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Image Features: Descriptors and matching

Image Features: Descriptors and matching. CSE 576, Spring 2005 Richard Szeliski. Today’s lecture. Feature detectors scale and affine invariant (points, regions) Feature descriptors patches, oriented patches SIFT (orientations) Feature matching exhaustive search hashing

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Image Features: Descriptors and matching

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  1. Image Features:Descriptors and matching CSE 576, Spring 2005 Richard Szeliski

  2. Today’s lecture • Feature detectors • scale and affine invariant (points, regions) • Feature descriptors • patches, oriented patches • SIFT (orientations) • Feature matching • exhaustive search • hashing • nearest neighbor techniques CSE 576: Computer Vision

  3. Pointers to papers: CSE 576: Computer Vision

  4. Invariant Local Features • Image content is transformed into local feature coordinates that are invariant to translation, rotation, scale, and other imaging parameters SIFT Features CSE 576: Computer Vision

  5. Advantages of local features • Locality: features are local, so robust to occlusion and clutter (no prior segmentation) • Distinctiveness: individual features can be matched to a large database of objects • Quantity: many features can be generated for even small objects • Efficiency: close to real-time performance • Extensibility: can easily be extended to wide range of differing feature types, with each adding robustness CSE 576: Computer Vision

  6. Scale Invariant Detection • Consider regions (e.g. circles) of different sizes around a point • Regions of corresponding sizes will look the same in both images CSE 576: Computer Vision

  7. Scale Invariant Detection • The problem: how do we choose corresponding circles independently in each image? CSE 576: Computer Vision

  8. Scale invariance • Requires a method to repeatably select points in location and scale: • The only reasonable scale-space kernel is a Gaussian (Koenderink, 1984; Lindeberg, 1994) • An efficient choice is to detect peaks in the difference of Gaussian pyramid (Burt & Adelson, 1983; Crowley & Parker, 1984 – but examining more scales) • Difference-of-Gaussian with constant ratio of scales is a close approximation to Lindeberg’s scale-normalized Laplacian (can be shown from the heat diffusion equation) CSE 576: Computer Vision

  9. scale = 1/2 Image 1 f f Image 2 region size region size Scale Invariant Detection • Solution: • Design a function on the region (circle), which is “scale invariant” (the same for corresponding regions, even if they are at different scales) Example: average intensity. For corresponding regions (even of different sizes) it will be the same. • For a point in one image, we can consider it as a function of region size (circle radius) CSE 576: Computer Vision

  10. scale = 1/2 Image 1 f f Image 2 s1 s2 region size region size Scale Invariant Detection • Common approach: Take a local maximum of this function Observation: region size, for which the maximum is achieved, should be invariant to image scale. Important: this scale invariant region size is found in each image independently! CSE 576: Computer Vision

  11. f f Good ! bad region size f region size bad region size Scale Invariant Detection • A “good” function for scale detection: has one stable sharp peak • For usual images: a good function would be a one which responds to contrast (sharp local intensity change) CSE 576: Computer Vision

  12. Scale Invariant Detection • Functions for determining scale Kernels: (Laplacian) (Difference of Gaussians) where Gaussian Note: both kernels are invariant to scale and rotation CSE 576: Computer Vision

  13. Scale space: one octave at a time CSE 576: Computer Vision

  14. Key point localization • Detect maxima and minima of difference-of-Gaussian in scale space • Fit a quadratic to surrounding values for sub-pixel and sub-scale interpolation (Brown & Lowe, 2002) • Taylor expansion around point: • Offset of extremum (use finite differences for derivatives): CSE 576: Computer Vision

  15. scale  Laplacian  y x  Harris  scale • SIFT (Lowe)2Find local maximum of: • Difference of Gaussians in space and scale  DoG  y x  DoG  Scale Invariant Detectors • Harris-Laplacian1Find local maximum of: • Harris corner detector in space (image coordinates) • Laplacian in scale 1 K.Mikolajczyk, C.Schmid. “Indexing Based on Scale Invariant Interest Points”. ICCV 20012 D.Lowe. “Distinctive Image Features from Scale-Invariant Keypoints”. Accepted to IJCV 2004 CSE 576: Computer Vision

  16. Scale Invariant Detection: Summary • Given:two images of the same scene with a large scale difference between them • Goal:find the same interest points independently in each image • Solution: search for maxima of suitable functions in scale and in space (over the image) • Methods: • Harris-Laplacian [Mikolajczyk, Schmid]: maximize Laplacian over scale, Harris’ measure of corner response over the image • SIFT [Lowe]: maximize Difference of Gaussians over scale and space CSE 576: Computer Vision

  17. Affine invariant detection • Above we considered:Similarity transform (rotation + uniform scale) • Now we go on to:Affine transform (rotation + non-uniform scale) CSE 576: Computer Vision

  18. Affine invariant detection • Harris-Affine [Mikolajczyk & Schmid, IJCV04]: • use Harris moment matrix to select dominant directions and anisotropy CSE 576: Computer Vision

  19. Affine invariant detection • Matching Widely Separated Views Based on Affine Invariant Regions, T. TUYTELAARS and L. VAN GOOL, IJCV 2004 CSE 576: Computer Vision

  20. f points along the ray Affine invariant detection • Take a local intensity extremum as initial point • Go along every ray starting from this point and stop when extremum of function f is reached • We will obtain approximately corresponding regions Remark: we search for scale in every direction CSE 576: Computer Vision

