoi jhkan se ìla ta peir mata, tèjhkan ètsi ste to prìtupo na eðnai sqetik kampto. Kat sunèpeia, h telik kat stash thc paramorf simhc epif neiac tan mia exomalusmènh èkdosh thc epif neiac èntashc tou pros pou, ètsi ste na mhn eðnai euaðsjhth sto jìrubo, stic allagèc twn pros pwn kai stic e- nallagèc tou fwtismoô. EkmetalleÔontac to elattwmèno q ro thc teqnik c an lushc idioqarakthristik n, k poioc mporeð na mei sei to mègejoc tou qarakthristikoô dianôsmatoc CFV se 25% tou arqikoô tou megèjouc

160 138 Kef laio 4. EktÐmhsh Trisdi statou ProsanatolismoÔ Pros pou (sthn perðptws mac se 100 stoiqeða apì ta arqik = 400), qwrðc ap leia shmantik n plhrofori n. Oi plhroforðec pou peril fjhkan sto CFV qrhsimopoi jhkan mazð me kat llhla ekpaideumèna dðktua parembol c aktinik n sunart sewn b shc ( Radial Basis Function Interpolation (RBF)) gia na ektim soun ton prosanatolismì tou pros pou, ìpwc ja perigrafeð sthn epìmenh Par grafo. 4.4 Parembol Aktinik n Sunart sewn B - shc O sqediasmìc enìc sust matoc parembol c mporeð na antimetwpisteð san èna prìblhma antistoiqi n epifanei n se èna uyhlì-di stato q ro ìpwc anafèretai sto biblðo [39]. Se mia tètoia perðptwsh, h ekm jhsh eðnai isodônamh me thn eôresh miac omal c epif neiac, h opoða paremb llei ( proseggðzei) ta stoiqeða pou qrhsimopoioôntai gia thn ekpaðdeush. Oi aktinikèc sunart seic b shc qrhsimopoioôntai ston proteinìmeno algìrijmo gia autì to skopì. Oi RBFs epilèqthkan gia touc akìloujouc lìgouc: ffl èqoun apl dom, ffl èqoun thn idiìthta thc fikalôterhc prosèggishcfl, ffl èqoun thn idiìthta thc kalôterhc ekm jhshc kai thc meiwmènhc euaisjhsðac sto mègejoc tou sunìlou twn plhrofori n pou qrhsimopoioôntai sthn ekpaðdeush. Upojètoume èna sônolo apì NK-di stata dianôsmata [x 1 x 2 ::: x N ], x i 2 R K kai èna sônolo apì diakritèc timec [l 1 l 2 ::: l N ], l i 2 R, ta o- poða antistoiqoôn se deðgmata miac gnwsthc sun rthshc f : R K! R, dhlad, f(x i )=l i. H parembol RBF lônei to prìblhma brðskontac mia

161 4.4. Parembol Aktinik n Sunart sewn B shc 139 omal sun rthsh ^f(x) pou ikanopoieð thn parak tw sqèsh: ^f(x i )=l i ; i =1;:::;N; (4.14) dhlad paremb llontac ta (x i ;l i ) kai prospaj ntac na proseggðsei to f(x) opoud pote alloô. H parembol aktinik n sunart sewn b shc orðzetai wc ex c: f(x) = NX 1 w i R i (x); (4.15) ìpou R i eðnai oi epilegmènec aktinwtèc sunart seic b shc kai w i eðnai ta grammik b rh pou qrhsimopoioôntai gia na sundu soun tic RBF. Sthn perðptws mac, qrhsimopoi jhkan isotropikèc gkaoussianèc a- ktinikèc sunart seic b shc: R(kx uk 2 ) = exp( 1 2ff 2 kx uk2 ): (4.16) Oi par metroi pou majaðnontai se mia tètoia perðptwsh parembol c RBF eðnai ta b rh w i sthn exðswsh (4.15), oi mèsec timèc u i kai oi apoklðseic ff i twn RBF R i. Pollèc proseggðseic gia thn ekpaðdeush miac parembol c RBF èqoun protajeð [39]. SÔmfwna me mða apì autèc, ta dianôsmata u i mporoôn na epileqjoôn Ðsa me ta dianôsmata x i, dhlad, u i = x i, ètsi ste k je RBF na eðnai kentrojethmènh se èna deðgma ekpaðdeushc x i. H apìklish gia ìlec tic gkaoussianèc sunart seic b shc mporeð na tejeð Ðsh me [39]: ff = d p 2N ; (4.17) ìpou N eðnai o arijmìc twn deigm twn ekapðdeushc, d eðnai h mègisth eukleðdeia apìstash metaxô duo opoiond pote deigm twn ekpaðdeushc x i, x j. Aut h epilog tou ff exasfalðzei ìti oi RBFs den eðnai oôte p ra polô aplwmènec oôte p ra polô sugkentrwmènec kai ìti ja proseggðsoun to

162 140 Kef laio 4. EktÐmhsh Trisdi statou ProsanatolismoÔ Pros pou q ro arket kal. Mìlic kajoristoôn pl rwc oi RBFs, mia apl diadikasða gia ton upologismì twn bar n w i sth sqèsh (4.15) ètsi ste to dðktuo parembol c na ikanopoieð thn exðswsh (4.14), eðnai na qrhsimopoihjeð o yeudoan strofoc pðnakac [40] sto parak tw grammikì sôsthma: Rw = l (4.18) ìpou ta stoiqeða r ji tou R eðnai Ðsa me ta R i (kx j x i k 2 ), ta dianôsmata w kai l perièqoun ta b rh w i kai tic bajmwtèc timèc l i antistoðqwc kai j; i =1; 2;:::;N. Olof nera plèon, autì to grammikì sôsthma èqei thn parak tw lôsh: ìpou R + eðnai o yeudoan strofoc tou R. w = R + l; (4.19) H parembol aktinik n sunart sewn b shc qrhsimopoi jhke sthn perðptws mac, gia thn ektðmhsh tou prosanatolismoô tou anjr pinou pros pou (peristrof, klðsh, kôlish) sthn eikìna I t, qrhsimopoi ntac san eðsodo to CFV ~u t thc antðstoiqhc eikìnac. Kat sunèpeia, to di nusma eisagwg c sthn ekpaðdeush kai sthn exètash thc diadikasðac tan to CFV thc perioq c pou eswkleðei to prìswpo h opoða par qjh apì ton algìrijmo parakoloôjhshc, en h èxodoc tan oi gwnðec peristrof c tou kefalioô. Pio sugkekrimèna, qrhsimopoi jhkan trða dðktua RBF, pou k - je èna qeirðzetai mia diaforetik gwnða (peristrof, klðsh, kôlish) tou pros pou. To eôroc tim n k je miac apì autèc tic gwnðec poikðlei: apì [ 90 :::90] gia thn peristrof, [ 60 :::60] gia thn klðsh kai [ 30 :::30] gia thn kôlish. Kat th di rkeia thc ekpaðdeushc tou sust matoc RBF, dhlad, kat th di rkeia thc axiolìghshc tou mèsou ìrou kai thc apìklishc twn RBFs kai twn bar n w i, qrhsimopoi jhkan san eðsodoc èna sônolo apì CFVs ~u t mazð me tic antðstoiqec gwnðec prosanatolismoô tou pros pou pou proèrqontai apì th b sh dedomènwn pou perièqei tic sqetikèc plhroforðec. Autì to sônolo tan èna uposônolo twn zeugari n CFV kai gwni n, proerqìmeno apì tic eikonoseirèc parakoloôjhshc kai

163 4.4. Parembol Aktinik n Sunart sewn B shc 141 ta dedomèna thc b shc. Se sumfwnða me th diadikasða ekpaðdeushc pou perigr fhke parap nw, qrhsimopoi jhkan tìsec RBFs ìsa kai ta deðgmata ~u t. Me lla lìgia, o arijmìc twn RBFs tan Ðsoc me ton arijmì eikìnwn twn eikonoseir n ekpaðdeushc. Gia na dokimasteð to sôsthma, èna qarakthristikì di nusma x 0 = ~u t0 qwrðc gn sh thc plhroforðac gwni n, qrhsimopoieðtai wc eðsodoc. To ekpaideumèno sôsthma RBF, paremb llei ta stoiqeða proc dokim sthn epif neia pou proèrqetai apì ta stoiqeða ekpaðdeushc kai ektim ton prosanatolismì tou pros pou. Prokeimènou na auxhjeð h apìdosh tou sust matoc wc proc thn ektðmhsh prosanatolismoô tou pros pou, ta dianôsmata eisìdou twn RBF epekt jhkan prosjètontac sto di nusma CFV ~u t th gwnða tou pros pou thc prohgoômenhc eikìnac. Pio sugkekrimèna, ta dðktua parembol c RBF taòsthkan th qronik stigm t me dianôsmata thc morf c: [~u t j t 1 ] T (4.20) ìpou t 1 eðnai mia apì tic treic gwnðec peristrof c tou pros pou. Kat th di rkeia thc ekpaðdeushc, oi timèc twn gwni n gia k je prohgoômenh qronik eikìna proerqìtan apì th b sh dedomènwn, en kat th di rkeia thc dokim c, qrhsimopoi jhkan oi ektim seic twn gwni n apì thn efarmog tou sust matoc sthn prohgoômenh qronik eikìna. H qr sh thc gwnðac thc prohgoômenhc qronik eikìnac sta dianôsmata eisìdou eis - gei thn ènnoia thc sunoq c. Pr gmati, e n diatðjentai bðnteo me ikanopoihtikì arijmì karè an deuterìlepto kai oi kin seic tou kefalioô eðnai omalèc, tìte oi gwnðec sth trèqousa eikìna den ja diafèroun shmantik apì ekeðnec sthn prohgoômenh eikìna. Kat sunèpeia, me th sumperðlhyh aut n twn plhrofori n to sôsthma mporeð na antimetwpðsei apotelesmatikìtera l jh pou proèkuyan sthn parakoloôjhsh. Apì thn llh, e n emfanðzontai apìtomec kin seic, tìte oi gwnðec thc prohgoômenhc qronik eikìnac ja eðnai sqetik asôndetec me ekeðnec thc trèqousac eikìnac me apotèlesma na èqoun epipt seic sthn apìdosh me ènan arnhtikì trìpo.

164 142 Kef laio 4. EktÐmhsh Trisdi statou ProsanatolismoÔ Pros pou EntoÔtoic, tètoiec metakin seic eðnai m llon sp niec kai elpðzoume pwc h parakoloôjhsh ja èqei ikanopoihtik apotelèsmata parèqontac swstèc timèc gia to CFV eisìdou. O prosanatolismìc tou pros pou gia thn pr th eikìna thc eikonoseir c jewr jhke gnwst. Pio sugkekrimèna, jewr jhke ìti sthn pr th eikìna to upì exètash prìswpo koit metwpik sthn k mera, qwrðc peristrofèc se opoioid pote apì touc treic xonec, ètsi ste kai oi treic gwnðec (peristrof, klðsh, kôlish) na eðnai Ðsec me mhdèn. Autì to sen - rio den eðnai mh realistikì, dedomènou ìti se pollèc efarmogèc to prìswpo eðnai metwpikì/oudètero sthn arq thc eikonoseir c kai polloð algìrijmoi pou sqetðzontai me prìswpa uiojetoôn thn Ðdia upìjesh. Epiplèon, o aniqneut c pros pou pou qrhsimopoieðtai gia na arqikopoi sei to proteinìmeno sôsthma, eðnai ènac metwpikìc aniqneut c pros pou kai ètsi, aut h upìjesh eðnai aparaðthth gia thn kat llhlh leitourgða tou. 4.5 Axiolìghsh tou Proteinìmenou sust matoc Prwtìkollo kai Dedomèna Axiolìghshc Ta peir mata pragmatopoi jhkan gia na axiolog soun thn apìdosh tou proteinìmenou algìrijmou se bðnteo pou katagr fhkan se realistikèc sunj kec. O stìqoc tou pr tou sunìlou peiram twn tan diplìc: gia na axiolog sei thn apìdosh tou algorðjmou parakoloôjhshc kai gia na brei mia kat llhlh metrik gia th mètrhsh thc omoiìthtac twn CFVs. H apìdosh tou algorðjmou axiolog jhke se epðpedo antikeimènou, dhlad, sth logik e n olìklhro to antikeðmeno upì exètash parakolouj jhke swst ìqi. Alhj c jetik TP (True Positives), yeud c jetik FP (False

