複合現実感のためのコンピュータビジョン技術

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

3. 3 ↪

4. ↪ ↪ ↪ 4

6. Xworld Yworld Zworld u v Xcamera Ycamera Zcamera u Xworld 6

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. Xworld u 8

9. ˜Xcamera = [ R T 0T 1] ˜Xworld Xcamera = RXworld+T 9

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. s ˜u = K [E 0] ˜Xcamera Xcamera u s ˜u = K [R T] ˜Xworld ˜Xcamera = [ R T 0T 1] ˜Xworld Xworld 11

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. u, Xworld H Xworld, Yworld 13

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. s ˜u = K [R T] ˜Xworld s ˜u = H ˜XXY 15

16. 16

17. Xworld uXworld [R T] 17

18. Yworld Xworld Zworld Yworld Xworld Zworld Yworld Xworld Zworld Yworld Xworld Zworld 18

19. s ˜u = K [R T] ˜Xworld [R T] 19

20. uXworld 20

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. Xworld u 22

23. 23

24. 24

25. 25

26. 26

27. u, Xworld H Xworld, Yworld 27

28. 28

29. 29

30. 30

31. 31

32. 32

33. H [R T] 33

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

36. 36

37. 37

38. min H ∥It−1 − It(H)∥ It It HIt(H) s ˜u = H ˜XXY 38

39. 39

40. P = K [R T] s ˜u = P ˜Xworld [R T] P Xworld u 40

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

43. P, P′ u, u′ Xworld (u, Xworld) u, u′ Xworld P, P′ 43

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. xEx′ = 0 E R tx, x′ 45

46. 46

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. 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. [ 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

51. M = [R T] min M ∥I − Ir(M)∥ M M 51

52. 52

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

複合現実感のためのコンピュータビジョン技術

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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複合現実感のためのコンピュータビジョン技術