Face Recognition Using EigenFaces

Presentation by: Zia Ahmed Shaikh (P/IT/2K15/07)

Authors: Matthew A. Turk and Alex P. Pentland

Vision and Modeling Group,

The Media Laboratory

Massachusetts Institute of Technology

Introduction

Problem Statement : Given an image, to identify it as a face and/or

extract face images from it. To retrieve the similar images (based on a

heuristic) from the given database of face images.

Why face recognition ?

Various potential applications, such as

person identification. human-computer interaction. security systems.

Faces are complex, multidimensional and meaningful visual stimuli.

Face Recognition is difficult.

Face Images are similar in overall configuration.

Difference From Image Recognition

Approach

Similar to Content Based Image Retrieval (CBIR).

Neural Networks and Self Organizing Maps (SOMs).

Principal Component Analysis (PCA).

Stages of Face Recognition(1) face location detection(2) feature extraction(3) facial image classification

Approaches of Feature Extraction(1) local feature : eyes, nose, mouth information easily affected by irrelevant information .(2) global feature :

• extract feature from whole image .

Face Recognition Using Eigenfaces

Face Images are projected into a feature space (“Face Space”) that best encodes the variation among known face images.

The face space is defined by the “eigenfaces”, which are the eigenvectors of the set of faces.

Eigen Space and Eigen Faces

Initialization :

Acquire the training set and calculate eigenfaces (using PCA projections) which define eigenspace.

When a new face is encountered, calculate its weight.

Determine if the image is face.

If yes, classify the weight pattern as known or unknown.

(Learning) If the same unknown face is seen several times incorporate it into known faces.

Steps In Face Recognition

PCA

Main assumption of PCA approach:

Face space forms a cluster in image space.PCA gives suitable representation.

Eigenfaces (1)Calculation of Eigenfaces

(1) Calculate average face : v.

(2) Collect difference between training images and average face in matrix A (M by N), where M is the number of pixels and N is the number of images.

(3) The eigenvectors of covariance matrix C (M by M) give the eigenfaces. M is usually big, so this process would be time consuming.

What to do? TAAC

Eigenfaces (2)

Calculation of Eigenvectors of CIf the number of data points is smaller than the dimension (N<M), then there will be only N-1 meaningful eigenvectors.

Instead of directly calculating the eigenvectors of C, we can calculate the eigenvalues and the corresponding eigenvectors of a much smaller matrix L (N by N).

if λi are the eigenvectors of L then A λi are the eigenvectors for C. The eigenvectors are in the descent order of the corresponding

eigenvalues.

AAL T

Eigenfaces (3)

Representation of Face Images using EigenfacesThe training face images and new face images

can be represented as linear combination of the eigenfaces.

When we have a face image u :

Since the eigenvectors are orthogonal :

i

iiau

iT

i ua

Eigenfaces (4)

Experiment and ResultsData used here are from the ORL database of faces. Facial images of 16 persons each with 10 views are used. - Training set contains 16×7 images. - Test set contains 16×3 images.

First three eigenfaces :

Classification Using Nearest NeighborSave average coefficients for each person.

Classify new face as the person with the closest average.

Recognition accuracy increases with number of Eigenfaces till 15. 　 Later Eigenfaces do not help much with recognition.

Best recognition rates

Training set 99% Test set 89%

0.4

0.6

0.8

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0 50 100 150

number of eigenfaces

accu

racy

validation set training set

References “A tutorial on Principal Components Analysis”, By Lindsay I Smith. “Eigenfaces for Recognition”, Turk, M. and Pentland A., (1991)

Journal of Cognitive Neuroscience, Vol. 3, No. 1, pp. 71-86. Davies, Ellis, and Shaepherd, Perceiving and Remembering Faces,

Academic Press, London, 1981. W. W. Bledsoe, "The model method in facial recognition" Panoramic

Research Inc. Palo Alto, CA, Rep. PRI:15, Aug. 1996. T.Kanade, "Picture processing system by computer complex and

recognition of human faces", Dept of Information Sciences, Kyoto University, Nov 1973.

A. L Yuille, D. S. Cohen, and P. W. Hallinan, "Feature Extraction from faces using deformable templates" proc, CVPR, San Diego, CA June 1989.

T. Kohenen and P.Lehtio "Storage and processing of information in distributed associative memory systems" in G.E Hinton and J.A. Anderson, Parallel Models of Associative Memory, Hillsdale, NJ: Lawrence Erlbum Associate, 1981, pp, 105-143