165 4.5. Axiolìghsh tou Proteinìmenou sust matoc 143 Positives) kai yeud c arnhtik FN (False Negatives) apotelèsmata apokt jhkan sugkrðnontac ta apotelèsmata me antðstoiqa pou par qjhsan qeirokðnhta. Peript seic ìpou h upì parakoloôjhsh perioq perieðqe perissìtero apì 70% tou pros pou, jewr jhke wc TP. 'Otan perissìtero apì to 30% thc upì parakoloôjhshc perioq c apoteloôntan apì to u- pìbajro tou bðnteou, to apotèlesma jewroôntan FP. Katast seic ìpou o algìrijmoc parakoloôjhshc èqane to stìqo tou (dhlad akoloujoôse to upìbajro), jewr jhke wc FN. upologðsthkan oi gnwstèc metrikèc thc akrðbeiac (P = an klhshc (R = TP TP+FN Me b sh autoôc touc arijmoôc, TP ) kai thc TP+FP ). O algìrijmoc efarmìsthke se 5 eswterikèc kai upaðjriec eikonoseirèc (5600 eikìnec) me kin seic pou antimetwpðzontai suqn se peript seic parakoloôjhshc, ìpwc h metatìpish kai h peristrof. Oi stoôntio (eswterikèc) eikonoseirèc apeikonðzoun èna tomo pou kineðtai se prokajorismènec tuqaðec troqièc, k tw apì bèltistec (omoiìmorfoc fwtismìc) mètriec (skièc kai fwteinèc/skoteinèc perioqèc) sunj kec fwtismoô pou dhmiourg jhkan qrhsimopoi ntac ton exoplismì enìc stoôntio. Oi upaðjriec eikonoseirèc apeikonðzoun èna tomo pou kineðtai se mia tuqaða troqi k tw apì realistikèc sunj kec. Apotelèsmata gia tic 3 diaforetikèc metrikèc pou qrhsimopoi jhkan, dhlad thn eukleðdeia apìstash, thn kanonikopoi menh susqètish kai thn apìluth diafor S t x;y pou dðnetai apì thn exðswsh (4.13) sunoyðzontai ston PÐnaka 4.1. K poioc mporeð na dei ìti h eukleðdeia apìstash epitugq nei thn kalôterh apìdosh. Epiplèon, aut ta peiramatik apotelèsmata parèqoun posotikèc apodeðxeic sqetik me thn ikanopoihtik apìdosh tou algorðjmou parakoloôjhshc. Apì th stigm pou o algìrijmoc parakoloôjhshc den eðnai to kèntro endiafèrontoc autoô tou KefalaÐou kai o algìrijmoc pou qrhsimopoieðtai moi zei me autìn pou prot jhke sto èggrafo [36], den par qjhsan nèa peir mata proc aut n thn kateôjunsh. Oi anagn stec enjarrônontai na sumbouleujoôn thn ergasða [36] kaj c kai to Kef laio 2 gia perissìtera apotelèsmata parakoloôjhshc upì di forec sunj kec.

166 144 Kef laio 4. EktÐmhsh Trisdi statou ProsanatolismoÔ Pros pou PÐnakac 4.1: Metrikèc akrðbeiac kai an klhshc thc upì parakoloôjhshc perioq c ìtan qrhsimopoieðtai h eukleðdeia apìstash, h kanonikopoihmènh susqètish kai h apìluth diafor S t x;y (4.13) gia na sugkrijoôn ta CFVs suneqìmenwn eikìnwn apì bðnteo. Metrik P R EukleÐdeia apìstash Kanonikopoihmènh susqètish js t x;y S t+1 k;l j Sto deôtero sônolo peiram twn, h proteinìmenh mèjodoc qrhsimopoi jhke gia na ektimhjeð o 3D prosanatolismìc tou pros pou se eikonoseirèc thc b shc dedomènwn IDIAP [12]. Aut h b sh dedomènwn epilèqthke epeid perièqei apotelèsmata prosanatolismoô pros pwn gia di forec eikonoseirèc pou katagr fhkan upì realistikèc sunj kec kai apeikonðzoun fusikèc katast seic. K je èna apì ta 23 bðnteo diarkeð apì 4 èwc 10 lept, èqei an lush eikonostoiqeðwn, kai 25 karè an deuterìlepto. Up rqoun dôo mèrh sth b sh dedomènwn. To èna apeikonðzei èna perib llon grafeðou kai to llo èna perib llon sunedrðashc. To kôrio sen rio thc b shc IDIAP eðnai ìti ta upokeðmena energoôn ìpwc sth kajhmerin zw touc mèsa sto grafeðo kat th di rkeia miac sunedrðashc. Sto sônolo touc, 16 diaforetik upokeðmena summetèqoun sthn b sh dedomènwn. H b sh dedomènwn perièqei to prosanatolismì twn pros pwn twn upokeimènwn upì th morf gwni n peristrof c, klðshc kai kôlishc (dhlad tic gwnðec Euler se sqèsh me to sôsthma suntetagmènwn thc k merac) gia k je mia eikìna enìc bðnteo. 'Endeka apì tic eikonoseirèc qrhsimopoi jhkan gia thn ekpaðdeush tou diktôou parembol c RBF kai oi upìloipec gia th dokim tou sust matoc. Sto sônolo, 9500 eikìnec qrhsimopoi jhkan gia na ekpaideuteð to sôsthma. Kat sunèpeia, ènac Ðsoc arijmìc apì RBFs qrhsimopoi jhke. Gia

167 4.5. Axiolìghsh tou Proteinìmenou sust matoc 145 k je RBF, k poioc prèpei na apojhkeôsei to kèntro thc (sthn perðptws mac èna 100-di stato di nusma gia thn eðsodo kai mia tim gia thn èxodo), thn apìklish (Ðdia gia ìlec tic RBFs) kai to antðstoiqo b roc. Oi par metroi tou paramorf simou montèlou epif neiac kajorðsthkan ètsi ste na dojeð mia omal antipros peush thc epif neiac èntashc tou pros pou, dhlad, qrhsimopoi jhke h analogða k = 10 (k eðnai h sklhrìthta twn m elathrðwn kai m hm zatwn kìmbwn). Kat sunèpeia, h telik kat stash thc paramorf simhc epif neiac tan mia exomalumènh èkdosh thc epif - neiac èntashc pros pou, prokeimènou na eðnai mhn eðnai euaðsjhth sto jìrubo, se diaforèc metaxô pros pwn kai se enallagèc tou fwtismoô. 'Ena leptì, dhlad, 1500 eikìnec epilèqthkan apì k je èna apì ta 12 bðnteo ekpaðdeushc tou sust matoc. H epilog tou aposp smatoc apì k je bðnteo pou qrhsimopoi jhke sta peir mata den tan tuqaða. Prospaj same na epilèxoume 1500 eikìnec stic opoðec to upokeðmeno parousðaze kin seic sto kef li ètsi ste na kalôptontai ìso to dunatìn perissìterec peript seic. H anðqneush pros pou ektelèsjhke sthn pr th eikìna tou epilegmènou aposp smatoc k je eikonoseir c kai h teqnik parakoloôjhshc pou perigr fetai sthn Par grafo 4.3 efarmìsthke sto upìloipo tou aposp smatoc ste na parakoloujhjeð h jèsh tou pros pou. Gia k je eikìna, to CFV upologðsthke ste na qrhsimopoihjeð kai peraitèrw gia thn ekpaðdeush thn dokim tou sust matoc RBF.Ta apotelèsmata parakoloôjhshc èdeixan ìti o algìrijmoc petuqaðnei ikanopoihtik apìdosh. Wstìso, se merikèc eikìnec o algìrijmoc parakoloôjhshc mporeð na q sei mèroc tou stìqou, dhlad tou pros pou. Autì mporeð na sumbeð eðte ìtan h metakðnhsh tou pros pou eðnai apìtomh eðte se peript seic pou den parousi zontai apìtomec kin seic. Sthn pr th perðptwsh, h gwnða tou pros pou sthn prohgoômenh qronik eikìna den bohj sthn ektðmhsh thc kateôjunshc sth trèqousa eikìna kai o algìrijmoc mporeð na parèqei shmantikì l joc (thc t xewc 8 o ). Sth deôterh perðptwsh, h gwnða tou pros pou thc prohgoômenhc qronik eikìnac mporeð na bel-

168 146 Kef laio 4. EktÐmhsh Trisdi statou ProsanatolismoÔ Pros pou ti sei thn ektðmhsh sth trèqousa eikìna. Kai stic dôo peript seic, o algìrijmoc parakoloôjhshc anak mptei sun jwc mèsa se merikèc mìno eikìnec. H metrik pou qrhsimopoi jhke gia thn axiolìghsh tou proteinìmenou algorðjmou tan to l joc (apìluth diafor ) se moðrec metaxô twn apotelesm twn thc b shc dedomènwn kai twn apotelesm twn pou par qjhsan gia k je mia gwnða peristrof c (PE), klðshc (TE) kai kôlishc (ME). Epiplèon, o prosanatolismìc tou kefalioô kajorðzei èna 3D di nusma sto q ro pou deðqnei pou to prìswpo eðnai gurismèno. H gwnða (DE) metaxô aut n twn dianusm twn pou proèrqontai apì ta apotelèsmata thc b shc dedomènwn kai apì aut pou par qjhsan, qrhsimopoieðtai san mia akìma metrik, ìpwc anafèretai kai sthn ergasða [12]. apì thn parak tw sqèsh: DE = 180 ß acos 3X i=1 To DE dðnetai (v g (i) Λ v e (i)); (4.21) ìpou acos eðnai to antðstrofo sunim tono, v g (i) kai v e (i) eðnai oi i-stèc sunist sec twn dianusm twn kateôjunshc v g kai v e antðstoiqa, pou kataskeu zontai apì ta apotelèsmata thc b shc dedomènwn kai apì aut pou par qjhsan antðstoiqa, wc ex c [12]: v q = [sin( p ); sin( t ) Λ cos( p ); cos( t ) Λ cos( p )] ; (4.22) ìpou q = fg; eg, p kai t eðnai oi gwnðec peristrof c kai klðshc tou pros pou. Epeid autì to di nusma exart tai mìno apì thn peristrof kai th klðsh tou pros pou, qrhsimopoi jhke mia akìma metrik. Aut h metrik (AE) eðnai h gwnða metaxô twn monadiaðwn dianusm twn a g, a e pou prokôptoun peristrèfontac duo fioudèterafl dianôsmata a n =[1; 0; 0] T proc tic gwnðec p, t, r pou up rqoun sth b sh kai autèc pou ektim jhkan apì to sôsthma wc ex c: wc a = R pr tr ra n ; (4.23)

169 4.5. Axiolìghsh tou Proteinìmenou sust matoc 147 ìpou R p, R t kai R r eðnai oi pðnakec peristrof c gia touc treic xonec peristrof c tou pros pou kai dðnontai ston PÐnaka PÐnakac 4.2: PÐnakec peristrof c gia touc treic xonec peristrof c R p = 0 cos( p ) sin( p ) R t = R r = sin( p ) cos( p ) cos( t ) 0 sin( t ) sin( t ) 0 cos( t ) cos( r ) sin( r ) 0 sin( r ) cos( r ) Peiramatik Apotelèsmata To sq ma 4.5 apeikonðzei tic gwnðec pou ektðmhse o proteinìmenoc algìrijmoc (peristrof, klðsh kai kôlish) mazð me tic antðstoiqec gwnðec pou up rqoun sthn b sh dedomènwn gia treic apì tic eikonoseirèc. Epiplèon, to apìluto l joc se bajmoôc metaxô twn tri n kat' ektðmhsh gwni n kai twn antðstoiqwn thc b shc, dhlad oi timèc PE, TE kai ME, parousi zontai sto sq ma 4.6 se sqèsh me to qrìno. K poioc mporeð na parathr sei eôkola ìti o proteinìmenoc algìrijmoc mporeð na upologðsei to 3D prosanatolismì tou pros pou me polô kal akrðbeia. Se orismènec peript seic, ìtan h kðnhsh tou pros pou eðnai èntonh kai xafnik, se meg lec peristrofèc, to l joc eðnai megalôtero apì to sunhjismèno. H gwnða AE metaxô tou 3D dianôsmatoc kateôjunshc pou kajorðzetai a- pì tic kat' ektðmhsh gwnðec kai to di nusma kateôjunshc pou kajorðzetai apì tic gwnðec pou eðnai kataqwrhmènec sth b sh dedomènwn parousi -

