2005 Journal of Software , ) , ) Automatic Selection of Kernel-Bandwidth for Mean-Shift Object Tracking

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1 -985/5/6(9)54 5 Joral o Sotware Vol6, No9 Mea-Sht,+,,, (, ) (, 479) Atomat Seleto o Kerel-Badwdth or Mea-Sht Obet Trag PENG Ng-Sog,+, YANG Je, LIU Zh, ZHANG Feg-Chao (Isttte o Image Proessg ad Patter Reogto, Shagha Jaotog Uversty, Shagha, Cha) (Isttte o Eletros ad Iormato, He a Uversty o See ad Tehology, Loyag 479, Cha) + Correspodg athor Ph , Fax , E-mal peggsog@sted Reeved 4-5-; Aepted 4--9 Peg NS, Yag J, L Z, Zhag FC Atomat seleto o erel-badwdth or Mea-Sht obet trag Joral o Sotware, 5,6(9)54 55 DOI 6/os654 Abstrat Class Mea-Sht based trag algorthm ses xed erel-badwdth, whh lmts the perormae whe the obet sale exeeds the sze o the trag wdow Based o the aalyss o smlarty o obet erel-hstogram deret sales, e the Bhattaharyya oeet, a theorem s od ad proved e the hages o obet sale ad posto wth the erel wll ot mpat loalzato aray o Mea-Sht based trag algorthm Usg ths theorem a atomat badwdth seleto method s proposed based o baward trag ad obet etrod regstrato The proposed method s appled to tra vehle hagg sze wth eoragg reslts Key words Mea-Sht; obet trag; erel-badwdth seleto; Bhattaharyya oeet; ae model Mea-Sht Bhattaharyya, Mea-Sht, Mea-Sht; ; ;Bhattaharyya ; TP9 A, Mea-Sht [,], Spported by the Natoal Natral See Fodato o Cha der Grat No774 ( ) (97 ),,,,,, ; (964 ),,,,, ; (978 ),,,, ; (975 ),,,

2 Mea-Sht 54, [ 6] Mea-Sht, Mea-Sht, [,4],,,, [5], Mea-Sht [6] Mea-Sht, Bhattaharyya,,, Bhattaharyya [7] Colls, Mea-Sht [7], Epaehov [], Mea-Sht, [6], Bhattaharyya,, Mea-Sht,,,,, [8],,,,, Mea-Sht,, Mea-Sht Mea-Sht A X x X Mea-Sht ms a ( a x) w( a) a x, a A ( a x) w( a) a,, w x Mea-Sht ms J ( x) g( a x) w( a) a [,], g [] ms [,],,, F F, B F, F B T F, B,, T, { }, T X,, { p } m p µ C ( X / r ) δ [ q( X ) µ] P,, [], δ Kroeer delta [] q R m C p µ m () () {,, m} C µ

3 544 ( X / ) r r, T, Joral o Sotware 5,6(9) m P P Bhattaharyya ρ p l p l,,, Bhattaharyya Coma J ( x), Mea-Sht [], Mea-Sht - Bhattaharyya m l p p l l Mea-Sht [,4] (),, [7],,,, (),,,,,,, ( ),,, Fg Mea-Sht trag reslts wth xed erel-badwdth (rom let to rght) Mea-Sht ( ) 4 4 Bhattaharyya, (a) (b) (a),, Bhattaharyya Mea-Sht,,,, (b), Bhattaharyya, + T, T T,, P P (), T + ; P T T F T F F P P (), T T ; P Bhattaharyya Bhattaharyya T, +, ( ) T Mea-Sht [,], + T ( ), Mea-Sht + T,

4 Mea-Sht 545,,,Mea-Sht T tbhattaharyya oeet e e o 7 6 tbhattaharyya oeet e e o 4 5 a ryya hata h B 5 4 a ryya hata h B (a) (b) Fg Bhattaharyya oeet o the wdows arod the obet etrod Bhattaharyya,Mea-Sht,,,,Mea-Sht,,,,,,,,,, x s x x e + y s y y e,( x, y) ( x, y ) e e x, e }, s s, s } x s, r r max( s x, s ) (5),,, T N, + N T,, T P,, P T T + T + y x y T + I { y T + { y ( P T + ) m{ I( P T ) I( P T + )},,, (6), I T P T G +, G < N T P, (6), O (NN ) T [8,9] T + (4),,

