IV 493 - «И» Аи - - - - PO - - - Кеые : PO - - - - - ; - И - - - - - - ; - И- - - - - - - - - [] - Веи СиАДИ ы 5 (5) 6 45
- - - (ODE) - - - D- - D - - - - - - - - PO - - - - - - - ( - ) - G - И- f R ( f ) с f : X : g f f ε ε ; Y : gε f f ε 46 Веи СиАДИ ы 5 (5) 6 f : gφ f f φ φ s s s ( α ): gα f f cosα snα snα cosα И - - D- - - Д] p q f : D- p q mpq f d; p q Z ; : m f d f : m m ; f m m - f - : f f g F φ s - - m m : J m m - -
cos sn sn cos : J ' J : 5 arcg J J J - d J dag J J R J J - J J J - : XY D- C - c : R ; R c c ; a - - ы : A A c A: R R R Д3] GL ;de GL A R A - O GL - O : AR AA A A Id;de A - ρ A ρ ρ R E - - O R : g : a b GL GL dg ; a b d dg : Ag d ; g Id AR - g ep A - : g g GL - : v d Lv v d; L V R () dg v g d - Э Д4]: * * d Lv d Lv v v Lv () ы - X R X - X X ; - ( Id ) Dff X - - - X - - Веи СиАДИ ы 5 (5) 6 47
- X R g : X X g - G - : g g g g G - - ODE g ; X v : ; dg d v g g (3) v g X R g ; g ; X - * V v Lv v Lv v d α Lv ; g G v g dg d - : V (4) v v d Lv v d g g g g v - α : v L α Kα (5) : L d a R K L : K e (6) - Э- - [5]: v dα d Dα v α v Dv α (7) Df f ; : v K l l l - - - - Д6 7] - - - g n ; n n : σ V n n n v d g (8) Э- σ : σ α ; d d v v k k k K l l d k d K k l k l l l α ; α α α (9) K K - 48 Веи СиАДИ ы 5 (5) 6
L K : K e : k l K k l k l e PO (9) : α α α α α α - (9) - - (sсшштчр) PO (pкrтмlо sакrц ШpТЦТгКТШЧ) - α α α (8) - PO - J KОЧЧОНв 995 Д8] - (sакrц) ; - - - : - - ( ) PO - - - (- ε π ) π ( ε ) - θ βπ ; - 4 : σ ; PO: 7 ; : ε ε ( ) - 3 6 9 ε (; ) (; ) (; -) (-; ) (; ) (; 77) (4; -) (-; -77) (-43; ) (; 77) 84 4 (; 55) (83; -) (-; -55) (-84; ) (; 55) 954 6 (; 36) (; -) (-; -36) (-; 3) (; 36) 987 8 (; 8) (56; -) (-; -8) (-54; 3) (; 8) 998 (3; ) (85; -) (-3; ) (-8; 5) (3; ) 3 6 9 (; ) (34; ) (; ) (-34; (; ) Веи СиАДИ ы 5 (5) 6 49
- : n g n n 34 - : n g n n 7 - - PO σ - D - - - - - - - - - PO - - - - - 3D : - - - - - PO [9] (- ) : l u l u Mamze f X ; X X X X X (lower) (upper) X PO X X : X V - : f X X - : 3 X V : (a) И - X : P bes X f И X : G bes f X ; (b) : cr bes V V P X cr Gbes X c3 r3 c c c 3 r r r - 3 ; (c) : X X V f X X 4 3 P G - bes bes - - Beg MF e al Compung large deformaon merc mappngs va geodesc flows of dffeomorphsms // Inernaonal ournal of compuer vson 5 6 39-57 - // 8 44 3 8-87 5 Веи СиАДИ ы 5 (5) 6
3 Baker A Mar groups: An nroducon o Le group heor prnger cence & Busness Meda 4 Arnold VI Khesn BA opologcal mehods n hdrodnamcs prnger cence & Busness Meda 998 5 Holm DD e al Geomerc mechancs and smmer: from fne o nfne dmensons London: Oford Unvers Press 9 6 Mller MI rouve A Younes L Geodesc shoong for compuaonal anaom // Journal of mahemacal magng and vson 6 4 9-8 7 Bruvers M Holm DD Geomer of mage regsraon: he dffeomorphsm group and momenum maps // Geomer Mechancs and Dnamcs - prnger ew York 5-9-56 8 Kenned J e al warm nellgence Morgan Kaufmann 9 Yang X aure-nspred opmzaon algorhms Elsever 4 APPLICAIO OF PO FOR OLVIG PROB- LEM OF IVARIA COMPARIO OF WO-DIMEIOAL CLOED CURVE DB Abramov O Baranov V Lekher Absrac he problem of esmang he norm of he dsance beween he wo closed smooh curves for paern recognon s consdered Dffeomorphc ransformaon curves based on he model of large deformaons s descrbed For esmang of he norm of he dsance beween wo closed curves s formed he funconal correspondng normalzed dsance beween he wo curves and he equaon of evoluon dffeomorphc ransformaons An algorhm for solvng he equaon of dffeomorphc ransformaon s proposed bul on he bass of PO whch can sgnfcanl reduce he number of compung operaons compared wh graden mehods for solvng he developed algorhms can be used n bonformacs and bomercs ssems classfcaon of mages and obecs machne vson ssems for paern recognon and obec rackng ssems Kewords: nvarance roaon group ranslaon group dffeomorphc ransformaon PO mehod References Beg MF e al Compung large deformaon merc mappngs va geodesc flows of dffeomorphsms // Inernaonal ournal of compuer vson 5 6 39-57 hukanov he Fourer ransform of a funcon of hree-dmensonal mage nvaran o he acon of he roaon group and ransfer Avomera 8 no 3 pp 8-87 3 Baker A Mar groups: An nroducon o Le group heor prnger cence & Busness Meda 4 Arnold VI Khesn BA opologcal mehods n hdrodnamcs prnger cence & Busness Meda 998 5 Holm D D e al Geomerc mechancs and smmer: from fne o nfne dmensons London: Oford Unvers Press 9 6 Mller M I rouve A Younes L Geodesc shoong for compuaonal anaom // Journal of mahemacal magng and vson 6 4 9-8 7 Bruvers M Holm D D Geomer of mage regsraon: he dffeomorphsm group and momenum maps // Geomer Mechancs and Dnamcs - prnger ew York 5-9-56 8 Kenned J e al warm nellgence Morgan Kaufmann 9 Yang X aure-nspred opmzaon algorhms Elsever 4 ( ) «-» «И» (6448 5 О-mal: abramov@kvarksudoru) ( ) «-» «И» (6448 5 Оmal: baranov@kvarksudoru) ( ) «-» «И» (6448 5 emal: lekher@malru) Abramov Dmr Borsovch (Omsk Russan) posgraduae of he Deparmen "Auomaed sems of Informaon Processng and Managemen" "badi" (6448 Omsk Mra 5 emal: abramov@kvarksudoru) Baranov erge Olegovch (Omsk Russan) posgraduae of he Deparmen "Auomaed sems of Informaon Processng and Managemen" "badi" (6448 Omsk Mra 5 emal: baranov@kvarksudoru) Lekher erge Vladmrovch (Omsk Russan) posgraduae of he Deparmen "Auomaed sems of Informaon Processng and Managemen" "badi" (6448 Omsk Mra 5 emal: lekher@malru) Веи СиАДИ ы 5 (5) 6 5