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PCA: Principal Components Analysis (PCA)

PCA, commonly referred to as the use of eigenfaces, is the technique pioneered by Kirby and Sirivich in 1988. With PCA, the probe and gallery images must be the same size and must first be normalized to line up the eyes and mouth of the subjects within the images. The PCA approach is then used to reduce the dimension of the data by means of data compression basics2 and reveals the most effective low dimensional structure of facial patterns. This reduction in dimensions removes information that is not useful4 and precisely decomposes the face structure in toorthogonal (uncorrelated) components known as eigenfaces. Each face image may be represented as a weighted sum (feature vector) of the eigenfaces, which are stored in a 1D array. A probe image is compared against a gallery image by measuring the distance between their respective feature vectors. The PCA approach typically requires the full frontal face to be presented each time; otherwise the image results in poor performance.4 The primary advantage of this technique is that it can reduce the data needed to identify the individual to 1/1000th of the data presented.

5This Document Last Updated: 7 August 2006 Page 2 of 10
Face Recognition Figure 1: Standard Eigenfaces: Feature vectors are derived using eigenfaces.6

LDA: Linear Discriminant Analysis

LDA is a statistical approach for classifying samples of unknown classes based on training samples with known classes.4 (Figure 2)This technique aims to maximize between-class (i.e., across users) variance and minimize within-class (i.e., within user)variance. In Figure 2 where each block represents a class, there are large variances between classes, but little variance within classes. When dealing with high dimensional face data, this technique faces the small sample size problem that arises where there are a small number of available training samples compared to the dimensionality of the sample space.7
Figure 2: Example of Six Classes Using LDA 8This Document Last Updated: 7 August 2006 Page 3 of 10Face Recognition

EBGM: Elastic Bunch Graph Matching

EBGM relies on the concept that real face images have many nonlinearcharacteristics that are not addressed by the linear analysismethods discussed earlier, such as variations in illumination(outdoor lighting vs. indoor fluorescents), pose (standing straightvs. leaning over) and expression (smile vs. frown). A Gaborwavelet transform creates a dynamic link architecture thatprojects the face onto an elastic grid.4 The Gabor jet is a node onthe elastic grid, notated by circles on the image below, whichdescribes the image behavior around a given pixel. It is the resultof a convolution of the image with a Gabor filter, which is used todetect shapes and to extract features using image processing. [Aconvolution expresses the amount of overlap from functions,blending the functions together.] Recognition is based on thesimilarity of the Gabor filter response at each Gabor node.4 Thisbiologically-based method using Gabor filters is a processexecuted in the visual cortex of higher mammals. The difficultywith this method is the requirement of accurate landmarklocalization, which can sometimes be achieved by combining PCAand LDA methods.4
Figure 4: Elastic Bunch Map Graphing.9

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