Face Recognition Using the Nearest Feature Line Method

1. Face Recognition Using the Nearest Feature Line Method Stan Z. Li and Juwei Lu Nearest_feature_line.pdf

2. Problem • Face recognition • Detect faces • Must account for different viewpoints, illumination, and expression • Which features to use? • How do you classify a new face image?

3. Geometric Feature Based Methods • Positives: • Data reduction • Insensitive to illumination • Insensitive to viewpoint • Negatives: • Extraction of facial features are unreliable. We win?

4. Template Matching • Eigenface representation • Face space constructed by • Karhunen-Loeve transform (?) • Principal Component Analysis • Every face image is a feature point (vector of weights) • Nearest Neighbor Classifier

5. “Generalize the representational capacity of available prototype images.”

6. Nearest Feature Line (NFL) • Assumption: Every test image has at least 2 distinct features. • Feature line (FL) ~variants of the two images under variations. • Classification using minimum distance between test feature point and FL’s.

7. The Feature Space • Eigenface space • Training set of N face images T = {z1, z2, … zN}. • Construct covariance matrix: 1/N * sum{n=1, N} (zn-z)(zn-z)^T, where z is the average of T. • Apply PCA to covariance matrix. • With first N’ eigenvectors, project each training image into the eigenface space by: xn = psi^T(zn-z), where psi is the set of N’ eigenvectors. • Classify a test image by projecting into eigenspace and assigning to nearest class (Nearest Neighbor).

8. Feature Line Distance x • x1 and x2 are training images of a single class in eigenface space. • x is the query (or test) image. • Any position along the line (Feature Line, FL) between x1 and x2 is a variation of these two images. p x2 x1

9. FL Distance cont’d. • Project p onto the x1, x2 Feature Line. • p = x1 + u(x2-x1) • Solve for u • u describes the position of p relative to x1 and x2 • When: • u = 0, p = x1 • u = 1, p = x2 • 0 < u < 1, p is an interpolating point between x1 and x2 • u > 1, p is a forward extrapolating point on the x2 side • u < 0, p is a backward extrapolating point on the x1 side

10. FL Distance cont’d. • The linear variations on FL provides MANY more feature points. • Variations aren’t linear though. • Use higher order curves • Use splines • However, FL is sufficient for the classification described as follows…..

11. NFL- Based Classification • Given a test image, x, assign it to a class in the training set. • For each pair of feature points, calculate the FL distance between it and x. • Sort the distances in ascending order (with class identifier, 2 feature points, and u). • The NFL distance is the first rank distance. • Yields best matched class and two best matched feature points.

12. Results • See paper.