170 148 Kef laio 4. EktÐmhsh Trisdi statou ProsanatolismoÔ Pros pou zetai sto sq ma 4.7. Gia par deigma, to apìluto mèso sf lma gia ìlec tic eikìnec thc pr thc eikonoseir c (sq ma 4.7a) eðnai 1:76 moðrec kai h apìklish tou eðnai 2:69 moðrec. Oi pðnakec 4.3, 4.4 kai 4.5 parousi zoun th mèsh tim, thn apìklish kai tic mesaðec timèc (se sqèsh me to qrìno) twn metrik n pou anafèrjhkan prohgoumènwc gia 5 eikonoseirèc. ParatÐjentai epðshc kai oi mèsec timèc gia ìlec tic eikonoseirèc. K poioc mporeð na parathr sei ìti h mèsh tim (gia ìlec tic eikonoseirèc) tou AE eðnai 3:20 moðrec kai h mèsh tim thc apìklishc eðnai 3:31 moðrec. Oi mèsec timèc kai gia tic upìloipec metrikèc eðnai epðshc mikrèc. Autì apodeiknôei ìti to proteinìmeno sôsthma mporeð na ektim sei epituq c ton 3D prosanatolismì tou pros pou se mia eikonoseir. Oi timèc twn laj n PE, TE, RE kai DE pou apokt jhkan apì ton kalôtero apì touc algorðjmouc pou parousi zontai sthn ergasða [12] paratðjentai ston PÐnaka 4.6 gia lìgouc sôgkrishc. K poioc mporeð na parathr sei pwc o proteinìmenoc algìrijmoc petuqaðnei kalôtera apotelèsmata se sqèsh me th mèjodo pou parousi zetai sto [12]. Gia par deigma, to mèsoc l joc gia to di nusma kateôjunshc (DE) gia ton proteinìmeno algìrijmo eðnai 3:8 o, pou eðnai meg lh beltðwsh se sqèsh me to l joc twn 21:3 o pou epiteôqjhke sto [12]. 'Oson afor thn upologistik poluplokìthta, 0:2 deuterìlepta an eikìna eðnai arket gia ton algìrijmo parakoloôjhshc kai 0:05 deuterìlepta an eikìna gia thn ektðmhsh tou prosanatolismoô tou pros pou se hlektronikì upologist me epexergast Intel Pentium 4 (3:01 GHz) me 1:5GB mn mh. Sunep c o algìrijmoc apaiteð 0:25 deuterìlepta an eikìna gia to sugkekrimèno montèlo upologist kai qwrðc kamða beltistopoðhsh ston k dika.

171 Μοίρες Μοίρες Μοίρες Μοίρες Μοίρες Μοίρες Μοίρες Μοίρες Μοίρες 4.5. Axiolìghsh tou Proteinìmenou sust matoc 149 Προτεινόμενος αλγόριθμος Αποτελέσματα ανθρώπων Προτεινόμενος αλγόριθμος Αποτελέσματα ανθρώπων Προτεινόμενος αλγόριθμος Αποτελέσματα ανθρώπων Χρόνος σε εικόνες Χρόνος σε εικόνες Χρόνος σε εικόνες (a) (b) (g) Προτεινόμενος αλγόριθμος Αποτελέσματα ανθρώπων Προτεινόμενος αλγόριθμος Αποτελέσματα ανθρώπων Προτεινόμενος αλγόριθμος Αποτελέσματα ανθρώπων Χρόνος σε εικόνες Χρόνος σε εικόνες Χρόνος σε εικόνες (d) (e) (st) Προτεινόμενος αλγόριθμος Αποτελέσματα ανθρώπων Χρόνος σε εικόνες Προτεινόμενος αλγόριθμος Αποτελέσματα ανθρώπων Χρόνος σε εικόνες Προτεινόμενος αλγόριθμος Αποτελέσματα ανθρώπων Χρόνος σε εικόνες (z) (h) (j) Sq ma 4.5: Oi gwnðec (se moðrec) twn kat' ektðmhsh gwni n apì to proteinìmeno sôsthma kai oi antðstoiqec timèc twn gwni n ìpwc dðnontai sth b sh dedomènwn gia aposp smata apì treic eikonoseirèc pou perièqoun ikanopoihtik kðnhsh sto prìswpo twn upokeimènwn: (a)-(g) gwnðec peristrof c, (d)-(st) gwnðec klðshc kai (z)-(j) gwnðec kôlishc.

172 Λάθος σε μοίρες Λάθος σε μοίρες Λάθος σε μοίρες Λάθος σε μοίρες Λάθος σε μοίρες Λάθος σε μοίρες Λάθος σε μοίρες Λάθος σε μοίρες Λάθος σε μοίρες 150 Kef laio 4. EktÐmhsh Trisdi statou ProsanatolismoÔ Pros pou Χρόνος σε εικόνες Χρόνος σε εικόνες Χρόνος σε εικόνες (a) (b) (g) Χρόνος σε εικόνες Χρόνος σε εικόνες Χρόνος σε εικόνες (d) (e) (st) Χρόνος σε εικόνες Χρόνος σε εικόνες Χρόνος σε εικόνες (z) (h) (j) Sq ma 4.6: To apìluto l joc se moðrec metaxô twn kat' ektðmhsh gwni n apì ton proteinìmeno algìrijmo kai twn antðstoiqwn tim n twn gwni n ìpwc dðnontai sth b sh dedomènwn gia aposp smata apì treic eikonoseirèc pou perièqoun ikanopoihtik kðnhsh sto prìswpo twn upokeimènwn: (a)-(g) gwnðec peristrof c, (d)-(st) gwnðec klðshc kai (z)-(j) gwnðec kôlishc.

173 Λάθος σε μοίρες Λάθος σε μοίρες Λάθος σε μοίρες 4.6. Sumper smata 151 Χρόνος σε εικόνες Χρόνος σε εικόνες Χρόνος σε εικόνες (a) (b) (g) Sq ma 4.7: H gwnða AE se moðrec metaxô twn 3D dianusm twn kateôjunshc twn kat' ektðmhsh gwni n apì ton proteinìmeno algìrijmo kaitwn antðstoiqwn tim ntwn gwni n ìpwc dðnontai sth b sh dedomènwn gia aposp smata apì treic eikonoseirèc pou perièqoun ikanopoihtik kðnhsh sto prìswpo twn upokeimènwn. PÐnakac 4.3: Mèsec timèc twn laj n PE, TE, RE, DE kai AE (se moðrec) gia tic eikonoseirèc thc b shc dedomènwn IDIAP upologismènec apì ton proteinìmeno algìrijmo. arijmìc eikonoseir c Mèsh tim PE TE RE DE AE mèsh tim Sumper smata Se autì to Kef laio perigr fhke ènac algìrijmoc gia ton upologismì tou 3D prosanatolismoô pros pou qrhsimopoi ntac èna 3D paramorf -

174 152 Kef laio 4. EktÐmhsh Trisdi statou ProsanatolismoÔ Pros pou PÐnakac 4.4: ApoklÐseic twn laj n PE, TE, RE, DE kai AE (semoðrec) gia tic eikonoseirèc thc b shc dedomènwn IDIAP upologismènec apì ton proteinìmeno algìrijmo. aijmìc eikonoseir c Apìklish PE TE RE DE AE mèsh tim PÐnakac 4.5: MesaÐec timèc twn laj n PE, TE, RE, DE kai AE (se moðrec) gia tic eikonoseirèc thc b shc dedomènwn IDIAP upologismènec apì ton proteinìmeno algìrijmo. aijmìc eikonoseir c MesaÐec timèc PE TE RE DE AE mèsh tim simo montèlo epif neiac. Se aut th teqnik, h fwteinìthta thc eikìnac pou perièqei to anjr pino prìswpo anaparðstatai apì èna 3D paramorf simo montèlo. DeÐxame pwc mporoôn na epektajoôn oi exis seic pa-

175 4.6. Sumper smata 153 PÐnakac 4.6: Mèsh tim, apìklish kai mesaða tim twn laj n PE, TE, RE kai DE (se moðrec) gia tic eikonoseirèc thc b shc dedomènwn IDIAP upologismènec apì ton kalôtero algìrijmo pou parousi zetai sthn ergasða [12]. PE TE RE DE Mèsh tim apìklish mesaða tim ramorf sewn gia na parakoloujhjeð epituq c to anjr pino prìswpo se mia eikonoseir kai gia na ekpaideôsei kat llhla trða dðktua parembol c RBF pou ektimoôn tic treic gwnðec tou pros pou (peristrof, klðsh kai kôlish). Ta apotelèsmata sth b sh dedomènwn IDIAP deðqnoun pwc o proteinìmenoc algìrijmoc petuqaðnei ikanopoihtik apotelèsmata.

176 154 Kef laio 4. EktÐmhsh Trisdi statou ProsanatolismoÔ Pros pou

177 BibliografÐa [1] M. Doi and Y. Aoki, Real-time video surveillance system using omni-directional image sensor and controllable camera," in Proceedings of SPIE, Real-Time Imaging VII, vol. 5012, April 2003, pp [2] U. Weidenbacher, G. Layher, P. Bayerl, and H. Neumann, Detection of head pose and gaze direction for human-computer interaction," in Perception and Interactive Technologies, Springer Berlin / Heidelberg, vol. 4021/2006, June 2006, pp [3] P. Lu, X. Zeng, X. Huang, and Y. Wang, Navigation in 3d game by markov model based head pose estimating," in Proceedings of the Third International Conference on Image and Graphics (ICIG'04), December 2004, pp [4] B. Yip and J. Jin, Pose determination and viewpoint determination of human head in video conferencing based on head movement," in Proceedings of the 10th International Multimedia Modelling Conference, Brisbane, Australia, January 2004, pp [5], 3d reconstruction of a human face with monocular camera based on head movement," in Proceedings of the Pan-Sydney area w- orkshop on Visual information processing (VIP 2003), Darlinghurst, Australia, 2003, pp

178 156 BibliografÐa [6] J. Ng and S. Gong, Multi-view face detection and pose estimation using a composite support vector machine across the view sphere," in IEEE International Workshop on Recognition, Analysis, and Tracking of Faces and Gestures in Real-Time Systems, Corfu, Greece, September 1999, pp [7] H. Song, U. Yang, J. Kim, and K. Sohn, A 3d head pose estimation for face recognition," in Proceedings of the IASTED International Conference on Signal and Image Processing (SIP 2003), Honolulu, USA, August , pp [8] C. Chien, Y. Chang, and Y. Chen, Facial expression analysis under various head poses," in Proceedings of Third IEEE Pacific Rim Conference on Multimedia, vol. 2532/2002, Taiwan, December , pp [9] E. Seemann, K. Nickel, and R. Stiefelhagen, Head pose estimation using stereo vision for human-robot interaction," in Proc. of the Sixth International Conference on Automatic Face and Gesture Recognition (AFGR04), Seoul, Korea, May , pp [10] R. Yang and Z. Zhang, Model-based head pose tracking with stereo vision," in Proc. of the Sixth International Conference onautomatic Face and Gesture Recognition (AFGR02), D.C., USA, May 2002, pp [11] L. M. Brown and Y.-L. Tian, Comparative study of coarse head pose estimation," in IEEE Workshop on Motion and Video Computing, December 2002, pp [12] S. Ba and J.-M. Odobez, Evaluation of multiple cue head pose estimation algorithms in natural environments," in IEEE Interna-

179 BibliografÐa 157 tional Conference on Multimedia and Expo (ICME), Amsterdam, July 2005, pp [13] E. Murphy-Chutorian and M. Trivedi, Head pose estimation in computer vision: A survey," IEEE Transactions on Pattern Analysis and Machine Intelligence, Accepted for future publication. [14] Q. Chen, T. Shimada, H. Wu, and T. Shioyama, Head pose estimation using both color and feature information," in 15th International Conference on Pattern Recognition (ICPR'00), vol. II, Barcelona, Spain, September 2000, pp [15] T. Huang, A. Bruckstein, R. Holt, and A. Netravali, Uniqueness of 3d pose under weak perspective: A geometrical proof," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 17, no. 12, pp , December [16] Z. Liu and Z. Zhang, Robust head motion computation by taking advantage of physical properties," in IEEE Workshop on Human Motion, Los Alamitos, CA, USA, December 2000, pp [17] Y. Hu, L. Chen, Y. Zhou, and H. Zhang, Estimating face pose by facial asymmetry and geometry," in IEEE Proceedings of the Sixth International Conference on Automatic Face and Gesture Recognition (FGR 2004), Seoul, Korea, May 2004, pp [18] M. L. Cascia and V. Athitsos, Fast, reliable head tracking under varying illumination: An approach based on registration of texturemapped 3d models," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 4, pp , April [19] C. Zhang and F. S. Cohen, 3-d face structure extraction and recognition from images using 3-d morphing and distance mapping,"