  21. Geometric Moments: Fact: moments mpq uniquely determine the function f Taking f to be the characteristic function of a region (1 inside, 0 outside), moments of orders up to 2 allow to approximate the region by an ellipse This ellipse will have the same moments of orders up to 2 as the original region Affine invariant detection • The regions found may not exactly correspond, so we approximate them with ellipses CSE 576: Computer Vision

  22. ( p = [x, y]T is relative to the center of mass) Affine invariant detection • Covariance matrix of region points defines an ellipse: Ellipses, computed for corresponding regions, also correspond CSE 576: Computer Vision

  23. Affine invariant detection • Algorithm summary (detection of affine invariant region): • Start from a local intensity extremum point • Go in every direction until the point of extremum of some function f • Curve connecting the points is the region boundary • Compute geometric moments of orders up to 2 for this region • Replace the region with ellipse CSE 576: Computer Vision

  24. MSER J.Matas et.al. “Distinguished Regions for Wide-baseline Stereo”. BMVC 2002. • Maximally Stable Extremal Regions • Threshold image intensities: I > I0 • Extract connected components(“Extremal Regions”) • Find a threshold when an extremalregion is “Maximally Stable”,i.e. local minimum of the relativegrowth of its square • Approximate a region with an ellipse CSE 576: Computer Vision

  25. Affine invariant detection • Under affine transformation, we do not know in advance shapes of the corresponding regions • Ellipse given by geometric covariance matrix of a region robustly approximates this region • For corresponding regions ellipses also correspond • Methods: • Search for extremum along rays [Tuytelaars, Van Gool]: • Maximally Stable Extremal Regions [Matas et.al.] CSE 576: Computer Vision

  26. Today’s lecture • Feature detectors • scale and affine invariant (points, regions) • Feature descriptors • patches, oriented patches • SIFT (orientations) • Feature matching • exhaustive search • hashing • nearest neighbor techniques CSE 576: Computer Vision

  27. Feature selection • Distribute points evenly over the image CSE 576: Computer Vision

  28. Adaptive Non-maximal Suppression • Desired: Fixed # of features per image • Want evenly distributed spatially… • Search over non-maximal suppression radius[Brown, Szeliski, Winder, CVPR’05] r = 8, n = 1388 r = 20, n = 283 CSE 576: Computer Vision

  29. Feature descriptors • We know how to detect points • Next question: How to match them? ? • Point descriptor should be: • Invariant 2. Distinctive CSE 576: Computer Vision

  30. Descriptors invariant to rotation • Harris corner response measure:depends only on the eigenvalues of the matrix M • Careful with window effects! (Use circular) CSE 576: Computer Vision

  31. Multi-Scale Oriented Patches • Interest points • Multi-scale Harris corners • Orientation from blurred gradient • Geometrically invariant to similarity transforms • Descriptor vector • Bias/gain normalized sampling of local patch (8x8) • Photometrically invariant to affine changes in intensity • [Brown, Szeliski, Winder, CVPR’2005] CSE 576: Computer Vision

  32. Descriptor Vector • Orientation = blurred gradient • Similarity Invariant Frame • Scale-space position (x, y, s) + orientation () CSE 576: Computer Vision

  33. MOPS descriptor vector • 8x8 oriented patch • Sampled at 5 x scale • Bias/gain normalisation: I’ = (I – )/ 40 pixels 8 pixels CSE 576: Computer Vision

  34. SIFT vector formation • Thresholded image gradients are sampled over 16x16 array of locations in scale space • Create array of orientation histograms • 8 orientations x 4x4 histogram array = 128 dimensions CSE 576: Computer Vision

  35. SIFT – Scale Invariant Feature Transform1 • Empirically found2 to show very good performance, invariant to image rotation, scale, intensity change, and to moderate affine transformations Scale = 2.5Rotation = 450 1 D.Lowe. “Distinctive Image Features from Scale-Invariant Keypoints”. Accepted to IJCV 20042 K.Mikolajczyk, C.Schmid. “A Performance Evaluation of Local Descriptors”. CVPR 2003 CSE 576: Computer Vision

  36. Invariance to Intensity Change • Detectors • mostly invariant to affine (linear) change in image intensity, because we are searching for maxima • Descriptors • Some are based on derivatives => invariant to intensity shift • Some are normalized to tolerate intensity scale • Generic method: pre-normalize intensity of a region (eliminate shift and scale) CSE 576: Computer Vision

  37. Today’s lecture • Feature detectors • scale and affine invariant (points, regions) • Feature descriptors • patches, oriented patches • SIFT (orientations) • Feature matching • exhaustive search • hashing • nearest neighbor techniques CSE 576: Computer Vision

  38. Feature matching • Exhaustive search • for each feature in one image, look at all the other features in the other image(s) • Hashing • compute a short descriptor from each feature vector, or hash longer descriptors (randomly) • Nearest neighbor techniques • k-trees and their variants (Best Bin First) CSE 576: Computer Vision

  39. Wavelet-based hashing • Compute a short (3-vector) descriptor from an 8x8 patch using a Haar “wavelet” • Quantize each value into 10 (overlapping) bins (103 total entries) • [Brown, Szeliski, Winder, CVPR’2005] CSE 576: Computer Vision

  40. Locality sensitive hashing CSE 576: Computer Vision

  41. Nearest neighbor techniques • k-D treeand • Best BinFirst(BBF) Indexing Without Invariants in 3D Object Recognition, Beis and Lowe, PAMI’99 CSE 576: Computer Vision

  42. Today’s lecture • Feature detectors • scale and affine invariant (points, regions) • Feature descriptors • patches, oriented patches • SIFT (orientations) • Feature matching • exhaustive search • hashing • nearest neighbor techniques Questions? CSE 576: Computer Vision

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