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Image Registration & Tracking dengan Metode Lucas & Kanade Sumber: -Forsyth & Ponce Chap. 19, 20 -Tomashi & Kanade: Good Feature to Track.

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Presentasi berjudul: "Image Registration & Tracking dengan Metode Lucas & Kanade Sumber: -Forsyth & Ponce Chap. 19, 20 -Tomashi & Kanade: Good Feature to Track."— Transcript presentasi:

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2 Image Registration & Tracking dengan Metode Lucas & Kanade Sumber: -Forsyth & Ponce Chap. 19, 20 -Tomashi & Kanade: Good Feature to Track

3 Feature Lucas-Kanade(LK) Extraksi feature dengan metode LK ini adalah sangat populer dalam aplikasi computer vision. Feature diekstraksi dengan mengambil informasi gradient image. Selanjutnya feature ini bisa dimanfaatkan untuk Image registration, yg. Selanjutnya diugnakan utk. tracking, recognition, dan lain-lain Pemilihan feature image yang tepat adalah sangat menentukan keberhasilan proses recognition, tracking, etc.

4 Sejarah Perkembangan LK Lucas & Kanade (IUW 1981) LK BAHHSTSBJHBBL GSICETSC Bergen, Anandan, Hanna, Hingorani (ECCV 1992) Shi & Tomasi (CVPR 1994) Szeliski & Coughlan (CVPR 1994) Szeliski (WACV 1994) Black & Jepson (ECCV 1996) Hager & Belhumeur (CVPR 1996) Bainbridge-Smith & Lane (IVC 1997) Gleicher (CVPR 1997) Sclaroff & Isidoro (ICCV 1998) Cootes, Edwards, & Taylor (ECCV 1998)

5 Image Registration

6 Penerapan metode LK

7 Penerapan pada aplikasi: Stereo LK BAHHSTSBJHBBL GSICETSC

8 Penerapan pada aplikasi: Stereo Dense optic flow LK BAHHSTSBJHBBL GSICETSC

9 Penerapan pada aplikasi: Stereo Dense optic flow Image mosaics LK BAHHSTSBJHBBL GSICETSC

10 Penerapan pada aplikasi: Stereo Dense optic flow Image mosaics Tracking LK BAHHSTSBJHBBL GSICETSC

11 Penerapan pada aplikasi: Stereo Dense optic flow Image mosaics Tracking Recognition LK BAHHSTSBJHBBL GSICETSC ?

12 Derivasi Rumusan Lucas & Kanade #1

13 rumusan L&K 1 I0(x)I0(x)

14 h I0(x)I0(x) I 0 (x+h)

15 rumusan L&K 1 h I0(x)I0(x) I(x)I(x)

16 h I0(x)I0(x) I(x)I(x)

17 I0(x)I0(x) R I(x)I(x)

18 I0(x)I0(x) I(x)I(x)

19 h0h0 I0(x)I0(x) I(x)I(x)

20 I 0 (x+h 0 ) I(x)I(x)

21 rumusan L&K 1 I 0 (x+h 1 ) I(x)I(x)

22 rumusan L&K 1 I 0 (x+h k ) I(x)I(x)

23 rumusan L&K 1 I 0 (x+h f ) I(x)I(x)

24 Derivasi Rumusan Lucas & Kanade #2

25 rumusan L&K 2 Sum-of-squared-difference (SSD) error E(h) =  [ I(x) - I 0 (x+h) ] 2 x e Rx e R E(h)  [ I(x) - I 0 (x) - hI 0 ’(x) ] 2 x e Rx e R

26 rumusan L&K 2  2[I 0 ’(x)(I(x) - I 0 (x) ) - hI 0 ’(x) 2 ] x e Rx e R  I 0 ’(x)(I(x) - I 0 (x)) x e Rx e R h  I 0 ’(x) 2 x e Rx e R = 0 = 0

27 Perbandingan  I 0 ’(x)[I(x) - I 0 (x)] h  I 0 ’(x) 2 x x h w(x)[I(x) - I 0 (x)]  w(x) x x  I 0 ’(x)

28 Perbandingan  I 0 ’(x)[I(x) - I 0 (x)] h  I 0 ’(x) 2 x h x w(x)[I(x) - I 0 (x)]  w(x) x x  I 0 ’(x)

29 Generalisasi metode Lucas- Kanade

30 Rumus Original h)=  x eR ( E [ I(x )-(x ] 2 ) + h  I 

31 Rumus Original Dimension of image h)=  x eR ( E [ I(x )-(x ] 2 ) + h 1-dimensional  I  LK BAHHSTSBJHBBL GSICETSC

32 Generalisasi 1a Dimension of image h)=  x eR ( E [ I(x )-(x ] 2 ) + h 2D:  I  LK BAHHSTSBJHBBL GSICETSC

33 Generalisasi 1b Dimension of image h)=  x eR ( E [ I(x )-(x ] 2 ) + h Homogeneous 2D:  I  LK BAHHSTSBJHBBL GSICETSC

34 Permasalahan A LK BAHHSTSBJHBBL GSICETSC Apakah iterasi bisa konvergen?

35 Permasalahan A Local minima:

36 Permasalahan A Local minima:

37 Permasalahan B -  I 0 ’(x)(I(x) - I 0 (x)) x e Rx e R h  I 0 ’(x) 2 x e Rx e R h is undefined if  I 0 ’(x) 2 is zero x e Rx e R LK BAHHSTSBJHBBL GSICETSC Zero gradient:

