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Biological Shape

Explore a comprehensive shape matching framework for object recognition using Shape Context and Thin Plate Spline Model. Find correspondences, estimate transformation, and measure similarity efficiently. Robust to outliers and noise, the algorithm excels in various domains with consistent performance.

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Biological Shape

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  1. Matching ShapesSerge Belongie*, Jitendra Malikand Jan Puzicha U.C. Berkeley*Present address: U.C. San Diego

  2. Biological Shape • D’Arcy Thompson: On Growth and Form, 1917 • studied transformations between shapes of organisms

  3. Deformable Templates: Related Work • Fischler & Elschlager (1973) • Grenander et al. (1991) • Yuille (1991) • von der Malsburg (1993)

  4. Matching Framework ... model target • Find correspondences between points on shape • Estimate transformation • Measure similarity

  5. Comparing Pointsets

  6. Shape Context Count the number of points inside each bin, e.g.: Count = 4 ... Count = 10 • Compact representation of distribution of points relative to each point

  7. Shape Context

  8. Comparing Shape Contexts Compute matching costs using Chi Squared distance: Recover correspondences by solving linear assignment problem with costs Cij [Jonker & Volgenant 1987]

  9. Matching Framework ... model target • Find correspondences between points on shape • Estimate transformation • Measure similarity

  10. Thin Plate Spline Model • 2D counterpart to cubic spline: • Minimizes bending energy: • Solve by inverting linear system • Can be regularized when data is inexact Duchon (1977), Meinguet (1979), Wahba (1991)

  11. MatchingExample model target

  12. Outlier Test Example

  13. Synthetic Test Results Fish - deformation + noise Fish - deformation + outliers ICP Shape Context Chui & Rangarajan

  14. Matching Framework ... model target • Find correspondences between points on shape • Estimate transformation • Measure similarity

  15. 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 sumShape context + 1.6*image appearance + 0.3*bending

  16. Object Recognition Experiments • COIL 3D Objects • Handwritten Digits • Trademarks • Exactly the same algorithm used on all experiments

  17. COIL Object Database

  18. Error vs. Number of Views

  19. Prototypes Selected for 2 Categories Details in Belongie, Malik & Puzicha (NIPS2000)

  20. Error vs. Number of Views

  21. Handwritten Digit Recognition • MNIST 600 000 (distortions): • LeNet 5: 0.8% • SVM: 0.8% • Boosted LeNet 4: 0.7% • 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 20 000: • K-NN, Shape Context matching: 0.63%

  22. Trademark Similarity

  23. 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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