Object Modeling with Layers

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Object Modeling with Layers

• Charudatta Phatak
• Computational Photography (15-862)
• Final Project Presentation

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Appearance Models

• A statistical model describing the shape and
  texture of the object of interest.
• Description of objects of D-dimensions in
  d-dimensional space with d lt D.
• Objective - Object matching and recognition.
• Commonly used for faces.

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Principal Component Analysis (PCA)

• Given a point set , in an
  M-dim space, PCA finds a basis such that
• coefficients of the point set in that basis are
  uncorrelated
• first r lt M basis vectors provide an approximate
  basis that minimizes the mean-squared-error (MSE)
  in the approximation (over all bases with
  dimension r)

15-463 Course Notes
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PCA

• Problems - Objects with features completely
  absent, occluded are not modeled very well.

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Layered Appearance Models

• Define layers describing each feature
• Weights for each layer
• PCA for each layer

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Results
First eigenvector for Layered model
First eigenvector for Normal model
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• Random Sampling

Normal model
Layered model
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• Additional Functionality

Adding Features
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Replacing Features
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Feature Matching
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Local Linear Embedding (LLE)

• Similar to PCA
• Select nearest neighbors
• Compute Reconstruction weights
• Compute embedded space coordinates

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LLE Results
Roweis, 2000.
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Normal vs. Layered LLE
Layers
Normal
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LLE Results
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Summary

• Layered PCA model successful for objects like car
• LLE model - needs more images in dataset for
  comprehensive analysis

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Questions ? Comments ?