Recognizing Face or Object from a Single Image: Linear vs. Kernel Methods on 2D Patterns
We consider the problem of recognizing face or object when only single training image per class is available, which is typically encountered in law enforcement, passport or identification card verification, etc. In such cases, many discriminant subspace methods such as Linear Discriminant Analysis (LDA) fail because of the non-existence of intra-class variation. In this paper, we propose a novel framework called 2-Dimensional Kernel PCA (2D-KPCA) for face or object recognition from a single image. In contrast to conventional KPCA, 2D-KPCA is based on 2D image matrices and hence can effectively utilize the intrinsic spatial structure information of the images. On the other hand, in contrast to 2D-PCA, 2D-KPCA is capable of capturing part of the higher-order statistics information. Moreover, this paper reveals that the current 2D-PCA algorithm and its many variants consider only the row information or column information, which has not fully exploited the information contained in the image matrices. So, besides proposing the unilateral 2D-KPCA, this paper also proposes the bilateral 2D-KPCA which could exploit more information concealed in the image matrices Furthermore, some approximation techniques are developed for improving the computational efficiency. Experimental results on the FERET face database and the COIL-20 object database show that: 1) the performance of KPCA is not necessarily better than that of PCA; 2) 2D-KPCA almost always outperforms 2D-PCA significantly; 3) the kernel methods are more appropriate on 2D pattern than on 1D patterns.
KeywordsPrincipal Component Analysis Face Recognition Linear Discriminant Analysis Single Image Kernel Method
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