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SIFT keypoint detection

SIFT keypoint detection. D. Lowe, Distinctive image features from scale-invariant keypoints , IJCV 60 (2), pp. 91-110, 2004. Keypoint detection with scale selection. We want to extract keypoints with characteristic scales that are covariant w.r.t . the image transformation.

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SIFT keypoint detection

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  1. SIFT keypoint detection D. Lowe, Distinctive image features from scale-invariant keypoints, IJCV 60 (2), pp. 91-110, 2004

  2. Keypoint detection with scale selection • We want to extract keypoints with characteristic scales that are covariantw.r.t. the image transformation

  3. Basic idea • Convolve the image with a “blob filter” at multiple scales and look for extrema of filter response in the resulting scale space T. Lindeberg, Feature detection with automatic scale selection,IJCV 30(2), pp 77-116, 1998

  4. Blob detection • Find maxima and minima of blob filter response in space and scale minima = * maxima Source: N. Snavely

  5. Blob filter • Laplacian of Gaussian: Circularly symmetric operator for blob detection in 2D

  6. Recall: Edge detection Edge f Derivativeof Gaussian Edge = maximumof derivative Source: S. Seitz

  7. Edge detection, Take 2 Edge f Second derivativeof Gaussian (Laplacian) Edge = zero crossingof second derivative Source: S. Seitz

  8. maximum From edges to blobs • Edge = ripple • Blob = superposition of two ripples Spatial selection: the magnitude of the Laplacianresponse will achieve a maximum at the center ofthe blob, provided the scale of the Laplacian is“matched” to the scale of the blob

  9. original signal(radius=8) increasing σ Scale selection • We want to find the characteristic scale of the blob by convolving it with Laplacians at several scales and looking for the maximum response • However, Laplacian response decays as scale increases:

  10. Scale normalization • The response of a derivative of Gaussian filter to a perfect step edge decreases as σ increases: • To keep response the same (scale-invariant), must multiply Gaussian derivative by σ • Laplacian is the second Gaussian derivative, so it must be multiplied by σ2

  11. Scale-normalized Laplacian response maximum Effect of scale normalization Original signal Unnormalized Laplacian response

  12. Blob detection in 2D • Scale-normalized Laplacian of Gaussian:

  13. Blob detection in 2D • At what scale does the Laplacian achieve a maximum response to a binary circle of radius r? r image Laplacian

  14. Blob detection in 2D • At what scale does the Laplacian achieve a maximum response to a binary circle of radius r? • To get maximum response, the zeros of the Laplacian have to be aligned with the circle • The Laplacian is given by (up to scale): • Therefore, the maximum response occurs at circle r 0 Laplacian image

  15. Scale-space blob detector • Convolve image with scale-normalized Laplacian at several scales

  16. Scale-space blob detector: Example

  17. Scale-space blob detector: Example

  18. Scale-space blob detector • Convolve image with scale-normalized Laplacian at several scales • Find maxima of squared Laplacian response in scale-space

  19. Scale-space blob detector: Example

  20. Efficient implementation • Approximating the Laplacian with a difference of Gaussians: (Laplacian) (Difference of Gaussians)

  21. Efficient implementation David G. Lowe. "Distinctive image features from scale-invariant keypoints.”IJCV 60 (2), pp. 91-110, 2004.

  22. Eliminating edge responses • Laplacian has strong response along edges

  23. Eliminating edge responses • Laplacian has strong response along edges • Solution: filter based on Harris response function over neighborhoods containing the “blobs”

  24. From feature detection to feature description • To recognize the same pattern in multiple images, we need to match appearance “signatures” in the neighborhoods of extracted keypoints • But corresponding neighborhoods can be related by a scale change or rotation • We want to normalize neighborhoods to make signatures invariant to these transformations

  25. p 2 0 Finding a reference orientation • Create histogram of local gradient directions in the patch • Assign reference orientation at peak of smoothed histogram

  26. SIFT features • Detected features with characteristic scales and orientations: David G. Lowe. "Distinctive image features from scale-invariant keypoints.”IJCV 60 (2), pp. 91-110, 2004.

  27. From keypoint detection to feature description • Detection is covariant: features(transform(image)) = transform(features(image)) • Description is invariant: features(transform(image)) = features(image)

  28. SIFT descriptors • Inspiration: complex neurons in the primary visual cortex D. Lowe, Distinctive image features from scale-invariant keypoints, IJCV 60 (2), pp. 91-110, 2004

  29. Properties of SIFT Extraordinarily robust detection and description technique • Can handle changes in viewpoint • Up to about 60 degree out-of-plane rotation • Can handle significant changes in illumination • Sometimes even day vs. night • Fast and efficient—can run in real time • Lots of code available Source: N. Snavely

  30. A hard keypoint matching problem NASA Mars Rover images

  31. Answer below (look for tiny colored squares…) NASA Mars Rover images with SIFT feature matchesFigure by Noah Snavely

  32. What about 3D rotations?

  33. What about 3D rotations? • Affine transformation approximates viewpoint changes for roughly planar objects and roughly orthographic cameras

  34. direction of the fastest change direction of the slowest change (max)-1/2 (min)-1/2 Affine adaptation Consider the second moment matrix of the window containing the blob: Recall: This ellipse visualizes the “characteristic shape” of the window

  35. Affine adaptation K. Mikolajczyk and C. Schmid, Scale and affine invariant interest point detectors, IJCV 60(1):63-86, 2004

  36. Keypoint detectors/descriptors for recognition: A retrospective Detected features S. Lazebnik, C. Schmid, and J. Ponce, A Sparse Texture Representation Using Affine-Invariant Regions, CVPR 2003

  37. Keypoint detectors/descriptors for recognition: A retrospective Detected features R. Fergus, P. Perona, and A. Zisserman, Object Class Recognition by Unsupervised Scale-Invariant Learning, CVPR 2003 – winner of 2013 Longuet-Higgins Prize

  38. Keypoint detectors/descriptors for recognition: A retrospective S. Lazebnik, C. Schmid, and J. Ponce, Beyond Bags of Features: Spatial Pyramid Matching for Recognizing Natural Scene Categories, CVPR 2006 – winner of 2016 Longuet-Higgins Prize

  39. level 2 Keypoint detectors/descriptors for recognition: A retrospective level 1 level 0 S. Lazebnik, C. Schmid, and J. Ponce, Beyond Bags of Features: Spatial Pyramid Matching for Recognizing Natural Scene Categories, CVPR 2006 – winner of 2016 Longuet-Higgins Prize

  40. Keypoint detectors/descriptors for recognition: A retrospective

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