180 158 BibliografÐa IEEE Transactions on Image Processing, vol. 11, no. 11, pp , November [20] B. Kwolek, Model based facial pose tracking using a particle filter," in IEEE Proceedings of the Geometric Modeling and Imaging New Trends (GMAI'06), July 2006, pp [21] S. O. Ba and J. Odobez, A probabilistic framework for joint head tracking and pose estimation," in Proceedings of the 17th International Conference on Pattern Recognition (ICPR"04), vol. 4, 2004, pp [22] S. Z. Li, X. Lu, X. Hou, X. Peng, and Q. Cheng, Learning multiview face subspaces and facial pose estimation using independent component analysis," IEEE Transactions on Image Processing, vol. 14, no. 6, pp , June [23] R. Stiefelhagen, Y. Jie, and A. Waibel, Simultaneous tracking of head poses in a panoramic view," in Proceedings of 15th International Conference on Pattern Recognition, 2000, vol. 3, Barcelona, Spain, September 2000, pp [24] V. Vapnik, The nature of statistical learning theory. Springer Verlag, [25] Y. Li, S. Gong, J. Sherrah, and H. Liddell, Support vector machine based multi-view face detection and recognition," Image and Vision Computing, vol. 1, no. 5, p , May [26] Y. Li, S. Gong, and H. Liddell, Support vector regression and classification based multi-view face detection and recognition," in IEEE International Conference on Automatic Face and Gesture Recognition, Grenoble, France, March 2004, pp

181 BibliografÐa 159 [27] A. Rajwade and M. Levine, Facial pose from 3d data," Image and Vision Computing, vol. 24, no. 8, pp , August [28] B. M. C. Nastar and A. Pentland, Generalized image matching: Statistical learning of physically-based deformations," in 4th European Conference on Computer Vision (ECCV'96), vol. 1, Cambridge, UK, April 1996, pp [29] B. Moghaddam, C. Nastar, and A. Pentland, A bayesian similarity measure for direct image matching," in International Conference on Pattern Recognition (ICPR 1996), Vienna, Austria, August 1996, pp [30] A. Pentland and S. Sclaroff, Closed-form solutions for physically based shape modeling and recognition," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 7, pp , July [31] C. Nastar and N. Ayache, Frequency-based nonrigid motion analysis: Application to four dimensional medical images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18, no. 11, pp , November [32] S. Krinidis, C. Nikou, and I. Pitas, Reconstruction of serially a- cquired slices using physics-based modelling," IEEE Transactions on Information Technology in Biomedicine, vol. 7, no. 4, pp , December [33] C. Nikou, G. Bueno, F. Heitz, and J. Armspach, A joint physicsbased statistical deformable model for multimodal brain image analysis," IEEE Transactions on Medical Imaging, vol. 20, no. 10, pp , October 2001.

182 160 BibliografÐa [34] C. Nastar and N. Ayache, Fast segmentation, tracking, and analysis of deformable objects," in Proceedings of the Fourth International Conference on Computer Vision (ICCV'93), Berlin, Germany, May 1993, pp [35] M. Krinidis, N. Nikolaidis, and I. Pitas, The discrete modal transform and its application to lossy image compression," Signal Processing: Image Communication, vol. 22, no. 5, pp , June [36], 2d feature point selection and tracking using 3d physics-based deformable surfaces," IEEE Transactions on Circuits and Systems for Video Technology, vol. 17, no. 7, pp , July [37] R. Lienhart and J. Maydt, An extended set of Haar-like features for rapid object detection," in IEEE International Conference on Image Processing (ICIP02), Rochester, New York, USA, September 2002, pp [38] P. Viola and M. J. Jones, Robust real-time object detection," Cambridge Research Laboratory, Tech. Rep. 01, [39] S. Haykin, Neural Networks: A comprehensive Foundation, 2nd E- dition. Englewood Cliffs: Macmillan Publishing Company, [40] D. Broomhead and D. Lowe, Multivariable functional interpolation and adaptive networks," Complex Systems, vol. 2, pp , 1998.

183 Kef laio 5 Kat tmhsh 'Egqrwmwn Eikìnwn Basismènh sthn Enèrgeia Idioqarakthristik n Paramorf simwn Montèlwn 5.1 Eisagwg H kat tmhsh eikìnac diadramatðzei ènan jemeli dh rìlo se pollèc efarmogèc thc teqnht c ìrashc. Stic proseggðseic anagn rishc protôpwn [1], h kat tmhsh eikìnac epitrèpei thn apomìnwsh eniaðwn antikeimènwn twn mer n touc, pou mporeð na dieukolônei sth sunèqeia thn anagn rish touc. Suneq c ereunhtik prosp jeia èqei katablhjeð epðshc sthn autìmath epishmeðwsh eikìnac (image annotation) [2] kai sthn an kthsh thc [3], ì- pou h kat tmhsh eikìnac eðnai qr simh, dedomènou ìti oi proanaferjeðsec diadikasðec eðnai akribèc kai qronobìrec. Epiplèon, di forec melètec basismènec sthn kat tmhsh eikìnac èqoun anaptuqjeð prìsfata sqetik me thn an lush skhn c [4]. H kat tmhsh eikìnac qrhsimopoieðtai epðshc san 161

184 162 Kef laio 5. Kat tmhsh Eikìnwn arqikì b ma sthn parakoloôjhsh antikeðmenwn [5], ìpou h akrib c jèsh enìc antikeimènou eðnai shmantik. Se ìlec tic proanaferjeðsec efarmogèc, o kôrioc stìqoc eðnai na qwristeð mia eikìna se omoiogeneðc perioqèc, èna b ma pou èqei apodeiqjeð ìti mporeð na wj sei th genik algorijmik apìdos touc. Proklhtik probl mata sthn kat tmhsh eikìnac prokôptoun apì thn Ôparxh eikìnwn pou apeikonðzoun fusikèc skhnèc se qamhlèc analôseic, anomoiogeneðc fwtismoôc, allagèc sto mègejoc thc kai poll lla. To anjr pino optikì sôsthma eðnai polô kalì sthn kat tmhsh miac eikìnac me fusik skhn se aisjhtik omoiogeneðc perioqèc. Wstìso, eðnai exairetik dôskolh h autìmath kat tmhsh tètoiwn eikìnwn se aisjhtik omoiogeneðc perioqèc. Wc ek toôtou, stic teleutaðec dôo dekaetðec, entatik èreuna èqei diexaqjeð se aut n thn perioq. To ereunhtikì endiafèron se autì to Kef laio strèfetai stouc anepðbleptouc (unsupervised) algorðjmouc kat tmhshc eikìnac, pou mporoôn na diairejoôn eurèwc se treic kathgorðec: algorðjmouc basismènouc se perioqèc, basismènouc se gr - fouc kai basismènouc se qarakthristik shmeða [6, 7]. Oi perissìterec tètoiec proseggðseic kat tmhshc eikìnac sthrðzontai sth beltistopoðhsh enìc krithrðou kat tmhshc. Prìsjetec plhroforðec gia tic proanaferjeðsec kathgorðec kat tmhshc eikìnac mporoôn na brejoôn stic ergasðec episkìphshc [8, 9]. Oi algìrijmoi kat tmhshc eikìnac pou basðzontai se perioqèc [10] - [12] prospajoôn na diaqwrðsoun thn eikìna omadopoi ntac geitonik eikonostoiqeða, basizìmenoi sth fwteinìthta, to qr ma kai thn uf thc eikìnac. Katìpin, oi parakeðmenec perioqèc sugqwneôontai, k tw apì k - poio krit rio pou perilamb nei thn omoiogèneia ta diaqwristik ìria twn perioq n. Sthn ergasða [10], proteðnetai h sunduasmènh qr sh statistik n katanom n apokrðsewn fðltrwn gia to qarakthrismì uf c mèsa se èna kajorismèno plaðsio epipèdwn. H kat tmhsh sthrðzetai basik sthn elaqistopoðhsh miac sun rthshc perioq n. Aut h sun rthsh orðzetai

185 5.1. Eisagwg 163 san mia Kullback-Leibler metrik bar n, h opoða basðzetai stic katanomèc twn apokrðsewn fðltrwn uf c pou upologðzontai mèsa stic perioqèc thc eikìnac kai sta diaqwristik ìria twn perioq n. Pollèc ereunhtikèc prosp jeiec èqoun pragmatopoihjeð se algorðjmouc kat tmhshc eikìnac pou basðzontai se gr fouc [13]-[16]. Autèc oi proseggðseic qrhsimopoioôn ènan mh kateujunìmeno gr fo gia na antiproswpeôsoun ta eikonostoiqeða thc eikìnac. K je akm tou gr fou è- qei èna b roc pou antiproswpeôei thn omoiìthta zeug n eikonostoiqeðwn. O stìqoc eðnai na elaqistopoihjeð to kìstoc diaqwrismoô tou gr fou se diaqwrizìmena sônola. Sthn teqnik [13], k je eikonostoiqeðo thc eikìnac antistoiqeð se ènan kìmbo tou gr fou kai ta geitonik eikonostoiqeða sundèontai me mh kateujunìmenec akmèc. H anomoiìthta metaxô twn eikonostoiqeðwn metriètai kai ta b rh orðzontai se k je akm tou gr fou. To krit rio kat tmhshc basðzetai sto bajmì metablhtìthtac twn geitonik n perioq n thc eikìnac. Kat sunèpeia, opoiad pote kat tmhsh prokaleðtai apì èna uposônolo twn akm n tou gr fou. Sth mèjodo pou anaptôqjhke sth [14], eis qjh èna jewrhtikì krit rio apokaloômeno kanonikopoihmènh perikop (normalized cut), gia th mètrhsh thc katallhlìthtac/ apotelesmatikìthtac miac perioq c thc eikìnac. H elaqistopoðhsh autoô tou krithrðou antimetwpðsthke san èna genikeumèno idioprìblhma. Ta idiodianôsmata qrhsimopoi jhkan gia na kataskeu - soun ikanopoihtik qwrðsmata thc eikìnac kai h diadikasða epanal fjhke prokeimènou na apokthjoôn oi omoiìmorfec perioqèc thc eikìnac. H katallhlìthta thc qr shc qarakthristik n gnwrism twn gia thn kat tmhsh eikìnac èqei diereunhjeð apì polloôc epist monec [17] - [19]. Qarakthristik gnwrðsmata qr matoc kai uf c axiopoioôntai mazð me th gn sh twn anjr pinwn optik n mhqanism n antðlhyhc prokeimènou na a- xiologhjeð h omoiogèneia twn perioq n thc eikìnac. Sthn ergasða [17], o algìrijmoc Mean-Shift qrhsimopoieðtai gia th an lush qarakthristik n gnwrism twn, ìpou o q roc twn qarakthristik n gnwrism twn mporeð na

186 164 Kef laio 5. Kat tmhsh Eikìnwn jewrhjeð san mia empeirik sun rthsh puknìthtac pijanìthtac thc antiproswpeuìmenhc paramètrou. O Mean-Shift orðzetai wc h diafor metaxô twn deigm twn qarakthristik n gnwrism twn kai tou stajmismènou mèsou ìrou touc, qrhsimopoi ntac ènan aktinikì summetrikì pur na gia ta b rh kai ta shmeða deigm twn san kèntro twn pur nwn. H mèjodoc Mean- Shift sugklðnei sta shmeða ìpou h ektðmhsh thc sun rthshc puknìthtac pijanìthtac èqei mhdenik klðsh. Kat sunèpeia, k je eikonostoiqeðo thc eikìnac sundèetai me th puknìthta thc perioq c pou brðsketai sth geitoni tou, met thn efarmog thc Mean-Shift an lushc q rou. Katìpin, taeikonostoiqeða omadopoioôntai apì ènan algìrijmo sugq neushc. Sth mèjodo pou perigr fetai sth [7], qrhsimopoi jhkan 2D apokrðseic fðltrwn uf c apl par jura fðltrwn stajeroô megèjouc prokeimènou na apokthjoôn qarakthristik gnwrðsmata uf c. H katanom twn qarakthristik n gnwrism twn uf c kajorðzetai apì th qr sh enìc mðgmatoc gkaoussian n katanom n. H mðxh twn katanom n katatèmnetai apotelesmatik apì ènan aplì algìrijmo suspeðrwshc pou proèrqetai apì mia prosèggish apwlestik c sumpðeshc dedomènwn. H kat tmhsh eikìnac epitugq netai me thn elaqistopoðhsh tou m kouc kwdikopoðhshc twn dianusm twn pou apartðzontai apì ta qarakthristik gnwrðsmata. Autì to Kef laio parousi zei ènan algìrijmo kat tmhshc ègqrwmwn eikìnwn, o opoðoc ja onom zetai sth sunèqeia kat tmhsh eikìnac idioqarakthristik n ( Modal Image Segmentation (MIS) ). Efalt rio thc mejìdou MIS apotèlese h teqnik pou parousi sthke sthn ergasða [20] kai sto Kef laio 2,ta opoða stoqeôoun sthn epilog kai thn parakoloôjhsh qarakthristik n shmeðwn se eikonoseirèc, qrhsimopoi ntac paramorf sima montèla epif neiac. Sto Kef laio 2, èna endi meso apotèlesma thc diadikasðac paramìrfwshc apodeðqjhke ìti eðnai ènac kainotìmoc sunduasmìc di forwn mask n anðqneushc gramm n kai akm n. Kat sunèpeia, ja mporoôse na apodeiqjeð kat llhlo gia thn anðqneush orðwn geitonik n perioq n miac eikìnac. Me b sh autìn ton sullogismì, eis goume mia nèa

