1. 3D reconstruction of cameras and structure x i = PX i x’ i = P’X i

2. Outline of Reconstruction method 1. Compute the fundamental matrix from point correspondences 2. Compute the camera matrices from the fundamental matrix 3. For each point correspondence x i x’ i, compute the point in space that projects to these 2 image points

3. Computation of the fundamental matrix x’ i F x i = 0 With the x’ I and x i known, this equation is linear in the unknown entries of the matrix F. Thus 8 pairs of corresponding points is sufficient to solve for the entries of F up to scale. Usually, more than 8 point correspondences are used in a least square solution.

4. Computation of the camera matrices

5. Triangulation

6. Reconstruction ambiguity (a)

7. Reconstruction ambiguity (b)

8. Fig 9.2 Reconstruction ambiguity

9. Ambiguity for calibrated camera

10. Projective ambiguity

11. Projective reconstruction theorem

12. Relationship between projective and Euclidean reconstructions

13. Projective reconstruction

14. Projective Reconstruction 2 views of a house Fig. 9.3 a

15. Two views of a 3D projective reconstruction ( camera calibration matrices and scene geometry are not required) Fig 9.3b

16. Stratified reconstruction

17. The step to affine reconstruction

18. The essence of affine reconstruction is to locate the plane at infinity

19. Translation motion, Scene constraints

20. Parallel lines, distance ratios on a line

21. Projective reconstruction can be upgraded to affine using parallel scene lines

22. Affine reconstruction

23. Affine reconstruction 2

24. Affine reconstruction 3

25. The infinite homography

26. Result 9.3

27. One of the cameras is affine

28. The step to metric reconstruction

29. Proof

30. Proof 2

31. Constraints

32. Constraints 2

33. Constraints from the same cameras in all images

34. Direct metric reconstruction uisng 

35. Metric Reconstruction Fig. 9.5

36. Metric Reconstruction Texture mapped piecewise planar model

37. Metric Reconstruction 2

38. Direct Reconstruction Fig 9.6

39. Direct Reconstruction

40. Direct reconstruction Fig. 9.6

41. Direct reconstruction 2

42. Direct reconstruction 3

43. Table 9.1