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Computer Vision

Mehdi Faraji farajimhd@gmail.com. Computer Vision. Local Invariant Features. SLIDES have been prepared by: Dr. Ghassabi. Outline. Why do we care about matching features? Problem Statement Properties of features Types of invariance Introduction to feature matching

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Computer Vision

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  1. Mehdi Faraji farajimhd@gmail.com Computer Vision Local Invariant Features SLIDES have been prepared by: Dr. Ghassabi

  2. Outline • Why do we care about matching features? • Problem Statement • Properties of features • Types of invariance • Introduction to feature matching • Matching using invariant descriptors • Feature Detection • Corner Detection • Moravec, harris • Harris properties (rotation, intensity, scale invariance) • Low’s key point • Feature description • SIFT (Scale Invariant Feature Transform) • SIFT Extensions: PCA-SIFT, GLoH ,SPIN image, RIFT, • Feature matching • Applications (examples) • Future Works • Conclusion Outline Motivation Problems statement How we solve it Future Work Reference

  3. Motivation • Why do we care about matching features? • image stitching, • object recognition, • Indexing and database retrieval, • Motion tracking • … Others Outline Motivation Problems statement How we solve it Future Work Reference

  4. Example: How do we build panorama? We need to match (align) images

  5. Matching with Features Detect feature points in both images

  6. Matching with Features Detect feature points in both images Find corresponding pairs

  7. Matching with Features Detect feature points in both images Find corresponding pairs Use these pairs to align images

  8. Types of variance • Illumination • Scale • Rotation • Affine • Full Perspective • Problems statements • Properties of good features Outline Motivation Problems statement How we solve it Future Work Reference

  9. Types of variance • Outline • Motivation • Problems statement • Types of variance • Problem1 • Problem2 • Properties of good features • How we solve it • Future Work • Reference • Illumination

  10. Types of variance • Outline • Motivation • Problems statement • Types of variance • Problem1 • Problem2 • Properties of good features • How we solve it • Future Work • Reference • Illumination • Scale

  11. Types of variance • Outline • Motivation • Problems statement • Types of variance • Problem1 • Problem2 • Properties of good features • How we solve it • Future Work • Reference • Illumination • Scale • Rotation

  12. Types of variance • Outline • Motivation • Problems statement • Types of variance • Problem1 • Problem2 • Properties of good features • How we solve it • Future Work • Reference • Illumination • Scale • Rotation • Affine

  13. Types of variance • Outline • Motivation • Problems statement • Types of variance • Problem1 • Problem2 • Properties of good features • How we solve it • Future Work • Reference • Illumination • Scale • Rotation • Affine • Full Perspective

  14. Problems statement • Problem 1: • Detect the same point independently in both images • Outline • Motivation • Problems statement • Types of variance • Problem1 • Problem2 • Properties of good features • How we solve it • Future Work • Reference no chance to match! We need a repeatable detector How to find landmarks to match across two images? How achieve landmarks invariance to scale, rotation, illumination distortions?

  15. Problems statement • Problem 2: • For each point correctly recognize the corresponding one • Outline • Motivation • Problems statement • Types of variance • Problem1 • Problem2 • Properties of good features • How we solve it • Future Work • Reference ? We need a reliable and distinctive descriptor How to distinguish one landmark from another?

  16. Properties of features • Distinctiveness • Invariance • Invariance to illumination, scale, Rotation, Affine, full perspective Good features should be robust to all sorts of distortions that can occur between images. • Outline • Motivation • Problems statement • Types of variance • Problem1 • Problem2 • Properties of good features • How we solve it • Future Work • Reference

  17. Methods using invariant descriptors • Methods using invariant descriptorsInvarianceto: transformation change in illumination image noiseDistinctiveness • Local features • Feature Detector • Feature descriptor • Feature-matching • Outline • Motivation • Problems statement • How we solve it • Methods of Feature matching • Invariant descriptors • Future Work • Reference

  18. Methods using invariant descriptors • Local features • Feature Detector • Point detector • Corner detectors • Moravec, harris, SUSAN, Trajkovic operators • Low’s key point • Region detector • Harris-Laplase, Harris affine, Hessian affine, edge-based, Intensity-based, salient region detectors • Feature descriptor • Feature-matching • Outline • Motivation • Problems statement • How we solve it • Methods of Feature matching • Invariant descriptors • Future Work • Reference

  19. Methods using invariant descriptors • Local features • Feature Detector • Feature descriptor • Filter-based • Steerable filters • Gabor filters • Complex filters • Distribution-based • Local • SIFT, PCA-SIFT, GLOH, Spin image, RIFT,, SURF • global • Shape context • Textons • Derivative-based • Others • Moment-based, Phase-based, Color-based • Feature-matching • Outline • Motivation • Problems statement • How we solve it • Methods of Feature matching • Invariant descriptors • Future Work • Reference

  20. Corner detectors

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

  22. Moravec corner detector:Idea flat no change in all directions

  23. Moravec corner detector:Idea flat

  24. Moravec corner detector:Idea flat edge no change along the edge direction

  25. Moravec corner detector:Idea corner isolated point flat edge significant change in all directions

  26. Moravec corner detector:Idea • Feature detection: the math • Consider shifting the window W by (u,v) • how do the pixels in W change? • compare each pixel before and after bysumming up the squared differences (SSD) • this defines an SSD “error” of E(u,v): W

  27. Window function Shifted intensity Intensity E u v Moravec corner detector:Idea 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}

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

  29. Harris corner detector : the math Noisy response due to a binary window function • Use a Gaussian function

  30. Harris corner detector : the math

  31. Harris corner detector : the math Equivalently, for small shifts [u,v] we have a bilinear approximation: , where M is a 22 matrix computed from image derivatives: • You can move the center of the green window to anywhere on the blue unit circle • Which directions will result in the largest and smallest E values? • We can find these directions by looking at the eigenvectors of M

  32. 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

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

  34. Selecting Good Features l1 and l2 are large

  35. Selecting Good Features large l1, small l2

  36. Selecting Good Features small l1, small l2

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

  38. Harris corner detector: the math Measure of corner response: (k – empirical constant, k = 0.04-0.06) • The Algorithm: • Find points with large corner response function R (R > threshold) • Take the points of local maxima of R

  39. Harris Detector 2 “Edge” “Corner” • R depends only on eigenvalues of M • R is large for a corner • R is negative with large magnitude for an edge • |R| is small for a flat region R < 0 R > 0 “Flat” “Edge” |R| small R < 0 1

  40. Another view

  41. Another view

  42. Another view

  43. Harris corner detector (input)

  44. Corner response R

  45. Threshold on R

  46. Local maximum of R

  47. Harris corner detector

  48. Summary of Harris detector

  49. 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

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