187 5.1. Eisagwg 165 sun rthsh enèrgeiac, pou ekfr zei thn topik omalìthta miac perioq c eikìnac, prokeimènou na katatmhjeð mia ègqrwmh eikìna. O pur nac aut c thc ergasðac apoteleðtai apì dôo b mata. Arqik, qrhsimopoieðtai mia mèjodoc kb ntishc qr matoc, pou basðzetai stic metatopðseic kìmbwn tou paramorf simou montèlou epif neiac, prokeimènou na lhfjeð mia qondroeid c antipros peush thc eikìnac. Afetèrou, h proteinìmenh sun rthsh enèrgeiac qrhsimopoieðtai san krit rio gia thn kat tmhsh thc eikìnac. 'Ena di gramma ro c, pou apeikonðzei tic diaforetikèc enìthtec tou MIS algorðjmou, parousi zetai sto sq ma 5.1. H fwteinìthta thc eikìnac kai oi qwrikèc thc plhroforðec sundu zontai kai apoteloôn exwterikèc dun meic enìc paramorf simou montèlou epif neiac. O proteinìmenoc algìrijmoc kb ntishc qr matoc basðzetai stic metatopðseic kìmbwn tou paramorf simou montèlou epif neiac (DSM) pou proseggðzei thn eikìna. H fwteinìthta thc eikìnac energeð wc exwterik dônamh tou 3D DSM.'Ena b roc, pou ekfr zei thn omalìthta twn topik n perioq n thc eikìnac, orðzetai gia k je eikonostoiqeðo thc eikìnac, ta opoða sth sunèqeia qwrðzontai gia na apotelèsoun om dec qr matoc. H teqnik thc an lushc idioqarakthristik n, pou qrhsimopoieðtai prokeimènou na perigrafoôn kai na analujoôn oi paramorf seic tou montèlou, stoqeôei sthn axiolìghsh thc proteinìmenhc sun rthshc enèrgeiac. EÐnai mia enallaktik prosèggish sthn mesh olokl rwsh tou sust matoc twn diaforik n exis sewn pou prokôptoun apì opoiad pote peperasmènh mèjodo stoiqeðwn [21]. BasÐzetai sth jèsh twn kìmbwn, dhlad, ekfr zei tic qronik exarthmènec paramorf seic se sqèsh me th jèsh twn kìmbwn tou sust matoc. Sthn proteinìmenh mèjodo, oi prìtupec exis seic paramìrfwshc epekt jhkan prokeimènou na epiteuqjeð mia gr gorh efarmog. H teqnik thc an lushc idioqarakthristik n qrhsimopoi jhke se poikðlec efarmogèc gia thn epðlush twn paramorf sewn montèlwn, dhlad, gia thn an lush thc kðnhshc stere n antikeimènwn [21], gia thn eujugr mmish seiriak epðkthtwn fet n [22], gia thn polutropik an lush

188 166 Kef laio 5. Kat tmhsh Eikìnwn Εικόνα εισόδου ένα DSM εφαρμόζεται σε κάθε εικονοστοιχείο Τα εικονοστοιχεία κατηγοριοποιούνται σε ομάδες χρώματος βασιζόμενα στις μετατοπίσεις των κόμβων του DSM Κβαντοποίηση Χρώματος Κατάτμηση Εικόνας Αρχικό μέγεθος του DSM Για κάθε DSM Χωρίζοντας τις περιοχές εικόνας Το DSM κλιμακώνεται Υπολογίζεται η E q Υπολογίζεται η μέση τιμή της E q Μέση τιμή E<E q o Οχι Μείωση του μεγέθους του DSM Επέκταση Περιοχών Ναι Καθορισμός μιας περιοχής Ανασυγκρότηση περιοχής Επέκταση περιοχής Συγχώνευση Περιοχών Κατετμημένη εικόνα Sq ma 5.1: Di gramma ro c tou proteinìmenou algorðjmou kat tmhshc eikìnac.

189 5.1. Eisagwg 167 eikìnwn egkef lou [23], gia sumpðesh eikìnac [24] kai gia thn parakoloôjhsh 2D antikeimènwn [20]. Se autì to Kef laio, h teqnik thc an lushc idioqarakthristik n qrhsimopoieðtai me ènan kajolik diaforetikì kai nèo trìpo, autìn thc kat tmhshc ègqrwmwn eikìnwn. H kôria sumbol autoô tou KefalaÐou eðnai ousiastik o sqediasmìc miac nèac sun rthshc enèrgeiac pou basðzetai sth qr sh thc teqnik a- n lushc idioqarakthristik n gia thn epðlush twn paramorf sewn tou montèlou pou qrhsimopoieðtai gia na proseggðsei thn eikìna. Oi topikèc qwrikèc plhroforðec twn perioq n eikìnac, pou exart ntai apì thn kb - ntishc qr matoc, qrhsimopoioôntai wc exwterikèc dun meic gia na kajodhg soun to DSM. H kat tmhsh eikìnac epitugq netai me to sunduasmì thc sun rthshc enèrgeiac tou DSM kai enìc algìrijmou sunènwshc perioq n pou prosarmìzetai sthn proteinìmenh sun rthsh enèrgeiac. Sto tèloc, ènac algìrijmoc sugq neushc perioq n parèqei thn kat tmhsh thc eikìnac. Oi leptomèreiec tou algorðjmou ja parasqejoôn parak tw. O MIS algìrijmoc dokim sthke sth b sh dedomènwn kat tmhshc eikìnwn tou Mpèrkleô [25], h opoða apoteleðtai apì èna uposônolo twn eikìnwn thc b shc Corel. Ta apotelèsmata deðqnoun ìti o MIS algìrijmoc xepern gnwstoôc algìrijmouc kat tmhshc eikìnac. SunoyÐzontac, oi suneisforèc autoô tou KefalaÐou eðnai oi ex c: Mia nèa sun rthsh enèrgeiac, pou proèrqetai apì th teqnik an lushc idioqarakthristik n, qrhsimopoieðtai wc krit rio gia thn kat tmhsh ègqrwmwn eikìnwn. Aut h sun rthsh enèrgeiac qrhsimopoieð èna upopro ìn thc diadikasðac paramìrfwshc gia na ekfr sei thn topik omalìthta miac perioq c thc eikìnac. 'Enac sunduasmìc twn qwrik n plhrofori n me th fwteinìthta thc eikìnac, qrhsimopoieðtai me ènan kainotìmo trìpo ste na apoteleð tic exwterikèc dun meic pou odhgoôn to DSM. Parousi zetai epðshc, ènac trìpoc gia na prosarmostoôn oi exis seic paramìrfwshc tou montèlou prokeimènou na epiteuqjeð mia gr gorh efarmog touc. ProteÐnetai ènac algìrijmoc kb ntishc qr matoc pou ekmetalleôetai tic

190 168 Kef laio 5. Kat tmhsh Eikìnwn metatopðseic kìmbwn tou 3D DSM.Tèloc, qrhsimopoieðtai ènac algìrijmoc suspeðrwshc perioq n [12], o opoðoc elaqistopoieð thn proteinìmenh sun rthsh enèrgeiac. To upìloipo tou KefalaÐou organ netai wc ex c. Sthn Par grafo 5.2, parousi zontai mia sôntomh perigraf thc diadikasðac paramìrfwshc tou montèlou pou basðzetai sthn teqnik thc an lushc idioqarakthristik n kai h apìkthsh thc sun rthshc enèrgeiac mazð me th gr gorh epðlush twn exis sewn paramìrfwshc pou proteðnetai. H mèjodoc kb ntishc qr matoc perigr fetai sthn Par grafo 5.3. Sthn Par grafo 5.4, eis getai o algìrijmoc kat tmhshc ègqrwmwn eikìnwn. H apìdosh thc proteinomènhc mejìdou exet zetai sthn Par grafo 5.5. Tèloc, ta sumper smata anafèrontai sthn Par grafo Teqnik thc An lushc Idioqarakthristik n kai Apìkthsh thc Proteinìmenhc Sun rthshc Enèrgeiac Se aut thn Par grafo, ja eisaqjeð mia kainoôrgia sun rthsh enèrgeiac pou pro lje apì thn teqnik thc an lushc idioqarakthristik n, h opoða èqei perigrafeð analutik sta Kef laia 2 kai 3. Epiplèon, ja perigrafeð mia gr gorh teqnik gia thn epðlush thc diadikasðac paramìrfwshc pou basðzetai sthn teqnik thc an lushc idioqarakthristik n. Se aut thn Par grafo, h fwteinìthta thc upì exètashc eikìnac perigr fetai se sqèsh me tic paramorf seic tou paramorf simou montèlou. To mègejoc tou montèlou ( se arijmì kìmbwn) pou qrhsimopoieðtai gia na proseggðsei thn epif neia thc eikìnac eðnai Ðso me to mègejoc thc eikìnac (se eikonostoiqeða). To tetr pleuro montèlo mac arqikopoieðtai kai ta stoiqeða ~u in w+j(r) upologðzontai wc akoloôjwc, qrhsimopoi ntac tic e- xis seic (2.5), (2.8), (2.9) kai (2.11) pou èqoun analujeð se prohgoômena

191 5.2. An lush Idioqarakthristik n kai Sun rthsh Enèrgeiac 169 Kef laia: ~u in w+j(r) = P N P h N w n=1 (1 +! 2 (i; j))q PN h n=1 n0 =1 F r (n; n 0 )ffi n;n 0(i; j) P N w n0 =1 ffi 2 n;n0(i; j) ; (5.1) ìpou F r (n; n 0 ) eðnai to r-stì stoiqeðo tou dianôsmatoc twn exwterik n dun mewn pou askoôntai sto eikonostoiqeðo (n; n 0 ), dhlad, F r (n; n 0 ) = f nn h+n0(r). Mia nèa sun rthsh enèrgeiac, pou ja apokaleðtai sto ex c enèrgeia idioqarakthristik n (ME), eis getai me th qrhsimopoðhsh twn stoiqeðwn ~u in w+j(r) tou DSM: 1 E = N h N w 1 vu uxxnw t N h i=1 j=1 (~u in w+j(x in w+j)+~u in w+j(y in w+j)) 2 ; (5.2) kai h ME perigr fetai apì thn enèrgeia E wc ex c: E q = 1 E. H bajmwt tim E q ja kaleðtai apì ed kai sto ex c enèrgeia idioqarakthristik n, epeid sqetðzetai mesa me thn enèrgeia tou paramorf simou montèlou kai ekfr zei thn topik omalìthta miac perioq c thc eikìnac. H qrhsimìtht thc sthn kat tmhsh eikìnac ja parousiasteð sthn Par grafo 5.4. Qrhsimopoi ntac ticexis seic (2.5) kai (2.12), oi paramorf seic u xy (r) kat m koc tou xona r tou paramorf simou montèlou pou antistoiqoôn sto (x; y) eikonostoiqeðo, me b sh thn teqnik an lushc idioqarakthristik n gia mia epðpedh topologða, mporoôn na perigrafoôn wc ex c: u xy (r) = Nh 1 X i=0 Nw 1 X j=0 P N h n=1 P N w (1 +! 2 (i; j)) P Nh n=1 P N w n0 =1 ffi 2 n;n0(i; j) ffi x;y(i; j); (5.3) n0 =1 F r (n; n 0 )ffi n;n 0(i; j) ìpou u xy (r) eðnai h r sunist sa tou stoiqeðou u (x 1)N w +y tou dianôsmatoc u kai r = x; y; z. H parap nw exðswsh parousi zei thn telik èkbash thc teqnik c an lushc idioqarakthristik n gia thn paramìrfwsh thc epif - neiac miac eikìnac. H ìlh diadikasða thc paramìrfwshc èqei barô upologistikì fìrto, eidik ìtan prìkeitai na qrhsimopoihjeð se efarmogèc

