Hui Kong

2005 Special Issue: Generalized 2D principal component analysis for face image representation and recognition

In the tasks of image representation, recognition and retrieval, a 2D image is usually transformed into a 1D long vector and modelled as a point in a high-dimensional vector space. This vector-space model brings up much convenience and many advantages. However, it also leads to some problems such as the Curse of Dimensionality dilemma and Small Sample Size problem, and thus produces us a series of challenges, for example, how to deal with the problem of numerical instability in image recognition, how to improve the accuracy and meantime to lower down the computational complexity and storage requirement in image retrieval, and how to enhance the image quality and meanwhile to reduce the transmission time in image transmission, etc. In this paper, these problems are solved, to some extent, by the proposed Generalized 2D Principal Component Analysis (G2DPCA). G2DPCA overcomes the limitations of the recently proposed 2DPCA (Yang et al., 2004) from the following aspects: (1) the essence of 2DPCA is clarified and the theoretical proof why 2DPCA is better than Principal Component Analysis (PCA) is given; (2) 2DPCA often needs much more coefficients than PCA in representing an image. In this work, a Bilateral-projection-based 2DPCA (B2DPCA) is proposed to remedy this drawback; (3) a Kernel-based 2DPCA (K2DPCA) scheme is developed and the relationship between K2DPCA and KPCA (Scholkopf et al., 1998) is explored. Experimental results in face image representation and recognition show the excellent performance of G2DPCA.

Generalized 2D principal component analysis

A two-dimensional principal component analysis (2DPCA) by J. Yang et al. (2004) was proposed and the authors have demonstrated its superiority over the conventional principal component analysis (PCA) in face recognition. But the theoretical proof why 2DPCA is better than PCA has not been given until now. In this paper, the essence of 2DPCA is analyzed and a framework of generalized 2D principal component analysis (G2DPCA) is proposed to extend the original 2DPCA in two perspectives: a bilateral-projection-based 2DPCA (B2DPCA) and a kernel-based 2DPCA (K2DPCA) schemes are introduced. Experimental results in face recognition show its excellent performance.

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.

Two-dimensional Fisher discriminant analysis: forget about small sample size problem [face recognition applications]

This paper addresses the small sample size (SSS) problem in linear discriminant analysis (LDA) utilizing a so called 2D Fisher discriminant analysis (2D-FDA) algorithm. As opposed to traditional LDA-based approaches, 2D-FDA is based on 2D image matrices rather than 1D vectors so the image matrix does not need to be transformed into a vector before feature extraction. The between-class scatter and the within-class scatter is constructed using the original image matrices. The advantage arising in this way is that the SSS problem existing in traditional linear discriminant analysis does not occur any more. To test the performance of 2D-FDA with small number of training samples, a series of experiments are conducted on two public databases: ORL and Yale face database B. In both two trials, the 2D-FDA outperforms the other linear subspace methods when there are only very limited training images for each subject.

Discriminant Low-dimensional Subspace Analysis for Face Recognition with Small Number of Training Samples

In this paper, a framework of Discriminant Low-dimensional Subspace Analysis (DLSA) method is proposed to deal with the Small Sample Size (SSS) problem in face recognition area. Firstly, it is rigorously proven that the null space of the total covariance matrix, S t , is useless for recognition. Therefore, a framework of Fisher discriminant analysis in a low-dimensional space is developed by projecting all the samples onto the range space of S t . Two algorithms are proposed in this framework, i.e., Unified Linear Discriminant Analysis (ULDA) and Modified Linear Discriminant Analysis (MLDA). The ULDA extracts discriminant information from three subspaces of this lowdimensional space. The MLDA adopts a modified Fisher criterion which can avoid the singularity problem in conventional LDA. Experimental results on a large combined database have demonstrated that the proposed ULDA and MLDA can both achieve better performance than the other state-of-the-art LDA-based algorithms in recognition accuracy.

Fusion of appearance image and passive stereo depth map for face recognition based on the bilateral 2DLDA

This paper presents a novel approach for face recognition based on the fusion of the appearance and depth information at the match score level. We apply passive stereoscopy instead of active range scanning as popularly used by others. We show that present-day passive stereoscopy, though less robust and accurate, does make positive contribution to face recognition. By combining the appearance and disparity in a linear fashion, we verified experimentally that the combined results are noticeably better than those for each individual modality. We also propose an original learning method, the bilateral two-dimensional linear discriminant analysis (B2DLDA), to extract facial features of the appearance and disparity images. We compare B2DLDA with some existing 2DLDA methods on both XM2VTS database and our database. The results show that the B2DLDA can achieve better results than others.

Ensemble LDA for face recognition

Linear Discriminant Analysis (LDA) is a popular feature extraction technique for face image recognition and retrieval. However, It often suffers from the small sample size problem when dealing with the high dimensional face data. Two-step LDA (PCA+LDA) [1][2][3] is a class of conventional approaches to address this problem. But in many cases, these LDA classifiers are overfitted to the training set and discard some useful discriminative information. In this paper, by analyzing the overfitting problem for the two-step LDA approach, a framework of Ensemble Linear Discriminant Analysis (EnLDA) is proposed for face recognition with small number of training samples. In EnLDA, a Boosting-LDA (B-LDA) and a Random Sub-feature LDA (RS-LDA) schemes are incorporated together to construct the total weak-LDA classifier ensemble. By combining these weak-LDA classifiers using majority voting method, recognition accuracy can be significantly improved. Extensive experiments on two public face databases verify the superiority of the proposed EnLDA over the state-of-the-art algorithms in recognition accuracy.

Generalized 2D Fisher Discriminant Analysis.

To solve the Small Sample Size (SSS) problem, the recent linear discriminant analysis using the 2D matrix-based data representation model has demonstrated its superiority over that using the conventional vector-based data representation model in face recognition [7]. But the explicit reason why the matrix-based model is better than vectorized model has not been given until now. In this paper, a framework of Generalized 2D Fisher Discriminant Analysis (G2DFDA) is proposed. Three contributions are included in this framework: 1) the essence of these ’2D’ methods is analyzed and their relationships with conventional ’1D’ methods are given, 2) a Bilateral and 3) a Kernel-based 2D Fisher Discriminant Analysis methods are proposed. Extensive experiment results show its excellent performance.

Bilateral Two Dimensional Linear Discriminant Analysis for Stereo Face Recognition

A new method called two-dimensional Fisher discriminant analysis (2D-FDA) is proposed to deal with the small sample size (SSS) problem in LDA based face recognition. Then appearance and depth information are combined to improve face recognition rate. Different from the conventional 1D-FDA (PCA plus LDA) 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. It was verified that 2D-FDA outperforms 1D FDA

Coupling Adaboost and Random Subspace for Diversified Fisher Linear Discriminant

Fisher linear discriminant (FLD) is a popular method for feature extraction in face recognition. However, It often suffers from the small sample size, bias and overfitting problems when dealing with the high dimensional face image data. In this paper, a framework of ensemble learning for diversified Fisher linear discriminant (EnL - DFLD) is proposed to improve the current FLD based face recognition algorithms. Firstly, the classifier ensemble in EnL - DFLD is composed of a set of diversified component FLD classifiers, which are selected intentionally by computing the diversity between the candidate component classifiers. Secondly, the candidate component classifiers are constructed by coupling the random subspace and adaboost methods, and it can also be shown that such a coupling scheme will result in more suitable component classifiers so as to increase the generalization performance of EnL - DFLD. Experiments on two common face databases verify the superiority of the proposed EnL - DFLD over the state-of-the-art algorithms in recognition accuracy