1. Categorization by Learning and Combing Object Parts
B. Heisele, T. Serre, M. Pontil, T. Vetter, T. Poggio.
Presented by Manish Jethwa

2. Overview
Learn discriminatory components of objects with Support Vector Machine (SVM) classifiers.

3. Background Global Approach Component-based techniques
Attempt to classify the entire object
Successful when applied to problems in which the object pose is fixed.
Component-based techniques
Individual components vary less when object pose changes than whole object
Useable even when some of the components are occluded.

4. Linear Support Vector Machines
Linear SVMs are used to discriminate between two classes by determining the separating hyperplane.
Support Vectors

5. f (x)= ∑αi yi < xi . x> + b
Decision function
The decision function of the SVM has the form:
i=1 l
f (x)= ∑αi yi < xi . x> + b
Number of training data points
New data point
Bias
Training data points
Adjustable coefficients
-solution of quadratic programming problem
-positive weights for Support Vectors
-zero for all other data points
Class label {-1,1}
f (x) defines a hyperplane dividing
The data. The sign of f (x) indicates
the class of x.

6. Significance of αi Correspond to the weights of the support vectors.
Learned from training data set.
Used to compute the margin M of the support vectors to the hyperplane.
Margin M = (√∑il i )-1

7. Non-separable Data EPerr ≤l -1E[D2/M2]
The notion of a margin extends to non-separable data also.
Misclassified points result in errors.
The hyperplane is now defined by maximizing the margin while minimizing the summed error.
The expected error probability of the SVM satisfies the following bound:
EPerr ≤l -1E[D2/M2]
Diameter of sphere
containing all training data

8. Measuring Error ρ= D2/M2 Error is dependant on the following ratio:
Renders ρ invariant to scale D1 M1 D2 M2 = D2 M2 D1 M1
ρ1= ρ2

9. Learning Components
Expansion left ρ

10. Learning Facial Components
Extracting face components is time consuming
Requires manually extracting each component from all training images.
Use textured head models instead
Automatically produce a large number of faces under differing illumination and poses
Seven textured head models used to generate 2,457 face images of size 58x58

11. Negative Training Set
Use extract 58x58 patches from 502 non-face images to give 10,209 negative training points.
Train SVM classifier on this data, then add false positives to the negative training set.
Increases negative training set with those images which look most like faces.

12. Learned Components
Start with fourteen manually selected 5x5 seed regions.
The eyes (17x17 pixels)
The nose (15x20 pixels)
The mouth (31x15 pixels)
The cheeks (21x20 pixels)
The lip (13x16 pixels)
The eyebrows (15x20 pixels)
The nostrils (22x12 pixels)
The bridge of the nose (15x20 pixels)
The corners of the mouth (15x20 pixels)

13. Combining Components Left Eye Expert Linear SVM Nose Mouth Combining
Shift component
Experts over
58x58 window
Left Eye
Expert
Linear SVM
Nose
Mouth
Combining
Classifier
Linear SVM
Determine
maximum output
and its location
Shift 58x58 window
over input image
Final decision
face / background

14. Experiments Training data for 3 classifiers: Test data
2,457 faces, 13,654 non-face grey images
Test data
1,834 faces, 24,464 non-face grey images
Components vs. Whole face
Components method performs better than benchmark: whole face detector, with 2nd degree polynomial SVM.

15. Results
Faces detected by the component-based classifier

16. Computer Examples

17. The Data Used images from MIT CBCL faces dataset:
Image are 19x19 pixels
Greyscale
Histogram equalized
Full training set contains
2,429 faces, 4,548 non-faces
Only used 100 face examples, 300 non-face
Test set contains
472 faces, 23,573 non-faces
All 24,045 images used

18. Learning Components Left eye component:
Extract three negative examples for every positive one
This provides a bias to correctly classify non-face examples. Minimize false positives.
Training set contains 400 examples:
100 left eye examples
300 non-left eye examples

19. Results Left Eye learned using 400 examples:
Training set classified 97% correctly
Test set classified 96.2% correctly (of 24,045)
Right Eye learned using 400 examples:
Training set classified 100% correctly
Test set classified 96.5% correctly (of 24,045)
Training set classified 95% correctly
Test set classified 95.7% correctly (of 24,045)

20. Locating Learned Components
Left eye is reasonably
well localized

21. Locating Learned Components
Histograms are fairly flat
compared to face images

22. Face detector Learned components Each learned from 400 examples
Left eye 8x6 pixels
Right eye 8x6 pixels
Mouth 11x 4 pixels
Each learned from 400 examples
100 positive
300 negative
Trained SVM with fixed location for components
No shifting

23. Face Detector Training
The output Oi from each component i (distance for the hyperplane) is used together with the center ( Xi , Yi ) location of corresponding component.
All components are combined into one input feature vector:
X = (Oleft, Xleft ,Yleft , Oright , Xright ,Yright , Omouth , Xmouth ,Ymouth )

24. Results The resulting SVM correct classified all 400 training examples
For non-face examples:
Placing component centers in random locations resulted in 100% correct classification.
Placing component centers in identical positions to face examples resulted in 98.4% accuracy.

25. Is this the best face detector ever?
Performed well on the given dataset.
Low resolution
But…
Dataset contains centered faces
Component positions were given
Did not shift component window and look for maximum
Did not have the opportunity to test against other algorithm
So…
We will never know.