Eigenfaces vs. Fisherfaces

By

Abdul Malik Khan

INTRODUCTIONFacial recognition is a problem of automatically identifying or verifying a person from a digital image

For the given paper the problem is: Given a set of face images labeled with the person’s identity (the learning set) and an unlabeled set of face images from the same group of people (the test set), identify each person in the test images.

MethodsIn this paper, following four pattern classification techniques for solving the face recognition problem are studied

CorrelationEigenface Linear Subspace Fisherface

Face images databaseTo implement the paper, yale cropped database is downloaded3

Database contains varied light source location of 38 persons, database is divided into 5 subsetsSubset 1: Light source is 0~15° off camera axis [6 images]Subset 2: Light source is 15~30° off camera axis [10 images]Subset 3: Light source is 30~45° off camera axis [4 images]Subset 4: Light source is 45~60° off camera axis [7 images]Subset 5: Light source is 60~75° off camera axis [4 images]

The data-base images are given in appendix-A

EXPERIMENTSVariation in Lighting

Extrapolation Interpolation

Variation in Facial Expression, Eye Wear, and LightingFull face Closely cropped face

Not Done due to time constraints

ExtrapolationEach method was trained on samples from Subset 11 and then tested using samples from Subsets 1, 2, and 32. Since there are 190 images in the training set, correlation is equivalent to the Eigenface method using 189 principal components. Next Figure shows the result from this experiment.

Extrapolation Results

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 30

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Extrpolation Results

Correlation

Eigen Face - 4

Eigen Face - 10

Eigen Face - 4 (wo-3)

Eigen Face - 10 (wo-3)

Fisher Face - 10 (wo-3)

25 PCA Weights

1 Subset 1 contains 228 images for which both the longitudinal and latitudinal angles of light source direction are within 15° of the camera axis, 38 images are used as test sets

2 To test the methods with an image from Subset 1, that image was removed from the training set, i.e. the “leaving-one-out” strategy was employed

25 Fisher Weights

Eigen Values magnitude

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Eigen values magnitude for Eigen Face

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Eigen values magnitude for Fisher Discriminator, Negetive values are in Red

InterpolationEach method was trained on samples from Subset 1 & 53 and then tested using samples from Subsets 2, 3 and 4. Next Figure shows the result from this experiment.

25 PCA Weights

25 Fisher Weights

3 Subset 1 contains 228 images for which both the longitudinal and latitudinal angles of light source direction are within 15° of the camera axis, Subset 5 contains 152 images for which effective longitudinal and latitudinal angles of light source direction are between 60 and75° of the camera axis

Interpolation Results

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Interpolation Results

CorrelationEigen Face - 4

Eigen Face - 10

Eigen Face - 4 (wo-3)

Eigen Face - 10 (wo-3)

Fisher Face - 10 (wo-3)Fisher Face - 25 (wo-3)

Eigen Values magnitude

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Eigen values magnitude

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Eigen values magnitude for Fisher Discriminator, Negetive values are in Red

Comments on results

References

M. Turk and A. Pentland, “Eigenfaces for Recognition,” J. Cognitive Neuroscience, vol. 3, no. 1, 1991.http://www.cs.princeton.edu/~cdecoro/eigenfaces/http://vision.ucsd.edu/extyaleb/CroppedYaleBZip/CroppedYale.zip

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