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3D Vision
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dominique-derick
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3D Vision

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  1. 3D Vision Interest Points

  2. correspondence and alignment • Correspondence: matching points, patches, edges, or regions across images ≈

  3. correspondence and alignment • Alignment: solving the transformation that makes two things match better T

  4. Example: estimating “fundamental matrix” that corresponds two views

  5. Example: tracking points x x x frame 22 frame 0 frame 49 Your problem 1 for HW 2!

  6. Human eye movements

  7. Human eye movements

  8. Interest points • Suppose you have to click on some point, go away and come back after I deform the image, and click on the same points again. • Which points would you choose? original deformed

  9. Overview of Keypoint Matching 1. Find a set of distinctive key- points 2. Define a region around each keypoint A1 B3 3. Extract and normalize the region content A2 A3 B2 B1 4. Compute a local descriptor from the normalized region 5. Match local descriptors

  10. Goals for Keypoints Detect points that are repeatable and distinctive

  11. Choosing interest points Where would you tell your friend to meet you?

  12. Moravec corner detector (1980) • We should easily recognize the point by looking through a small window • Shifting a window in anydirection should give a large change in intensity

  13. Moravec corner detector flat

  14. Moravec corner detector flat

  15. Moravec corner detector flat edge

  16. Moravec corner detector corner isolated point flat edge

  17. Window function Shifted intensity Intensity Moravec corner detector Change of intensity for the shift [u,v]: Four shifts: (u,v) = (1,0), (1,1), (0,1), (-1, 1) Look for local maxima in min{E}

  18. Problems of Moravec detector • Noisy response due to a binary window function • Only a set of shifts at every 45 degree is considered • Responds too strong for edges because only minimum of E is taken into account • Harris corner detector (1988) solves these problems.

  19. Harris corner detector Noisy response due to a binary window function • Use a Gaussian function

  20. Harris corner detector Only a set of shifts at every 45 degree is considered • Consider all small shifts by Taylor’s expansion

  21. Harris corner detector Equivalently, for small shifts [u,v] we have a bilinear approximation: , where M is a 22 matrix computed from image derivatives:

  22. Harris corner detector Responds too strong for edges because only minimum of E is taken into account • A new corner measurement

  23. Harris corner detector Intensity change in shifting window: eigenvalue analysis 1, 2 – eigenvalues of M direction of the fastest change Ellipse E(u,v) = const direction of the slowest change (max)-1/2 (min)-1/2

  24. Harris corner detector 2 edge 2 >> 1 Corner 1 and 2 are large,1 ~ 2;E increases in all directions Classification of image points using eigenvalues of M: 1 and 2 are small;E is almost constant in all directions edge 1 >> 2 flat 1

  25. Harris corner detector Measure of corner response: (k – empirical constant, k = 0.04-0.06)

  26. Another view

  27. Another view

  28. Another view

  29. Harris corner detector (input)

  30. Corner response R

  31. Threshold on R

  32. Local maximum of R

  33. Harris corner detector

  34. Harris Detector: Summary • Average intensity change in direction [u,v] can be expressed as a bilinear form: • Describe a point in terms of eigenvalues of M:measure of corner response • A good (corner) point should have a large intensity change in all directions, i.e. R should be large positive

  35. threshold R R x(image coordinate) x(image coordinate) Harris Detector: Some Properties • Partial invariance to affine intensity change • Only derivatives are used => invariance to intensity shift I I+b • Intensity scale: I  aI

  36. Harris Detector: Some Properties • Rotation invariance Ellipse rotates but its shape (i.e. eigenvalues) remains the same Corner response R is invariant to image rotation

  37. Harris Detector is rotation invariant Repeatability rate: # correspondences# possible correspondences

  38. Harris Detector: Some Properties • But: non-invariant to image scale! All points will be classified as edges Corner !

  39. Harris Detector: Some Properties • Quality of Harris detector for different scale changes Repeatability rate: # correspondences# possible correspondences