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Model Fitting

Model Fitting. Hao Jiang Computer Science Department Oct 8, 2009. Hough transform for circles. For a fixed radius r, unknown gradient direction. Circle: center (a,b) and radius r. Hough space. Image space. Source: K. Grauman. Hough transform for circles.

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Model Fitting

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  1. Model Fitting Hao Jiang Computer Science Department Oct 8, 2009

  2. Hough transform for circles • For a fixed radius r, unknown gradient direction • Circle: center (a,b) and radius r Hough space Image space Source: K. Grauman

  3. Hough transform for circles • For a fixed radius r, unknown gradient direction • Circle: center (a,b) and radius r Intersection: most votes for center occur here. Image space Hough space Source: K. Grauman

  4. Hough transform for circles • For an unknown radius r, unknown gradient direction • Circle: center (a,b) and radius r r b a Hough space Image space Source: K. Grauman

  5. Hough transform for circles • For an unknown radius r, unknown gradient direction • Circle: center (a,b) and radius r r b a Hough space Image space Source: K. Grauman

  6. Hough transform for circles • For an unknown radius r, known gradient direction • Circle: center (a,b) and radius r x θ Image space Hough space Source: K. Grauman

  7. Hough transform for circles For every edge pixel (x,y) : For each possible radius value r: For each possible gradient direction θ: // or use estimated gradient a = x – r cos(θ) b = y + r sin(θ) H[a,b,r] += 1 end end Source: K. Grauman

  8. Example: detecting circles with Hough Crosshair indicates results of Hough transform, bounding box found via motion differencing. Source: K. Grauman

  9. Example: detecting circles with Hough Original Edges Votes: Penny Note: a different Hough transform (with separate accumulators) was used for each circle radius (quarters vs. penny). Source: K. Grauman

  10. Example: detecting circles with Hough Original Edges Votes: Quarter Source: K. Grauman Coin finding sample images from: Vivek Kwatra

  11. General Hough Transform • Hough transform can also be used to detection arbitrary shaped object. Template Target

  12. General Hough Transform • Hough transform can also be used to detection arbitrary shaped object. Template Target

  13. General Hough Transform • Hough transform can also be used to detection arbitrary shaped object. Template Target

  14. General Hough Transform • Hough transform can also be used to detection arbitrary shaped object. Template Target

  15. General Hough Transform • Rotation Invariance

  16. Example Say we’ve already stored a table of displacement vectors as a function of edge orientation for this model shape. model shape Source: L. Lazebnik

  17. Example Now we want to look at some edge points detected in a new image, and vote on the position of that shape. displacement vectors for model points

  18. Example range of voting locations for test point

  19. Example range of voting locations for test point

  20. Example votes for points with θ =

  21. Example displacement vectors for model points

  22. Example range of voting locations for test point

  23. Example votes for points with θ =

  24. visual codeword withdisplacement vectors training image Application in recognition • Instead of indexing displacements by gradient orientation, index by “visual codeword” B. Leibe, A. Leonardis, and B. Schiele, Combined Object Categorization and Segmentation with an Implicit Shape Model, ECCV Workshop on Statistical Learning in Computer Vision 2004 Source: L. Lazebnik

  25. Application in recognition • Instead of indexing displacements by gradient orientation, index by “visual codeword” test image Source: L. Lazebnik

  26. RANSAC • RANSAC – Random Sampling Consensus • Procedure: • Randomly generate a hypothesis • Test the hypothesis • Repeat for large enough times and choose the best one

  27. Line Detection

  28. Line Detection

  29. Line Detection

  30. Line Detection Count “inliers”: 7

  31. Line Detection Inlier number: 3

  32. Line Detection After many trails, we decide this is the best line.

  33. Probability of Success • What’s the success rate of RANSAC given a fixed number of validations? • Given a success rate, how to choose the minimum number of validations?

  34. Object Detection Using RANSAC Target Template

  35. Scale and Rotation Invariant Feature • SIFT (D. Lowe, UBC)

  36. Stable Feature

  37. Stable Feature Local max/min point’s values are stable when the scale changes

  38. SIFT Filtering the image using filters at different scales. (for example using Gaussian filter)

  39. Difference of Gaussian

  40. SIFT Feature Points (b) Shows the points at the local max/min of DOG scale space for the image in (a).

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