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Matching Shapes Serge Belongie * , Jitendra Malik and Jan Puzicha U.C. Berkeley * Present address: U.C. San Diego PowerPoint Presentation
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Matching Shapes Serge Belongie * , Jitendra Malik and Jan Puzicha U.C. Berkeley * Present address: U.C. San Diego - PowerPoint PPT Presentation


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Matching Shapes Serge Belongie * , Jitendra Malik and Jan Puzicha U.C. Berkeley * Present address: U.C. San Diego. Biological Shape. D’Arcy Thompson: On Growth and Form , 1917 studied transformations between shapes of organisms. Deformable Templates: Related Work.

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Matching ShapesSerge Belongie*, Jitendra Malikand Jan Puzicha U.C. Berkeley*Present address: U.C. San Diego
biological shape
Biological Shape
  • D’Arcy Thompson: On Growth and Form, 1917
    • studied transformations between shapes of organisms
deformable templates related work
Deformable Templates: Related Work
  • Fischler & Elschlager (1973)
  • Grenander et al. (1991)
  • Yuille (1991)
  • von der Malsburg (1993)
matching framework
Matching Framework

...

model

target

  • Find correspondences between points on shape
  • Estimate transformation
  • Measure similarity
shape context
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
comparing shape contexts
Comparing Shape Contexts

Compute matching costs using Chi Squared distance:

Recover correspondences by solving linear assignment problem with costs Cij

[Jonker & Volgenant 1987]

matching framework9
Matching Framework

...

model

target

  • Find correspondences between points on shape
  • Estimate transformation
  • Measure similarity
thin plate spline model
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)

matching example
MatchingExample

model

target

synthetic test results
Synthetic Test Results

Fish - deformation + noise

Fish - deformation + outliers

ICP Shape Context Chui & Rangarajan

matching framework14
Matching Framework

...

model

target

  • Find correspondences between points on shape
  • Estimate transformation
  • Measure similarity
terms in similarity score
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

object recognition experiments
Object Recognition Experiments
  • COIL 3D Objects
  • Handwritten Digits
  • Trademarks
  • Exactly the same algorithm used on all experiments
prototypes selected for 2 categories
Prototypes Selected for 2 Categories

Details in Belongie, Malik & Puzicha (NIPS2000)

handwritten digit recognition
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%
conclusion
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