5 546 Joral o Sotware 5,6(9) O (N),,, o o T +, o +, d + o+, + + T +, Mea-Sht T, T,, + T + +,,, +, Mea-Sht, +, d, d d, o + + d (7), (7), (6) From rame to +(orward trag) From Form rame rame + to + (baward to (baward trag) trag) o o + o d d Ital trag wdow Fg Uregstered trag wdow Regstered trag wdow d + Trag wdow baward trag Illstratos o baward trag ad obet etrod regstrato +, (5),, Mea-Sht, Beg Ed T Mea-Sht T + ; T + Mea-Sht T ; T T T +, r r ε, ε > ; 4 T,T +, ; 5 s x s y ; 6 rrmax(s x,s y ) T +

6 Mea-Sht 547 ε, ( ), 6 r r ( s x ) + ( s y ) RGB 4 Mea-Sht,, ;, ;, [9] Fg4 Comparso o Mea-Sht trag reslts (let to rght) 4 Mea-Sht ( ) Table Parameters o or method σ vale orer operator Threshold orer operator Sze o the G Max lterates Mea-Sht 5(a) 5(b) 4 5(b), 5()~ 5(e) 6, 6(a) (+ ) ( ) 6(b) (+ ) ( ) 5(a),, 5(b), ( + ),, ;, 6(b) 5(b)

7 548 Joral o Sotware 5,6(9) 5 Fg5 Trag wdows ad the orers extrated rom them (a) Fg Comparso o orer orrespodees 6 (b) 4 Mea-Sht,, -, Bhattaharyya,, Mea-Sht, Mea-Sht, Mea-Sht [4], [],,, Reerees [] Faaga K, Hostetler LD The estmato o the gradet o a desty to, wth applatos patter reogto IEEE Tras o Iormato Theory, 975,() 4 [] Cheg Y Mea sht, mode seeg ad lsterg IEEE Tras o Patter Aalyss ad Mahe Itellgee, 995,7(8)

8 Mea-Sht 549 [] Coma D, Ramesh V, Meer P Real-Tme trag o o-rgd obets sg mea sht I Werer B, ed IEEE It l Pro o the Compter Vso ad Patter Reogto, Vol Stoghto Prtg Hose, 4 49 [4] Ylmaz A, Shaqe K, Shah M Target trag arbore orward loog rared magery It l Joral o Image ad Vso Comptg,,(7)6 65 [5] Brads GR Compter vso ae trag or se a pereptal ser terae I Rega Speer Spple, ed IEEE Worshop o Applatos o Compter Vso Stoghto Prtg Hose, [6] Coma D, Ramesh V, Meer P Kerel-Based obet trag IEEE Tras o Patter Aalyss ad Mahe Itellgee,, 5(5) [7] Colls RT Mea-Sht blob trag throgh sale spae I Daelle M, ed IEEE It l Co o Compter Vso ad Patter Reogto, Vol Baltmore Vtor Graphs, 4 4 [8] Olso CF Maxmm-Lelhood mage mathg IEEE Tras o Patter Aalyss ad Mahe Itellgee,,4(6) [9] H W, Wag S, L RS, Levso S Trag o obet wth SVM regresso I Jaobs A, Baldw T, eds IEEE It l Co o Compter Vso ad Patter Reogto, Vol Baltmore Vtor Graphs, 4 45 [] Mohammad GA A ast globally optmal algorthm or template mathg sg low-resolto prg IEEE Tras o Image Proessg,,(4)66 5, () F ;(),,, F F F { },,, ;() B,,, v, B { b },, v ;(4) m P,,,, { p },,, b { } + v m,v max( v, v, v) bp,, v, p C bp C C /( p C p C σ σ b σ σ σ ( X / r ) ( X / r ) dσ,, dσ,,, ;, ;,,,, v v ( X / r ) dσ + ( X / r ) ( X / r ) ( X / r ) σ b dσ C S ξ dσ C S ξ F dσ ) r r /,, F, S S F S S F ( ) ( ) ( ) X / r X / r X / r [], X / r < X / r ξ ξ F >, X / r F F ( ) (A) (A), ξ r < ξ r, ξ / r > ξ / r F, ( F ),, C σ T ( X / r ) d C / σ C (A)

9 55 Joral o Sotware 5,6(9), (A) p > p, v p + bp,,, (A4) v bp bp, B, bp bp, p < p v <, P P P F F B > < v p bp > < v p bp > < v v p > bp < v < Bhattaharyya, m p,, p ) p,, p ) v, V, bp p,, ( m ( m (A5) {V },, { P },, Bhattaharyya 7 (A4) (A5), (V,V )> (V,V ),, β > α, Bhattaharyya P Bhattaharyya P P P F F F B B B v bp T T v T v VV bp V bp VV α V V β V V V p p p Fg7 Trag wdows ad smlarty o ther erel-hstogram 7