Tri-Direction 2D-Fisher Discriminant Analysis (T2D-FDA) for Feature Extraction

Abstract

A new image feature extraction method for face recognition called Tri-direction 2D-Fisher Discriminant Analysis (T2D-FDA) is proposed to deal with the Small Sample Size (SSS) problem in conventional 1D-Fisher Discriminant Analysis (1D-FDA). Moreover, the essence of T2D-FDA is investigated, and the equivalence of the left-multiplying 2D-FDA of the original image matrices and the left-multiplying D2D-FDA of diagonal image matrices is verified if each column is viewed as a computational unit. Different from the 1D-LDA based approaches, the T2D-FDA is based on 2D image matrices rather than column vectors, so the image matrix does not need to be transformed into a long vector before feature extraction. The advantage arising in this way is that the SSS problem does not exist anymore because within-class scatter matrices constructed is full-rank in T2D-FDA. The proposed method is applied to face recognition where only few training images exist for each subject. Experiment results show T2D-FDA outperforms the current linear subspace methods in SSS problem on four public databases: ORL, Yale, AR and FERET face databases. INDEX TERMS Small sample size (SSS) problem, 2D-fisher discriminant analysis (2D-FDA), face recognition, within-class scatter matrices, linear subspace methods.

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