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Computer Vision Group University of California Berkeley Matching Shapes Serge Belongie *, Jitendra Malik and Jan Puzicha U.C. Berkeley * Present address: U.C. San Diego
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Computer Vision Group University of California Berkeley Biological Shape D’Arcy Thompson: On Growth and Form, 1917 –studied transformations between shapes of organisms
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Computer Vision Group University of California Berkeley Deformable Templates: Related Work Fischler & Elschlager (1973) Grenander et al. (1991) Yuille (1991) von der Malsburg (1993)
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Computer Vision Group University of California Berkeley Matching Framework Find correspondences between points on shape Estimate transformation Measure similarity modeltarget...
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Computer Vision Group University of California Berkeley Comparing Pointsets
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Computer Vision Group University of California Berkeley Shape Context Count the number of points inside each bin, e.g.: Count = 4 Count = 10... FCompact representation of distribution of points relative to each point
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Computer Vision Group University of California Berkeley Shape Context
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Computer Vision Group University of California Berkeley Comparing Shape Contexts Compute matching costs using Chi Squared distance: Recover correspondences by solving linear assignment problem with costs C ij [Jonker & Volgenant 1987]
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Computer Vision Group University of California Berkeley Matching Framework Find correspondences between points on shape Estimate transformation Measure similarity modeltarget...
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Computer Vision Group University of California Berkeley 2D counterpart to cubic spline: Minimizes bending energy: Solve by inverting linear system Can be regularized when data is inexact Thin Plate Spline Model Duchon (1977), Meinguet (1979), Wahba (1991)
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Computer Vision Group University of California Berkeley Matching Example modeltarget
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Computer Vision Group University of California Berkeley Outlier Test Example
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Computer Vision Group University of California Berkeley Synthetic Test Results Fish - deformation + noiseFish - deformation + outliers ICPShape ContextChui & Rangarajan
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Computer Vision Group University of California Berkeley Matching Framework Find correspondences between points on shape Estimate transformation Measure similarity modeltarget...
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Computer Vision Group University of California Berkeley Terms in Similarity Score Shape Context difference Local Image appearance difference –orientation –gray-level correlation in Gaussian window –… (many more possible) Bending energy We used the weighted sum Shape context + 1.6*image appearance + 0.3*bending
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Computer Vision Group University of California Berkeley Object Recognition Experiments COIL 3D Objects Handwritten Digits Trademarks FExactly the same algorithm used on all experiments
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Computer Vision Group University of California Berkeley COIL Object Database
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Computer Vision Group University of California Berkeley Error vs. Number of Views
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Computer Vision Group University of California Berkeley Prototypes Selected for 2 Categories Details in Belongie, Malik & Puzicha (NIPS2000)
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Computer Vision Group University of California Berkeley Error vs. Number of Views
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Computer Vision Group University of California Berkeley Handwritten Digit Recognition MNIST 60 000: –linear: 12.0% –40 PCA+ quad: 3.3% –1000 RBF +linear: 3.6% –K-NN: 5% –K-NN (deskewed) : 2.4% –K-NN (tangent dist.) : 1.1% –SVM: 1.1% –LeNet 5: 0.95% MNIST 600 000 (distortions): –LeNet 5: 0.8% –SVM: 0.8% –Boosted LeNet 4: 0.7% MNIST 20 000: –K-NN, Shape Context matching: 0.63%
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Computer Vision Group University of California Berkeley
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Computer Vision Group University of California Berkeley Trademark Similarity
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Computer Vision Group University of California Berkeley Conclusion Introduced new matching algorithm matching based on shape contexts and TPS Robust to outliers & noise Forms basis of object recognition technique that performs well in a variety of domains using exactly the same algorithm
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