A Framework of 2D Fisher Discriminant Analysis: Application to Face Recognition with Small Number of Training Samples

A novel framework called 2D Fisher discriminant analysis (2D-FDA) is proposed to deal with the small sample size (SSS) problem in conventional one-dimensional linear discriminant analysis (1D-LDA). Different from the 1D-LDA based approaches, 2D-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 any more because the between-class and within-class scatter matrices constructed in 2D-FDA are both of full-rank. This framework contains unilateral and bilateral 2D-FDA. It is applied to face recognition where only few training images exist for each subject. Both the unilateral and bilateral 2D-FDA achieve excellent performance on two public databases: ORL database and Yale face database B.