192 170 Kef laio 5. Kat tmhsh Eikìnwn pragmatikoô qrìnou. Gia autìn ton lìgo, parousi zoume mia gr gorh epðlush thc diadikasða paramìrfwshc tou montèlou, h opoða basðzetai sto metasqhmatismì Idioqarakthristik n diakritoô qrìnou (DMT) pou parousi zetai sto Kef laio 3 kai sthn ergasða [24]. Ta stoiqeða twn paramorf sewn u tou 3D DSM pou efarmìzontai sthn epif neia thc eikìnac I(x; y) dðnontai apì thn exðswsh (3.21), h opoða mporeð na xanagrafeð wc ex c: kai u xy (r) = F(i; j) = Nh 1 X i=0 Nw 1 X j=0 h 1+ ffi x;y (i; j) F(i; j) q PN P ; (5.4) h N w n=1 n0 =1 ffi 2 n;n0(i; j) x =1;:::;N h ; y =1;:::;N w ; sin 2 ßi 2Nh 1 + sin 2 ßj 2Nw ic(i; j); (5.5) ìpou F(i; j) eðnai o metasqhmatismìc DMT, C(i; j) eðnai o 2D diakritìc metasqhmatismìc sunhmðtonou (DCT) [29], =4 k, k eðnai h sklhrìthta m twn elathrðwn tou montèlou kai m h m za k je kìmbou tou montèlou. OmoÐwc, ta stoiqeða ~u in w+j(r) mporoôn na xanagrafoôn qrhsimopoi ntac ton DMT wc ex c: ~u in w+j(r) =F(i; j): (5.6) K poioc mporeð eôkola na parathr sei ìti o DMT antistoiqeð se ènan mh diaqwrðsimo metasqhmatismì. Kat sunèpeia, h upologistik poluplokìtht tou gia mia N N eikìna eðnai thc t xhc O(N 4 ). Wc ek toôtou, afoô o 2D DMT mporeð na upologisteð apì ton DCT mèsw thc (5.5), h poluplokìthta tou mporeð na meiwjeð se O(N 2 log 2 N), e n qrhsimopoihjoôn gr goroi upologismoð tou DCT [30]. Gia ìla ta peir mata pou pragmatopoi jhkan se autì to Kef laio, oi upologismoð tou genikeumènou dianôsmatoc ~u in w+j(r) kai oi paramorf seic u xy (r) kat m koc tou r xona tou DSM upologðsthkan qrhsimopoi ntac tic exis seic (5.6) kai (5.4), antistoðqwc.

193 5.3. Kb ntish Qr matoc Kb ntish Qr matoc Se aut thn Par grafo perigr fetai en suntomða, to pr to b ma tou proteinìmenou algorðjmou kat tmhshc eikìnac, dhlad mia mèjodoc kb - ntishc qr matoc. H mèjodoc aut, parèqei ènan mikrì arijmì qrwm twn pou mporoôn na perigr youn epark c tic diaforetikèc perioqèc miac eikìnac. H basik idèa thc, proèrqetai apì mia parìmoia teqnik filtrarðsmatoc om dwn, h opoða eis qjh sthn ergasða [31]. Aut h teqnik epekt jhke, ètsi ste to di nusma qarakthristik n gnwrism twn thc teqnik c filtrarðsmatoc om dwn na perilamb nei tic metatopðseic (3.25) tou kìmbwn tou DSM, antð twn plhrofori n qr matoc k je eikonostoiqeðou thc eikìnac. 'Ena DSM megèjouc R w R w efarmìzetai sto eikonostoiqeðo x q = (x q ;y q ) thc eikìnac I. Ta stoiqeða tou dianôsmatoc exwterik n dun mewn f sthn exðswsh (3.16) jewr jhkan Ðsa me mhdèn kat m koc tou x kai y xona, dhlad, f i (x) = f i (y) = 0 kai i = 0;:::;R 2 w. Apì thn llh, ta stoiqeða aut n twn dun mewn kat m koc tou z xona ( xonac fwteinìthtac) jewr jhkan an loga proc th fwteinìthta tou eikonostoiqeðou (x q ;y q ): f (x q 1)Nw+yq(z q ) = I(x q ;y q ), ìpou f (x q 1)Nw +yq(z q ) eðnai ta stoiqeða tou z xona tou (x q 1)N w + y q -stoô stoiqeðou tou dianôsmatoc f. Upì autèc tic sunj kec, to montèlo paramorf netai mìno kat m koc tou z xona, anaparist ntac th fwteinìthta thc eikìnac. Epeid trða diaforetik qr mata up rqoun gia k je eikonostoiqeðo miac ègqrwmhc eikìnac, qrhsimopoieðtai kai èna diaforetikì montèlo gia k je qr ma. Gia k je kìmbo tou DSM, upologðzetai h akìloujh apìstash: d iq = ku q u i k; (5.7) ìpou u i perièqei tic metatopðseic tou i-stoô kìmbou tou montèlou DSM gia ìlec tic qrwmatikèc sunist sec kai k k dhl nei thn EukleÐdeia apìstash. Taxinom ntac se aôxousa seir ìla ta eikonostoiqeða x i tou parajôrou

194 172 Kef laio 5. Kat tmhsh Eikìnwn W pou eðnai kentrarismèno sto eikonostoiqeðo x q, wc proc tic apost seic touc d iq, eôkola paraskeu zetai to di nusma G q,to opoðo kai apokaleðtai ìmoia om da tou eikonostoiqeðou x q : G q = fx i ; i 2 [1;R 2 w]g; (5.8) ìpou x i eðnai to i-stì eikonostoiqeðo sto par juro W. O kat llhloc arijmìc stoiqeðwn k je ìmoiac om dac kajorðzetai me th qrhsimopoðhsh twn apost sewn d iq sthn ektðmhsh tou Fisher, ìpwc perigr fetai sthn ergasða [31]. O arijmìc stoiqeðwn twn omoðwn om dwn mporeð na jewrhjeð wc mia par metroc gia ton èlegqo thc afaðreshc tou jorôbou kai thn exom lunsh thc eikìnac, energ ntac kat trìpo parìmoio me èna filtr risma thc. Efarmìzontac èna DSM megèjouc R w R w se k je eikonostoiqeðo x q thc eikìnac I, k je eikonostoiqeðo thc eikìnac sundèetai me èna b roc pou deðqnei thn omalìthta thc perioq c gôrw apì autì to eikonostoiqeðo. To b roc g(x q ) orðzetai wc ex c: g(x q )=e Tq ; (5.9) ìpou T q eðnaihmègisth apìstash d iq twn G q. Sunep c, ta eikonostoiqeða stic omoiìmorfec perioqèc thc eikìna sundèontai me megalôtera b rh se sqèsh me ta eikonostoiqeða stic perioqèc me èntonh uf. Autì to b roc qrhsimopoieðtai gia na pragmatopoihjeð o kbantismìc thc eikìnac. Mia tropopoihmènh èkdosh tou genikoô algorðjmou Lloyd [32] qrhsimopoi jhke gia na pragmatopoihjeð h kb ntish ègqrwmwn eikìnwn. Upojètoume ìti h eikìna I kbantopoieðtai se ènan arijmì qrwm twn C n. H arqik tim tou C n tðjetai dipl sia thc mèshc tim c tou g(x q ) gia olìklhrh thn eikìna. To stajmismèno mètro D n thc om dac qr matoc C n dðnetai apì th sqèsh: X D n = g(x i )kx i c n k 2 ; (5.10) x i 2 C n

195 5.4. Kat tmhsh eikìnac 173 ìpou c n kajorðzetai apì: c n = P x(i)2 g(x C n i)x(i) P x(i)2 g(x : (5.11) C n i) H metrik diastrèblwshc qrhsimopoieðtai gia na aniqneujoôn poiec om dec prèpei na diaqwristoôn ètsi ste na epiteuqjeð o arqikìc arijmìc twn om dwn qr matoc. H qr sh twn bar n g(x i ) sthn (5.10) diasfalðzei ìti ta eikonostoiqeða stic anomoiìmorfec perioqèc thc eikìnac den ja ephre soun tìso ton kbantismì thc eikìnac ìso kai ta eikonostoiqeða stic omoiìmorfec perioqèc thc eikìnac. Sto telikì b ma thc mejìdou, ìlec oi om dec qr matoc, twn opoðwn h el qisth apìstash metaxô twn kèntrwn touc eðnai mikrìterh apì èna prokajorismèno kat tato ìrio, sugqwneôontai qrhsimopoi ntac è- nan susswreutikì algìrijmo omadopoðhshc [33]. H kbantismènh eikìna apoktiètai anajètontac se k je eikonostoiqeðo to piokontinì tou kèntro apì thn om da qrwm twn. 'Ena par deigma tou proteinìmenou algìrijmou kb ntishc miac ègqrwmhc eikìnac apeikonðzetai sto sq ma 5.2. H pr th eikìna (sq ma 5.2a) diaqwrðsthke se 7 om dec qr matoc, h deôterh eikìna (sq ma 5.2b) se 11 om dec kai h trðth (sq ma 5.2g) se 12 om dec qr matoc. 5.4 Kat tmhsh eikìnac basismènh sthn E- nèrgeia Idioqarakthristik n Se aut thn Par grafo, eis getai ènac algìrijmoc kat tmhshc ègqrwmwn eikìnwn pou sundu zei thn kb ntishc qr matoc kai 3D paramorf sima montèla epif neiac. O algìrijmoc kb ntishc qr matoc pou perigr fhke sthn prohgoômenh Par grafo, efarmìzetai sthn eikìna prokeimènou na exaqjeð mia qondroeid c antipros peush thc. Kat sunèpeia, h fwtei-

196 174 Kef laio 5. Kat tmhsh Eikìnwn (a) (b) (g) (d) (e) (st) Sq ma 5.2: (a)-(g) Oi arqikèc eikìnec. (d)-(st) Oi antðstoiqec kbantismènec eikìnec. nìthta thc eikìnac se aut thn Par grafo, eðnai h èxodoc thc mejìdou kb ntishc.

197 5.4. Kat tmhsh eikìnac 175 Upojètoume pwc èna 3D DSM megèjouc R W R W efarmìzetai se èna eikonostoiqeðo x q = (x q ;y q ) thc eikìnac I. Se aut thn Par grafo, ta stoiqeða tou dianôsmatoc exwterik n dun mewn f sthn exðswsh (2.4) pou energoôn sto DSM lamb nontai na eðnai Ðsa se mhdèn kat m koc tou z xona (fwteinìthta thc eikìnac), dedomènou ìti èqoun dh qrhsimopoihjeð sth mèjodo kb ntishc qr matoc. Ston algìrijmo kat tmhshc eikìnac, qrhsimopoioôntai mìno oi qwrikèc plhroforðec tou DSM, dhlad, oi x kai y sunist sec tou DSM. Kat sunèpeia, ta stoiqeða twn exwterik n dun mewn kat m koc tou x xona axiologoôntai wc ex c: f i;x = ( xi μx; I(x i )=I(x q ) 0; alloô ; (5.12) ìpou μx eðnai to kèntro puknìthtac ìlwn twn eikonostoiqeðwn x i pou èqoun thn Ðdia fwteinìthta meto x q. OmoÐwc, oi sunist sec twn exwterik n dun mewn kat m koc tou y xona jewr jhkan Ðsec me th qwrik plhroforða y tou DSM: f i;y = ( y i μy; I(x i )=I(x q ) ; (5.13) 0; alloô ìpou μy eðnai to kèntro puknìthtac ìlwn twn eikonostoiqeðwn x i pou èqoun thn Ðdia fwteinìthta meto x q. Gia na epiteuqjeð h kat tmhsh eikìnac, h mèjodoc MIS efarmìzei se k je eikonostoiqeðo x q thc eikìnac, èna 3D DSM megèjouc R W R W kai sth sunèqeia ekmetalleôetai thn proteinìmenh sun rthsh enèrgeiac E q gia to eikonostoiqeðo x q qrhsimopoi ntac thn (5.2). H bajmwt tim E q ekfr zei thn topik omalìthta miac perioq c thc eikìnac, dhlad, ìso mikrìterh eðnai h tim E q, tìso pijanìtero h perioq thc eikìnac gôrw apì to eikonostoiqeðo x q na antistoiqeð se mia omoiìmorfh perioq. Wc ek toôtou, to E q mporeð na jewrhjeð mia èndeixh gia to an èna eikonostoiqeðo eðnai kont sta sônora diaforetik n perioq n thc eikìnac ìqi. Sto sq ma 5.3, apeikonðzetai h enèrgeia ME E q gia ìla ta eikonostoiqeða dôo