38 Permasalahan B Zero gradient: ?

39 Permasalahan B’ -  (x)(I(x) - I 0 (x)) x e Rx e R h y  2 x e Rx e R Aperture problem (mis. Image datar): LK BAHHSTSBJHBBL GSICETSC

40 Permasalahan B’ No gradient along one direction: ?

41 Jawaban problem A & B Possible solutions: –Manual intervention LK BAHHSTSBJHBBL GSICETSC

42 Possible solutions: –Manual intervention –Zero motion default LK BAHHSTSBJHBBL GSICETSC Jawaban problem A & B

43 Possible solutions: –Manual intervention –Zero motion default –Coefficient “dampening” LK BAHHSTSBJHBBL GSICETSC Jawaban problem A & B

44 Possible solutions: –Manual intervention –Zero motion default –Coefficient “dampening” –Reliance on good features LK BAHHSTSBJHBBL GSICETSC Jawaban problem A & B

45 Possible solutions: –Manual intervention –Zero motion default –Coefficient “dampening” –Reliance on good features –Temporal filtering LK BAHHSTSBJHBBL GSICETSC Jawaban problem A & B

46 Possible solutions: –Manual intervention –Zero motion default –Coefficient “dampening” –Reliance on good features –Temporal filtering –Spatial interpolation / hierarchical estimation LK BAHHSTSBJHBBL GSICETSC Jawaban problem A & B

47 Possible solutions: –Manual intervention –Zero motion default –Coefficient “dampening” –Reliance on good features –Temporal filtering –Spatial interpolation / hierarchical estimation –Higher-order terms LK BAHHSTSBJHBBL GSICETSC Jawaban problem A & B

48 Kembali lagi: Rumus Original h)=  x eR ( E [ I(x )-(x ] 2 ) + h  I 

49 Rumus Original Transformations/warping of image h)=  x eR ( E [ I(x )-  I  (x ] 2 ) + h Translations: LK BAHHSTSBJHBBL GSICETSC

50 Permasalahan C Bagaimana bila ada gerakan(motion) tipe lain?

51 Generalisasi 2a Transformations/warping of image A, h)=  x eR ( E [ I(AxAx )-(x ] 2 ) + h Affine:  I  LK BAHHSTSBJHBBL GSICETSC

52 Generalisasi 2a Affine:

53 Generalisasi 2b Transformations/warping of image A)=  x eR ( E [ I(A x )-(x ] 2 ) Planar perspective:  I  LK BAHHSTSBJHBBL GSICETSC

54 Generalisasi 2b Planar perspective: Affine +

55 Generalisasi 2c Transformations/warping of image h)=  x eR ( E [ I(f(x, h) )-(x ] 2 ) Other parametrized transformations  I  LK BAHHSTSBJHBBL GSICETSC

56 Generalisasi 2c Other parametrized transformations

57 Permasalahan B” -(J T J) -1 J (I(f(x,h)) - I 0 (x)) h ~ Generalized aperture problem: LK BAHHSTSBJHBBL GSICETSC -  I 0 ’(x)(I(x) - I 0 (x)) x e Rx e R h  I 0 ’(x) 2 x e Rx e R

58 Permasalahan B” ? Generalized aperture problem:

59 Rumus Original h)=  x eR ( E [ I(x )-(x ] 2 ) + h  I 

60 Rumus Original Image type h)=  x eR ( E [ I(x )-(x ] 2 ) + h Grayscale images  I  LK BAHHSTSBJHBBL GSICETSC

61 Generalisasi 3 Image type h)=  x eR ( E || I(x )-  I  (x || 2 ) + h Color images LK BAHHSTSBJHBBL GSICETSC

62 Rumus Original h)=  x eR ( E [ I(x )-(x ] 2 ) + h  I 

63 Rumus Original Anggapan pixel punya konstan brightness (Constancy assumption) h)=  x eR ( E [ I(x )-  I  (x ] 2 ) + h Brightness constancy LK BAHHSTSBJHBBL GSICETSC

64 Permasalahan C Bagaimana bila iluminasi cahaya bervariasi?

65 Generalisasi 4a Constancy assumption h,h, )=  x eR ( E [ I(x )- II (x ] 2 )+  + h Linear brightness constancy LK BAHHSTSBJHBBL GSICETSC

