Face Recognition Using 2D-FLDA Based on Approximate SVD Obtained with Kronecker Products with One Training Sample

Abstract

Aims: In a face recognition task, it is a challenging problem to find lots of images for a person. Even, sometimes there can be only one image, available for a person. In these cases many of the methods are exposed to serious performance drops even some of these fail to work. Recently this problem has become remarkable for researchers. In some of these studies the database is extended using a synthesized image which is constructed from the singular value decomposition (SVD) of the single training image. In this paper, for such a method, SVD based 2 Dimensional Fisher Linear Discriminant Analysis (2D-FLDA), it is proposed a new approach to find the SVD of the image matrix with the aim of to increase the recognition performance. Study Design: In this paper, in a face recognition task with 2D-FLDA, in one training sample case, instead of original SVD of the image matrix, the approximate SVD of its based on multiple kronecker product sums is used. In order to obtain it, image matrix is first reshaped thus it is to be lower dimensional matrices and, then the sum of multiple kronecker products (MKPS) is applied in this lower dimensional space. Methodology: Experiments are performed on two known databases Ar-Face and ORL face databases. The performance of the proposed method is evaluated when there are facial expression, lightning conditions and pose variations. Results: In each experiment, the approximate SVD approach based on multiple kronecker product sum gets approximately 3% better results when compared with the original SVD. Conclusion: Experimental results verify that the proposed method achieves better recognition performance over the traditional one. The reason for this is the proposed approximate SVD has the advantages of simplicity, and also as the kronecker factors possess additional linear structure, kronecker product can capture potential self-similarity.