198 176 Kef laio 5. Kat tmhsh Eikìnwn diaforetik n eikìnwn. To mègejoc tou paramorf simou montèlou tan kìmboi, pou efarmìsthke se eikìnec eikonostoiqeðwn. H eikìna sto sq ma 5.3a apoteleðtai apì omoiìmorfec perioqèc, sugkrinìmenh me thn eikìna tou sq matoc 5.3g, h opoða perièqei perissìterec enallagèc se perioqèc. O mèsoc ìroc E q gia thn eikìna sto sq ma 5.3a eðnai 0:3807, en gia thn eikìna sto sq ma 5.3g eðnai sqedìn h dipl sia (0:6855), dedomènou ìti h teleutaða èqei perissìtera eikonostoiqeða pou brðskontai se sônora diaforetik n perioq n. To mègejoc R w R w tou DSM kajorðzei to mègejoc thc perioq c thc eikìnac pou exet zetai. Dedomènou ìti eðnai dôskolo na gnwrðzoume ek twn protèrwn to kat llhlo mègejoc R w R w tou DSM, proteðnetai èna metablhtì mègejoc parajôrou, pou orðzetai wc h kalôterh dunat perioq gia thn anðqneush twn orðwn diaforetik n perioq n sthn eikìna I. Mikrèc paramorf simec epif neiec (dhlad, par jura mikroô megèjouc R w R w ) eðnai qr simec gia thn akrib anðqneush twn orðwn geitonik n perioq n, en meg lec paramorf simec epif neiec (dhlad, par jura meg lou megèjouc R w R w )eðnai kat llhlec gia thn anðqneush omoiìmorfwn perioq n. Xekin ntac me èna meg lo mègejoc gia to DSM, to opoðo exart tai apì to arqikì mègejoc thc eikìnac I (p.q. èna DSM gia mia eikìna), èna DSM efarmìzetai se k je eikonostoiqeðo thc eikìnac. Katìpin, o algìrijmoc mei nei epanalhptik to mègejoc tou DSM mèqri enìc orismènou orðou (to mikrìtero mègejoc pou qrhsimopoieðtai eðnai 8 8), èwc ìtou h mèsh tim thc enèrgeiac E q (gia olìklhrh thn eikìna) na xeper sei èna kat tato ìrio E o. Wc ek toôtou, o MIS algìrijmoc xekin me mia akatèrgasth kat tmhsh thc upì exètash eikìnac, ìpou oi omoiìmorfec perioqèc entopðzontai. Se k je epan lhyh, ìpou to mègejoc tou DSM mei netai, epitugq netai kalôterh anðqneush twn sunìrwn twn geitonik n perioq n. 'Otan èna DSM uperbaðnei ta ìria thc eikìnac, h pr th/teleutaða seir h st lh thc eikìnac sta ìria thc, epanalamb - netai ètsi ste na apotelèsei tic exwterikèc dun meic tou DSM. Gia thn

199 5.4. Kat tmhsh eikìnac 177 (a) (b) (g) (d) Sq ma 5.3: 'Ena par deigma thc ME enèrgeiac E q gia duo diaforetikèc eikìnec thc b shc tou Mpèrkleô. (a) Mia eikìna meomoiìmorfec perioqèc (b) h enèrgeia thc E q. (g) Mia eikìna me pollèc diaforetikèc perioqèc kai perigr mmata kai (d) h enèrgeia thc E q. axiolìghsh miac kat llhlhc tim c gia to kat fli E o, upologðsthkan di - forec timèc thc E q gia diaforetik megèjh tou paramorf simou montèlou se diaforetikèc eikìnec. Aut ta peir mata èdeixan ìti k poioc mporeð na epitôqei mia kal èndeixh gia thn omalìthta thc perioq c miac eikìnac, me ton kajorismì tou kat tatou orðou E o Ðso me 0:01. Gia upologistikoôc lìgouc, ta diadoqik paramorf sima montèla epif neiac klimak nontai se k je epan lhyh. To telikì apotèlesma eðnai mia eikìna me fwteinìth-

200 178 Kef laio 5. Kat tmhsh Eikìnwn tec tic timèc E q, oi opoðec proèkuyan apì thn proanaferjeðsa diadikasða. 'Ena par deigma thc proanaferjeðsac diadikasðac apeikonðzetai sto sq ma 5.4. (a) (b) (g) Sq ma 5.4: Par deigma tou metablhtoô megèjouc tou paramorf simou montèlou epif neiac pou efarmìzetai sthn eikìna tou sq matoc 5.2g. (a) H ME enèrgeia E q gia ìla ta eikonostoiqeða miac eikìnac me mègejoc paramorf simou montèlou sthn pr th epan lhyh (mèsh tim thc E q =0:2676), (b) h ME enèrgeia E q gia ìla ta eikonostoiqeða miac eikìnac me mègejoc paramorf simou montèlou sth deôterh epan lhyh (mèsh tim thc E q = 0:1361) kai (g) h ME enèrgeia E q gia ìlata eikonostoiqeða miac eikìnac me mègejoc paramorf simou montèlou sthn trðth epan lhyh (mèsh tim thc E q = 0:0001,) ìpou kai o algìrijmoc sugklðnei. Mìlic anatejeð se ìla ta eikonostoiqeða thc eikìnac x q mia tim E q, efarmìzetai ènac algìrijmoc epèktashc perioq c, o opoðoc eðnai mia tropopoðhsh thc mejìdou pou parousi sthke sthn ergasða [12]. H mèjodoc epèktashc perioq c basðzetai stic timèc E q k je eikonostoiqeðou thc eikìnac. O arijmìc twn diaforetik n perioq n thc eikìnac exart tai apì tic timèc E q. Arqik, upologðzetai h mèsh tim μ E q kai h apìklish ff Eq

201 5.4. Kat tmhsh eikìnac 179 twn E q thc eikìnac kai apoktiètai èna kat tato ìrio T : T = μ E q + ffff E q; (5.14) H bajmwt tim ff tèjhke Ðsh me 0:7, epeid apodeðqjhke pwc pareðqe kal peiramatik apotelèsmata. Met san upoy fiec arqikèc perioqèc thc eikìnac jewr jhkan ta eikonostoiqeða pou eðqan enèrgeia idioqarakthristik n E q < T. Oi arqikèc perioqèc sundèjhkan me geitonik eikonostoiqeða me b sh thn sundesimìthta tess rwn shmeðwn, me skopì na apotelèsoun omoiìmorfec perioqèc thc eikìnac. Telik c, jewr jhkan ìti apoteloôn perioqèc thc eikìnac mìno ìtan to mègejoc touc ikanopoioôse thn parak tw idiìthta: R N R W 2 s; (5.15) ìpou s eðnai o par gontac klim kwshc pou qrhsimopoi jhke sth deigmatolhyða tou paramorf simou montèlou (megèjouc R W R W ) ston upologismì thc E q. 'Otan ìlec oi perioqèc kajoristoôn, h mèjodoc epèktashc perioq n parèqei tic upoy fiec diaforetikèc (se qr ma) perioqèc thc eikìnac. Arqik, afairoôntai ìlec oi trôpec mèsa stic perioqèc (san trôpa jewreðtai mia mikr perioq pou brðsketai mèsa se mia llh meg lh perioq thc eikìnac). Katìpin, upologðzetai h mèsh tim μ E q ìlwn twn mh katatetmhmènwn eikonostoiqeðwn (eikonostoiqeða pou den an koun se k poia perioq ) kai ta eikonostoiqeða me E q < μ E q sundèontai gia na apotelèsoun perioqèc. An mia auxanìmenh perioq eðnai dðpla mìno se mia llh perioq, tìte prostðjetai se ekeðnh thn perioq. Aut h diadikasða epanalamb netai kai me mikrìtera megèjh tou DSM prokeimènou na brejoôn akribèstera ta ìria ìlwn twn perioq n. Tèloc, h ME enèrgeia E q upologðzetai gia ìla ta enapomeðnonta mh katatetmhmèna eikonostoiqeða kai aut me tic el qistec timèc E q sundèontai me tic geitonikèc touc perioqèc. Autì to teleutaðo b ma epanalamb netai èwc ìtou ìla ta eikonostoiqeða na prostejoôn se

202 180 Kef laio 5. Kat tmhsh Eikìnwn mia perioq eikìnac. 'Ena par deigma tou algorðjmou epèktashc perioq n apeikonðzetai sto sq ma 5.5a. 'Enac susswreutikìc algìrijmoc sugq neushc [33], akoloujeð th mèjodo epèktashc perioq n, dedomènou ìti h diadikasða kat tmhshc mporeð na odhg sei se upèr-kat tmhsh. H sugq neush basðzetai stic omoiìthtec qr matoc twn geitonik n perioq n. UpologÐzetai h eukleðdeia apìstash twn istogr mmwn qr matoc metaxô opoiwnd pote dôo geitonik n perioq n thc eikìnac kai apojhkeôetai se ènan pðnaka E. H mèsh tim kai h apìklish tou pðnaka E upologðzontai. To zeug ri twn perioq n me thn el qisth eukleðdeia apìstash sugqwneôetai kai h diadikasða epanalamb netai mèqri èna mègisto kat tato ìrio thc eukleðdeiac apìstashc, to opoðo eðnai Ðso me th mèsh tim tou pðnaka E elattwmèno kat thn apìklish tou. O omoiìmorfoc q roc qr matoc CIE LUV qrhsimopoieðtai. 'Ena par - deigma tou algìrijmou sugq neushc se mia ègqrwmh eikìna apeikonðzetai sto sq ma 5.5b. H allhlepðdrash metaxô tou proteinìmenou algorðjmou kb ntishc, thc ME enèrgeiac, thc mejìdou epèktashc perioq n kai thc diadikasðac sugqwneôshc melet jhke peiramatik. 'Ena sônolo peiram - twn perigr fetai leptomer c sthn Par grafo Peiramatik Apotelèsmata Prwtìkollo kai Dedomèna Axiolìghshc Ektetamèna peir mata pragmatopoi jhkan se eikìnec me fusikèc skhnèc me skopì na axiologhjeð h apìdosh thc proteinomènhc mejìdou MIS. H proteinìmenh mèjodoc qrhsimopoi jhke gia na katatm sei ègqrwmec eikìnec se omoiìmorfec (se qr ma) perioqèc sth b sh dedomènwn kat tmhshc tou Mpèrkleô [25]. Aut h b sh dedomènwn epilèqthke epeid perièqei katatm seic eikìnwn apì 30 diaforetikoôc anjr pouc. Oi misèc katatm seic eðnai se ègqrwmec eikìnec kai oi llec misèc se eikìnec epipèdou

203 5.5. Peiramatik Apotelèsmata 181 (a) (b) Sq ma 5.5: (a) H arqik kat tmhsh thc eikìnac tou sq matoc 5.2g met thn efarmog thc mejìdou epèktashc perioq n kai (b) kai h telik kat tmhsh met th sugq neush twn perioq n. gkri. H b sh dedomènwn apoteleðtai apì di forec eikìnec thc b shc Corel kai perièqei apotelèsmata kat tmhshc gia 300 eikìnec me skopì thn axiolìghsh algorðjmwn kat tmhshc eikìnac kai anðqneushc sunìrwn. To perieqìmeno aut n twn eikìnwn eðnai topða, z a, portrèta kai di fora antikeðmena. O proteinìmenoc algìrijmoc efarmìsthke se ìlec tic 300 eikìnec kai ta apotelèsmata sugkrðjhkan me ta antðstoiqa thc b shc. Oi metrikèc pou qrhsimopoi jhkan gia thn posotik axiolìghsh tou proteinìmenou algìrijmou tan ta akìlouja: ffl H 'Endeixh TuqaÐac Pijanìthtac (Probabilistic Rand index (PR) [34] epitrèpei th sôgkrish enìc algorðjmou kat tmhshc eikìnwn me lla apotelèsmata katam sewn. Metr to mèroc twn zeugari n eikonostoiqeðwn, ta opoða an koun stic Ðdiec perioqèc sta sugkrinìmena apotelèsmata. H PR upologðzetai gia ìla ta dedomèna kai paðrnei timèc sto di sthma [0; 1], ìpou 0 shmaðnei pwc h upì exètash kat tmhsh den èqei kamða omoiìthta me thn sugkrinìmenh kat tmhsh kai 1 shmaðnei ìti oi duo katatm seic eðnai Ðdiec.