66 Generalisasi 4a

67 Generalisasi 4b Constancy assumption h, )=  x eR (E [ I(x )-  B (x ] 2 ) + h Illumination subspace constancy LK BAHHSTSBJHBBL GSICETSC

68 Permasalahan C’ Bagaimana bila texture berubah?

69 Generalisasi 4c Constancy assumption h, )=  x eR (E [ I(x )- ] 2 + h Texture subspace constancy  B (x) LK BAHHSTSBJHBBL GSICETSC

70 Permasalahan D Jelas proses konvergensi menjadi lambat bila jumlah #parameters bertambah !!!

71 Percepat konvergensi dengan: –Coarse-to-fine, filtering, interpolation, etc. LK BAHHSTSBJHBBL GSICETSC Jawaban problem D

72 Percepat konvergensi dengan: –Coarse-to-fine, filtering, interpolation, etc. –Selective parametrization Jawaban problem D LK BAHHSTSBJHBBL GSICETSC

73 Percepat konvergensi dengan: –Coarse-to-fine, filtering, interpolation, etc. –Selective parametrization –Offline precomputation Jawaban problem D LK BAHHSTSBJHBBL GSICETSC

74 Percepat konvergensi dengan: –Coarse-to-fine, filtering, interpolation, etc. –Selective parametrization –Offline precomputation Difference decomposition LK BAHHSTSBJHB GSICETSC Jawaban problem D BL

75 Jawaban problem D Difference decomposition

76 Jawaban problem D Difference decomposition

77 Percepat konvergensi dengan: –Coarse-to-fine, filtering, interpolation, etc. –Selective parametrization –Offline precomputation Difference decomposition –Improvements in gradient descent LK BAHHSTSBJHB GSICETSC Jawaban problem D BL

78 Percepat konvergensi dengan: –Coarse-to-fine, filtering, interpolation, etc. –Selective parametrization –Offline precomputation Difference decomposition –Improvements in gradient descent Multiple estimates of spatial derivatives LK BAHHSTSBJHB GSICETSC Jawaban problem D BL

79 Jawaban problem D Multiple estimates / state-space sampling

80 Generalisasi metode Lucas-Kanade  x eR [ I(x )-(x ] 2 ) + h  I  Modifikasi yg. Dibuat selama ini adalah:

81 Rumus Original Error norm h)=  x eR ( E [ I(x )-  I  (x ] 2 ) + h Squared difference: LK BAHHSTSBJHBBL GSICETSC

82 Permasalahan E Permasalahan dengan ourliers? >> Gunakan robust norm

83 Generalisasi 5a Error norm h)=  x eR ( E ( I(x )-  I  (x ) ) + h Robust error norm:  LK BAHHSTSBJHBBL GSICETSC

84 Rumus Original h)=  x eR ( E [ I(x )-(x ] 2 ) + h  I 

85 Rumus Original Image region / pixel weighting h)=  x eR ( E [ I(x )-  I  (x ] 2 ) + h Rectangular: LK BAHHSTSBJHBBL GSICETSC

86 Permasalahan E’ Bagaimana bila background terjadi clutter (bergoyang)?

87 Generalisasi 6a Image region / pixel weighting h)=  x eR ( E [ I(x )-  I  (x ] 2 ) + h Irregular: LK BAHHSTSBJHBBL GSICETSC

88 Permasalahan E” Bagaimana bila objek terhalang (foreground occlusion)?

89 Generalisasi 6b Image region / pixel weighting h)=  x eR ( E [ I(x )-  I  (x ] 2 ) + h Weighted sum: w(x)w(x) LK BAHHSTSBJHBBL GSICETSC

90 Generalisasi metode Lucas-Kanade  x eR [ I(x )-(x ] 2 ) + h  I  Modifikasi:

91 Generalisasi 6c Image region / pixel weighting h)=  x eR ( E [ I(x )-  I  (x ] 2 ) + h Sampled: LK BAHHSTSBJHBBL GSICETSC

92 Generalisasi metode Lucas-Kanade: Ringkasan =  x eR ( I( )- w(x)w(x)   (x ) ) h) ( E f(x, h) h)=  x eR ( E [ I(x )-(x ] 2 ) + h  I 

93 Ringkasan Generalisasi –Dimension of image –Image transformations / motion models –Pixel type –Constancy assumption –Error norm –Image mask L&K ? Y n Y n Y

94 Ringkasan Common problems: –Local minima –Aperture effect –Illumination changes –Convergence issues –Outliers and occlusions L&K ? Y maybe Y n

95 Penanganan aperture effect: –Manual intervention –Zero motion default –Coefficient “dampening” –Elimination of poor textures –Temporal filtering –Spatial interpolation / hierarchical –Higher-order terms Ringkasan L&K ? n Y n


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