
Harris interest points Comparing interest points

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Comparing interest points (SSD, ZNCC, SIFT) Scale & affine invariant interest points Evaluation and comparison of different detectors Region descriptors and their performance
Description regions have to be adapted to scale changes Description regions have to be adapted to scale changes
We want to find the characteristic scale by convolving it with, for example, Laplacians at several scales and looking for the maximum response We want to find the characteristic scale by convolving it with, for example, Laplacians at several scales and looking for the maximum response However, Laplacian response decays as scale increases:
The response of a derivative of Gaussian filter to a perfect step edge decreases as σ increases The response of a derivative of Gaussian filter to a perfect step edge decreases as σ increases
The response of a derivative of Gaussian filter to a perfect step edge decreases as σ increases The response of a derivative of Gaussian filter to a perfect step edge decreases as σ increases To keep response the same (scaleinvariant), must multiply Gaussian derivative by σ Laplacian is the second Gaussian derivative, so it must be multiplied by σ2
Laplacian of Gaussian: Circularly symmetric operator for blob detection in 2D Laplacian of Gaussian: Circularly symmetric operator for blob detection in 2D
Laplacian of Gaussian: Circularly symmetric operator for blob detection in 2D Laplacian of Gaussian: Circularly symmetric operator for blob detection in 2D
The 2D Laplacian is given by The 2D Laplacian is given by For a binary circle of radius r, the Laplacian achieves a maximum at
We define the characteristic scale as the scale that produces peak of Laplacian response We define the characteristic scale as the scale that produces peak of Laplacian response
For a point compute a value (gradient, Laplacian etc.) at several scales For a point compute a value (gradient, Laplacian etc.) at several scales Normalization of the values with the scale factor Select scale at the maximum → characteristic scale Exp. results show that the Laplacian gives best results
Scale invariance of the characteristic scale Scale invariance of the characteristic scale
Scale invariance of the characteristic scale Scale invariance of the characteristic scale
HarrisLaplace (Mikolajczyk & Schmid’01) HarrisLaplace (Mikolajczyk & Schmid’01) Laplacian detector (Lindeberg’98) Difference of Gaussian (Lowe’99)
invariant points + associated regions [Mikolajczyk & Schmid’01]
Detection of maxima and minima of Laplacian in scale space
Fast computation, scale space processed one octave at a time Fast computation, scale space processed one octave at a time
Scale invariant interest points Affine invariant interest points
Evaluation of interest points Descriptors and their evaluation
Scale invariance is not sufficient for large baseline changes
Initialize with scaleinvariant Harris/Hessian/Laplacian points Initialize with scaleinvariant Harris/Hessian/Laplacian points Estimation of the affine neighbourhood with the second moment matrix [Lindeberg’94] Apply affine neighbourhood estimation to the scaleinvariant interest points [Mikolajczyk & Schmid’02, Schaffalitzky & Zisserman’02] Excellent results in a recent comparison
Based on the second moment matrix (Lindeberg’94) Based on the second moment matrix (Lindeberg’94)
Iterative estimation – initial points Iterative estimation – initial points
Iterative estimation – iteration #1 Iterative estimation – iteration #1
Iterative estimation – iteration #2 Iterative estimation – iteration #2
Iterative estimation – iteration #3, #4 Iterative estimation – iteration #3, #4
Extremal regions: connected components in a thresholded image (all pixels above/below a threshold) Extremal regions: connected components in a thresholded image (all pixels above/below a threshold) Maximally stable: minimal change of the component (area) for a change of the threshold, i.e. region remains stable for a change of threshold Excellent results in a recent comparison
Harris interest points Comparing interest points (SSD, ZNCC, SIFT) Scale & affine invariant interest points Evaluation and comparison of different detectors Region descriptors and their performance
Quantitative evaluation of interest point/region detectors Quantitative evaluation of interest point/region detectors  points / regions at the same relative location and area
Repeatability rate : percentage of corresponding points Two points/regions are corresponding if  location error small
 area intersection large
[K. Mikolajczyk, T. Tuytelaars, C. Schmid, A. Zisserman, J. Matas, F. Schaffalitzky, T. Kadir & L. Van Gool ’05]
Different types of transformation  Viewpoint change
 Scale change
 Image blur
 JPEG compression
 Light change
Two scene types Transformations within the sequence (homographies)
Good performance for large viewpoint and scale changes Good performance for large viewpoint and scale changes Results depend on transformation and scene type, no one best detector Detectors are complementary Performance of the different scale invariant detectors is very similar (HarrisLaplace, Hessian, LoG and DOG) Scaleinvariant detector sufficient up to 40 degrees of viewpoint change
Harris interest points Comparing interest points (SSD, ZNCC, SIFT) Scale & affine invariant interest points Evaluation and comparison of different detectors Region descriptors and their performance
Regions invariant to geometric transformations except rotation  normalization with dominant gradient direction
Regions not invariant to photometric transformations  normalization with mean and standard deviation of the image patch
Gaussian derivativebased descriptors Gaussian derivativebased descriptors  Differential invariants (Koenderink and van Doorn’87)
 Steerable filters (Freeman and Adelson’91)
Moment invariants [Van Gool et al.’96] SIFT (Lowe’99) Shape context [Belongie et al.’02] SIFT with PCA dimensionality reduction Gradient PCA [Ke and Sukthankar’04] SURF descriptor [Bay et al.’08] DAISY descriptor [Tola et al.’08, Windler et al’09]
Descriptors should be Descriptors should be  Distinctive
 Robust to changes on viewing conditions as well as to errors of the detector
Detection rate (recall)  #correct matches / #correspondences
False positive rate  #false matches / #all matches
Variation of the distance threshold  distance (d1, d2) < threshold
SIFT based descriptors perform best Significant difference between SIFT and low dimension descriptors as well as crosscorrelation Robust region descriptors better than pointwise descriptors Performance of the descriptor is relatively independent of the detector
Binaries for detectors and descriptors Binaries for detectors and descriptors  Building blocks for recognition systems
Carefully designed test setup  Dataset with transformations
 Evaluation code in matlab
 Benchmark for new detectors and descriptors
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