204 182 Kef laio 5. Kat tmhsh Eikìnwn ffl H Kanonikopoihmènh 'Endeixh TuqaÐac Pijanìthtac (Normalized Probabilistic Rand index (NPR)) [35] eðnai mia epèktash thc PR kai kanonikopoieðtai me tic anamenìmenec timèc thc PR sta dedomèna dokim c. Autì to gegonìc k nei thn NPR pio euaðsjhth kai me megalôtero eôroc. ffl To Olikì L joc Sunoq c (Global Consistency error (GCE) [25] metr ei thn anoq se sqèsh me to kat pìso mia kat tmhsh mporeð na jewrhjeð par gwgh miac llhc. Mhdenikèc timèc tou GCE shmaðnoun ìti oi katatm seic eðnai Ðdiec, en mh mhdenikèc timèc shmaðnoun pwc up rqoun diaforèc stic katatm seic twn sugkrinìmenwn eikìnwn. ffl H Apìklish thc PlhroforÐac (Variation of Information (VI) [36] metr thn posìthta thc plhroforðac pou q netai h apoktiètai a- pì th mia perioq thc eikìnac me k poia geitonik thc. Oi timèc VI eðnai p nta jetikèc kai mhdèn shmaðnei ìti ìlec oi perioqèc twn sugkrinìmenwn eikìnwn eðnai ìmoiec. ffl To L joc Metatìpishc Sunìrwn (Boundary Displacement error (BDE) [8] eðnai to mèso l joc metatìpishc metaxô twn orðwn twn perioq n twn sugkrinìmenwn eikìnwn. Mikrìterec timèc tou BDE dhl noun kalôterh poiìthta kat tmhshc Peiramatik Apotelèsmata To pr to sônolo peiram twn asqol jhke me thn axiolìghsh thc akrðbeiac twn katatm sewn pou par qjhsan apì to MIS algìrijmo gia èna diaforetikì sônolo paramètrwn. O par gontac ston paronomast (5.5) mporeð na qrhsimopoihjeð gia na epitôqei pollaplèc katatm seic miac eikìnac. H NPR upologðsthke gia diaforetikèc timèc tou se di forec eikìnec thc b shc dedomènwn tou Mpèrkleô. To sq ma 5.6 apeikonðzei

205 5.5. Peiramatik Apotelèsmata 183 to NPR deðkth se sqèsh me diaforetikèc timèc tou. O NPR deðkthc aux netai, ìso aux netai kai to mèqri th tim 50. Apì ekeð kai pèra, h akrðbeia kat tmhshc eðnai stajer gia èna eurô f sma tim n tou, deðqnontac kat sunèpeia thn eurwstða tou MIS algorðjmou gia diaforetikèc timèc tou. Wc ek toôtou, mia kat llhlh tim gia to mporeð na tejeð Ðsh me 50. K poioc mporeð na pei ìti o par gontac sthn exðswsh (5.5) dra ousiastik wc mia par metroc pou teðnei na uper-katatmeð thn eikìna, ìso mei netai h tim thc. Autì to gegonìc faðnetai kai sto sq ma 5.7, ìpou h enèrgeia ME E q apeikonðzetai gia diaforetikèc timèc tou par gonta gia èna DSM pou efarmìzetai se mia omoiìmorfh perioq eikìnac. H ME enèrgeia E q diathreð mia stajer tim gia timèc tou 50, to opoðo eðnai mia llh èndeixh thc algorijmik c eurwstðac se sqèsh me to. Merik apotelèsmata kat tmhshc gia diaforetikèc timèc tou parousi zontai sto sq ma 5.8. P li, apì posotik poyh, den parousi zetai meg lh euaisjhsða se allagèc tou. Prokeimènou na axiologhjeð h upologistik poluplokìthta tou MIS algorðjmou, upologðsthke o mèsoc upologistikìc qrìnoc gia èna sônolo eikìnwn (20 eikìnec pou epilèqjhkan tuqaða apì th b sh dedomènwn tou Mpèrkleô). O upologistikìc qrìnoc upologðsthke gia dôo diaforetikèc ekdìseic tou MIS algorðjmou. Sthn pr th èkdosh (pou onom zetai MIS-Sl), qrhsimopoi jhkan oi arqikèc exis seic paramìrfwshc prokeimènou na upologisteð h ME enèrgeia, en sth deôterh, qrhsimopoi jhke mia gr gorh efarmog thc diadikasðac paramìrfwshc, ìpwc perigr fhke sthn Par grafo 5.2. 'Ola ta peir mata ektelèsjhkan se ènan upologist me epexergast Intel Pentium 4 (3:01 Ghz), me 1:5 MB mn mh RAM gia kai ègqrwmec eikìnec. Gia mia eikìna, apaitoôntai 73:2 deuterìlepta an eikìna gia ton MIS-Sl algìrijmo, en 2:6 deuterìlepta an eikìna eðnai arket gia ton proteinìmeno algìrijmo MIS. Epiplèon, gia mia eikìna, apaitoôntai 198:6 deuterìlepta an eikìna gia ton algìrijmo MIS-Sl, en 2:9 deuterìlepta an eikìna

206 184 Kef laio 5. Kat tmhsh Eikìnwn (a) (b) (g) (d) (e) (st) Sq ma 5.6: (a),(g),(e) Oi arqikèc eikìnec kai (b),(d),(st) oi antðstoiqec timèc tou NPR deðkth gia diaforetikèc timèc tou.

207 5.5. Peiramatik Apotelèsmata 185 Sq ma 5.7: H ME enèrgeia E q gia diaforetikèc timèc tou gia èna montèlo DSM pou efarmìzetai se mia omoiìmorfh perioq mia eikìnac. eðnai arket gia ton proteinìmeno algìrijmo MIS. Kat sunèpeia, h u- pologistik taqôthta tou algorðjmou MIS eðnai kal gia thn kat tmhsh eikìnwn megèjouc thc t xhc kai mporeð na jewrhjeð kat llhloc gia thn kat tmhsh meg lwn eikìnwn se efarmogèc mh pragmatikoô qrìnou (offline processing). O stìqoc tou trðtou sunìlou peiram twn tan na brejeð h kalôterh apìdosh metaxô tri n diaforetik n parallag n tou proteinìmenou algorðjmou kat tmhshc. Stic pr tec dôo parallagèc, h proteinìmenh mèjodoc kb ntishc antikatast jhke apì dôo diaforetikèc proseggðseic. Sthn pr th prosèggish (pou onom zetai K-means-MIS), o gnwstìc algìrijmoc K-mèswn [37] qrhsimopoi jhke prokeimènou na kathgoriopoihjoôn ta qr mata thc eikìnac se ènan prokajorismèno arijmì om dwn qr matoc. Qrhsimopoi jhke o q roc qr matoc RGB, dedomènou ìti autìc qrhsimopoi jhke kai gia ton MIS.O arijmìc om dwn qr matoc tèjhke na eðnai Ðsoc me autìn pou proèkuye apì thn proteinìmenh mèjodo kb ntishc, prokeimènou na epiteuqjeð mia dðkaih sôgkrish. Sth deôterh parallag,

208 186 Kef laio 5. Kat tmhsh Eikìnwn (a) (b) (g) (d) (e) (st) (z) (h) (j) Sq ma 5.8: (a)-(g) Oi katatm seic twn eikìnwn gia = 0, (d)-(st) oi katatm seic twn eikìnwn gia = 50 kai (z)-(j) oi katatm seic twn eikìnwn gia = 100.

209 5.5. Peiramatik Apotelèsmata 187 qrhsimopoi jhke h diadikasða kb ntishc pou parousi zetai sthn ergasða [31] (kai onom zetai Q-MIS), prokeimènou na meiwjeð o arijmìc twn qrwm twn thc eikìnac. Sthn trðth parallag (pou onom zetai NRM-MIS), oi perioqèc thc eikìnac pou proèkuyan apì ton MIS den sugqwneôjhkan. Oi parallagèc Kmeans-MIS, Q-MIS, NRM-MIS kai MIS dokim sthkan se 100 ègqrwmec eikìnec, pou epilèqjhkan tuqaða apì th b sh dedomènwn Mpèrkleô kai ta apotelèsmata sunoyðzontai ston PÐnaka 5.1. Se ìla ta peir mata, oi par metroi pou qrhsimopoi jhkan gia touc tèsseric algorðjmouc parèmeinan oi Ðdioi. OPÐnakac 5.1 parousi zei tic mèsec timèc gia ta l jh BDE, VI kai GCE gia tic tèsseric parallagèc tou algorðjmou MIS. K poioc mporeð na dei ìti o algìrijmoc MIS epitugq nei thn kalôterh apìdosh. Aut ta peiramatik apotelèsmata parèqoun stoiqeða sqetik me thn allhlepðdrash tou proteinìmenou algorðjmou kb ntishc, thc ME enèrgeiac kai tou algìrijmou epèktashc perioq n o opoðoc basðzetai sth ME. PÐnakac 5.1: Mèsec timèc gia ta l jh PR, BDE, VI kai GCE pou apokt jhkan se 100 ègqrwmec eikìnec thc Mpèrkleô b shc dedomènwn gia tic tèsseric parallagèc tou MIS algorðjmou. Algìrijmoi Mèsec Timèc PR BDE VI GCE MIS Kmeans-MIS Q-MIS NRM-MIS To teleutaðo sônolo peiram twn stoqeôei sthn exètash thc apìdoshc tou MIS algorðjmou kai th sôgkrish thc me llouc gnwstoôc algìrijmouc kat tmhshc eikìnac. Prokeimènou na epiteuqjeð anepðblepth kat -

210 188 Kef laio 5. Kat tmhsh Eikìnwn tmhsh, h par metroc tou DSM tèjhke Ðsh me 0, 50 kai 100. O PÐnakac 5.2 parousi zei tic mèsec timèc gia ta l jh BDE, VI kai GCE sth b sh dedomènwn tou Mpèrkleô gia 5 anepðbleptouc algorðjmouc kat tmhshc eikìnac. Oi timèc upologðzontai kat mèso ìro se ìlo to sônolo twn eikìnwn (300 ston arijmì) thc b shc dedomènwn tou Mpèrkleô. O proteinìmenoc algìrijmoc MIS sugkrðjhke me ton algìrijmo CTM [7], ton Mean-Shift [17], ton Ncuts [14] kai ton NNG [13]. Ta apotelèsmata gia touc tèsseric algorðjmouc pro ljan apì tic ergasðec [7, 9]. K poioc mporeð na parathr sei ìti o proteinìmenoc algìrijmoc epitugq nei kalôtera apotelèsmata apì touc llouc algorðjmouc kat tmhshc eikìnac se treic (apì tic tèsseric) posotikèc metrikèc kat tmhshc kai gia tic treic diaforetikèc timèc tou. Autì to gegonìc parèqei posotik stoiqeða ìti o MIS parousi zei kal sunoq gia poikðlec timèc thc paramètrou. Pio analutik, k poioc mporeð na parathr sei ìti to mèso l joc BDE gia ton proteinìmeno algìrijmo eðnai 7:8263, to opoðo eðnai mia meg lh beltðwsh se sqèsh me to l joc 9:4211 pou epitugq netai apì ton CTM sthn [7] (sqedìn 17% aôxhsh sthn akrðbeia kat tmhshc). Ta l jh BDE kai GCE timwroôn to prìblhma thc upèr-kat tmhshc. Ta l jh PR, VI faðnontai perissìtero na susqetðzontai me tic katatm seic pou pro ljan qeirokðnhta apì anjr pouc. Kat sunèpeia, mporoôn na jewrhjoôn antikeimenik krit ria thc apìdoshc kat tmhshc eikìnac. O MIS epitugq nei thn kalôterh mèsh tim twn laj n PR, VI sth b sh dedomènwn Mpèrkleô. Oi apoklðseic twn laj n PR,BDE,VIkai GCE gia olìklhrh th b sh dedomènwn gia ton algìrijmo MIS ( =50)eÐnai Ðsec me 0:0234, 0:0291, 0:0264 kai 0:0253 antðstoiqa, oi opoðec parèqoun epðshc plhroforðec sqetik me thn eurwstða thc apìdoshc tou MIS algorðjmou. Merik apotelèsmata kat tmhshc eikìnac tou proteinìmenou algorðjmou parousi zontai sto sq ma 5.9.

211 5.5. Peiramatik Apotelèsmata 189 (a) (b) (g) (d) (e) (st) (z) (h) (j) Sq ma 5.9: Kat tmhsh eikìnac apì ton MIS algìrijmo. O par gontac ston paranomast (5.5) eðnai Ðsoc me 50. Oi eikìnec an koun sth b sh dedomènwn tou Mpèrkleô.