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Image Registration & Tracking dengan Metode Lucas & Kanade

Image Registration & Tracking dengan Metode Lucas & Kanade. Sumber: Forsyth & Ponce Chap. 19, 20 Tomashi & Kanade: Good Feature to Track. Feature Lucas-Kanade(LK). Extraksi feature dengan metode LK ini adalah sangat populer dalam aplikasi computer vision.

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Image Registration & Tracking dengan Metode Lucas & Kanade

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

  2. 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.

  3. 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) SC G SI CET BAHH ST S BJ HB BL Sejarah Perkembangan LK • Lucas & Kanade (IUW 1981) LK

  4. Image Registration

  5. Penerapan metode LK

  6. SC G SI CET BAHH ST S BJ HB BL LK Penerapan pada aplikasi: • Stereo

  7. Penerapan pada aplikasi: • Stereo • Dense optic flow SC G SI CET BAHH ST S BJ HB BL LK

  8. Penerapan pada aplikasi: • Stereo • Dense optic flow • Image mosaics SC G SI CET BAHH ST S BJ HB BL LK

  9. Penerapan pada aplikasi: • Stereo • Dense optic flow • Image mosaics • Tracking SC G SI CET BAHH ST S BJ HB BL LK

  10. Penerapan pada aplikasi: • Stereo • Dense optic flow • Image mosaics • Tracking • Recognition ? SC G SI CET BAHH ST S BJ HB BL LK

  11. Derivasi RumusanLucas & Kanade#1

  12. I0(x) rumusan L&K 1

  13. h I0(x) I0(x+h) rumusan L&K 1

  14. rumusan L&K 1 h I0(x) I(x)

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

  16. rumusan L&K 1 I0(x) I(x) R

  17. rumusan L&K 1 I0(x) I(x)

  18. rumusan L&K 1 h0 I0(x) I(x)

  19. rumusan L&K 1 I0(x+h0) I(x)

  20. rumusan L&K 1 I0(x+h1) I(x)

  21. rumusan L&K 1 I0(x+hk) I(x)

  22. rumusan L&K 1 I0(x+hf) I(x)

  23. Derivasi RumusanLucas & Kanade#2

  24. E(h) = S [ I(x) - I0(x+h) ]2 E(h) S [ I(x) - I0(x) - hI0’(x) ]2 xeR xeR rumusan L&K 2 • Sum-of-squared-difference (SSD) error

  25. SI0’(x)(I(x) - I0(x)) xeR h SI0’(x)2 xeR rumusan L&K 2 S 2[I0’(x)(I(x) - I0(x) ) - hI0’(x)2] xeR =0

  26. w(x)[I(x) - I0(x)] S I0’(x) x h Sw(x) x SI0’(x)[I(x) - I0(x)] x h SI0’(x)2 x Perbandingan

  27. Perbandingan w(x)[I(x) - I0(x)] S I0’(x) x h Sw(x) x SI0’(x)[I(x) - I0(x)] x h SI0’(x)2 x

  28. Generalisasi metode Lucas-Kanade

  29. Rumus Original S [ ] ( I ( x h ) - I0 ( x ) E h ) = + 2 x e R

  30. SC G SI CET BAHH ST S BJ HB BL LK Rumus Original • Dimension of image S [ ] ( I ( x h ) - I0 ( x ) E h ) = + 2 x e R 1-dimensional

  31. SC G SI CET BAHH ST S BJ HB BL LK Generalisasi 1a • Dimension of image S [ ] ( I ( x h ) - I0 ( x ) E h ) = + 2 x e R 2D:

  32. Generalisasi 1b • Dimension of image S [ ] ( I ( x h ) - I0 ( x ) E h ) = + 2 x e R Homogeneous 2D: SC G SI CET BAHH ST S BJ HB BL LK

  33. SC G SI CET BAHH ST S BJ HB BL LK Permasalahan A Apakah iterasi bisa konvergen?

  34. Permasalahan A Local minima:

  35. Permasalahan A Local minima:

  36. h is undefined if SI0’(x)2 is zero xeR Permasalahan B Zero gradient: -SI0’(x)(I(x) - I0(x)) h xeR SI0’(x)2 xeR SC G SI CET BAHH ST S BJ HB BL LK

  37. ? Permasalahan B Zero gradient:

  38. Permasalahan B’ Aperture problem (mis. Image datar): -S (x)(I(x) - I0(x)) xeR hy S 2 xeR SC G SI CET BAHH ST S BJ HB BL LK

  39. ? Permasalahan B’ No gradient along one direction:

  40. Jawaban problem A & B • Possible solutions: • Manual intervention SC G SI CET BAHH ST S BJ HB BL LK

  41. Jawaban problem A & B • Possible solutions: • Manual intervention • Zero motion default SC G SI CET BAHH ST S BJ HB BL LK

  42. Jawaban problem A & B • Possible solutions: • Manual intervention • Zero motion default • Coefficient “dampening” SC G SI CET BAHH ST S BJ HB BL LK

  43. Jawaban problem A & B • Possible solutions: • Manual intervention • Zero motion default • Coefficient “dampening” • Reliance on good features SC G SI CET BAHH ST S BJ HB BL LK

  44. Jawaban problem A & B • Possible solutions: • Manual intervention • Zero motion default • Coefficient “dampening” • Reliance on good features • Temporal filtering SC G SI CET BAHH ST S BJ HB BL LK

  45. Jawaban problem A & B • Possible solutions: • Manual intervention • Zero motion default • Coefficient “dampening” • Reliance on good features • Temporal filtering • Spatial interpolation / hierarchical estimation SC G SI CET BAHH ST S BJ HB BL LK

  46. Jawaban problem A & B • Possible solutions: • Manual intervention • Zero motion default • Coefficient “dampening” • Reliance on good features • Temporal filtering • Spatial interpolation / hierarchical estimation • Higher-order terms SC G SI CET BAHH ST S BJ HB BL LK

  47. Kembali lagi: Rumus Original S [ ] ( I ( x h ) - I0 ( x ) E h ) = + 2 x e R

  48. Rumus Original • Transformations/warping of image S [ ] ( I ( x h ) - I0 ( x ) E h ) = + 2 x e R Translations: SC G SI CET BAHH ST S BJ HB BL LK

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

  50. Generalisasi 2a • Transformations/warping of image S [ ] ( I ( Ax h ) - I0 ( x ) E A, h ) = + 2 x e R Affine: SC G SI CET BAHH ST S BJ HB BL LK

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