Face Recognition Using the Nearest Feature Line Method

Stan Z. Li and Juwei Lu

Nearest_feature_line.pdf

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?

Geometric Feature Based Methods

Positives:

Data reduction

Insensitive to illumination

Insensitive to viewpoint

Negatives:

Extraction of facial features are unreliable. We win?

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

“Generalize the representational capacity of available prototype images.”

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.

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).

Feature Line Distance

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

x1

x2

x

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

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…..

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.

Results

See paper.

Face Recognition Using the Nearest Feature Line Method

Robert Tamburo

2003-07-25T13:11:09