A framework of 2D Fisher discriminant analysis: application to face recognition with small number of training samples

• Published in: 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) Vol. 2; pp. 1083 - 1088 vol. 2
• Main Authors: Kong, H., Wang, L., Teoh, E.K., Wang, J.-G., Venkateswarlu, R.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 2005
• Subjects: Covariance matrix; Eigenvalues and eigenfunctions; Face recognition; Feature extraction; Image databases; Linear discriminant analysis; Null space; Principal component analysis; Scattering; Vectors
• ISBN: 0769523722; 9780769523729
• ISSN: 1063-6919; 1063-6919
• DOI: 10.1109/CVPR.2005.30

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.