1. Object Modeling with Layers
Charudatta Phatak
Computational Photography (15-862)
Final Project Presentation

2. 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 < D.
Objective - Object matching and recognition.
Commonly used for faces.

3. 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 < M basis vectors provide an approximate basis that minimizes the mean-squared-error (MSE) in the approximation (over all bases with dimension r) x1 x0
1st principal component
2nd principal component
* Course Notes

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

5. Layered Appearance Models
Define layers describing each feature
Weights for each layer
PCA for each layer

6. Results First eigenvector for Layered model
First eigenvector for Normal model

7. Random Sampling
Normal model
Layered model

8. Additional Functionality
Adding Features

9. Replacing Features

10. Feature Matching

11. Local Linear Embedding (LLE)
Similar to PCA
Select nearest neighbors
Compute Reconstruction weights
Compute embedded space coordinates

12. LLE Results
Roweis, 2000.

13. Normal vs. Layered LLE
Layers
Normal

14. LLE Results

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

16. Questions ? Comments ?