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# 複合現実感のためのコンピュータビジョン技術

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ComputerVision Technology for AR

ComputerVision Technology for AR

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### 複合現実感のためのコンピュータビジョン技術

1. 1. 第4章 拡張現実感のための コンピュータビジョン技術 !1
2. 2. !2
3. 3. 3 ↪
4. 4. ↪ ↪ ↪ 4
5. 5. 5
6. 6. Xworld Yworld Zworld u v Xcamera Ycamera Zcamera u Xworld 6
7. 7. [ u v 1] fu 0 cu 0 fv cv 0 0 1 r11 r12 r13 t1 r21 r22 r23 t2 r31 r32 r33 t3 Xworld Yworld Zworld 1 s = s ˜u = K [r1 r2 r3 T] ˜Xworld s ˜u = K [R T] ˜Xworld Xworld u 7
8. 8. Xworld u 8
9. 9. ˜Xcamera = [ R T 0T 1] ˜Xworld Xcamera = RXworld+T 9
10. 10. Xworld = [ 0 0 0] Xcamera = T T = [ 0 0 0] Xworld = [ 1 0 0] Xcamera = r1 Xcamera = RXworld+T ˜Xcamera = [ R T 0T 1] ˜Xworld r1 Xworld 10
11. 11. s ˜u = K [E 0] ˜Xcamera Xcamera u s ˜u = K [R T] ˜Xworld ˜Xcamera = [ R T 0T 1] ˜Xworld Xworld 11
12. 12. Zworld = 0 s ˜u = K [r1 r2 r3 T] Xw Yw 0 1 = K [r1 r2 T] Xworld Yworld 1 = H ˜XXY 12
13. 13. u, Xworld H Xworld, Yworld 13
14. 14. [b1 b2 b3] = ± K−1 H λ = ∥b1∥ + ∥b2∥ 2 [r1 r2 T] = 1 λ [b1 b2 b3] r3 = r1 × r2 Xworld Yworld Zworld 14
15. 15. s ˜u = K [R T] ˜Xworld s ˜u = H ˜XXY 15
16. 16. 16
17. 17. Xworld uXworld [R T] 17
18. 18. Yworld Xworld Zworld Yworld Xworld Zworld Yworld Xworld Zworld Yworld Xworld Zworld 18
19. 19. s ˜u = K [R T] ˜Xworld [R T] 19
20. 20. uXworld 20
21. 21. [ u v 1] fu 0 cu 0 fv cv 0 0 1 r11 r12 r13 t1 r21 r22 r23 t2 r31 r32 r33 t3 Xworld Yworld Zworld 1 s = s ˜u = K [r1 r2 r3 T] ˜Xworld s ˜u = K [R T] ˜Xworld Xworld u 21
22. 22. Xworld u 22
23. 23. 23
24. 24. 24
25. 25. 25
26. 26. 26
27. 27. u, Xworld H Xworld, Yworld 27
28. 28. 28
29. 29. 29
30. 30. 30
31. 31. 31
32. 32. 32
33. 33. H [R T] 33
34. 34. [Rt−1 Tt−1] [Rt Tt] E = ∑ i ∥u′i − proj(K, R, T, Xwi)∥2 s ˜u = K [R T] ˜Xworldproj i Xwi 34
35. 35. ⇢ 35
36. 36. 36
37. 37. 37
38. 38. min H ∥It−1 − It(H)∥ It It HIt(H) s ˜u = H ˜XXY 38
39. 39. 39
40. 40. P = K [R T] s ˜u = P ˜Xworld [R T] P Xworld u 40
41. 41. s ˜u = P ˜Xworld s′˜u′ = P′ ˜Xworld P, P′ u, u′ Xworld (u, Xworld) P, P′ u, u′ Xworld u, u′, P, P′ Xworld Ycamera Xcamera Zcamera Xcamera′ Zcamera′ Ycamera′ u u′ Yworld Zworld Xworld P P′ 41
42. 42. 42
43. 43. P, P′ u, u′ Xworld (u, Xworld) u, u′ Xworld P, P′ 43
44. 44. E = ∑ i ∑ j∈Fi ∥u′j − proj(K, Ri, Ti, Xwj)∥2 i j Fi i [R T] Xwj E = ∑ i ∥u′i − proj(K, R, T, Xwi)∥2 [R T] <cf.> 44
45. 45. xEx′ = 0 E R tx, x′ 45
46. 46. 46
47. 47. Xcamera = RworldXworld + Tworld Xcamera = s(RatamXatam + Tatam) Xcamera XcameraXatam s T Xatam = R Xworld s + T = R′Xworld + T R [ Rworld Tworld 0T 1 ] = [ sRatam sTatam 0T 1 ] [ R′ T 0T 1] Yatam Zatam Xatam Zcamerai Ycamerai Xcamerai Zcameraj Xcameraj Ycameraj 47
48. 48. Xworld = [ 0 0 0] Xcamera = T T = [ 0 0 0] Xworld = [ 1 0 0] Xcamera = r1 Xcamera = RXworld+T ˜Xcamera = [ R T 0T 1] ˜Xworld r1 Xworld 48
49. 49. [ Rworld Tworld 0T 1 ] = [ sRatam sTatam 0T 1 ] [ R′ T 0T 1] s i, j Tworldi = sRatamiT + sTatami Tworldj = sRatamjT + sTatamj s = ∥Tworldi − RatamiR−1 atamjTworldj∥ ∥Tatami − RatamiR−1 atamjTatamj∥ [R T]s [Rworldi Tworldi] [Rworldj Tworldj] [Ratami Tatami] [Ratamj Tatamj] 49
50. 50. 50
51. 51. M = [R T] min M ∥I − Ir(M)∥ M M 51
52. 52. 52
53. 53. 第4章 拡張現実感のための コンピュータビジョン技術 Fin. 53