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Scene planes and homographies

Scene planes and homographies. Homographies given the plane and vice versa. Proof of result 12.1. Example 12.2 A calibrated stereo rig. A calibrated stereo rig 2. A calibrated stereo rig 3. The homography induced by a plane Fig.12.1. Fig 12.1 Legend.

philip-avila
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Scene planes and homographies

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  1. Scene planes and homographies

  2. Homographies given the plane and vice versa

  3. Proof of result 12.1

  4. Example 12.2 A calibrated stereo rig

  5. A calibrated stereo rig 2

  6. A calibrated stereo rig 3

  7. The homography induced by a plane Fig.12.1

  8. Fig 12.1 Legend

  9. Homographies compatible with epipolar Geometry

  10. Two sets of 4 arbitrary points from 2 images

  11. Epipolar geometry define conditions on homographies

  12. Counting degrees of freedom

  13. Compatibility constraints Fig.12.2 ae’ = H e

  14. Compatibility constraints 2 Fig. 12.2 b HT le’ = le

  15. Compatibility constraints 3Fig. 12.2 c

  16. Fig 12.2 Compatibility constraints

  17. Result 12.3

  18. Homographies are compatible with fundamental matrix

  19. Corollary 12.4

  20. Result 12.5

  21. 13.6 Plane induced homographies given F and image correspondences:(a) 3 points, (b) a line and a point

  22. 12.2.1 Three points

  23. Three points

  24. The first (explicit) method is preferred

  25. Degenerate geometry for an implicit computation of the homography Fig. 12.3

  26. Fig. 12.3 Legend

  27. Determining the points Xi is not necessary in first method All that is important

  28. Result 12.6

  29. Proof

  30. Proof 2

  31. Consistency conditions

  32. Consistency conditions 2

  33. Algorithms 12.1 The optimal estimate of homography induced by a plane defined by 3 points

  34. 12.2.2 A point and line

  35. A one parameter family of homographies Fig 12.4 (a), (b)

  36. Fig 12.4 Legend

  37. Result 12.7

  38. Proof of result 12.7

  39. Proof of result 12.7 (2)

  40. Proof of result 12.7 (3)

  41. Result 12.8

  42. Result 12.8 2

  43. Geometric interpretation of the point map H(m) Explore the

  44. A homography between corresponding line images Fig. 12.5

  45. Fig. 12.5 Legend

  46. Degenerate homographies

  47. Degenerate homographies 2

  48. A degenerate homography Fig. 12.6

  49. Fig. 12.6 Legend

  50. 12.3 Computing F given the homography induced by a plane

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