(2D)2LDA: An efficient approach for face recognition

doi:10.1016/j.patcog.2006.01.018

Pattern Recognition

Volume 39, Issue 7, July 2006, Pages 1396-1400

https://doi.org/10.1016/j.patcog.2006.01.018 Get rights and content

Abstract

Although 2DLDA algorithm obtains higher recognition accuracy, a vital unresolved problem of 2DLDA is that it needs huge feature matrix for the task of face recognition. To overcome this problem, this paper presents an efficient approach for face image feature extraction, namely, (2D)²LDA method. Experimental results on ORL and Yale database show that the proposed method obtains good recognition accuracy despite having less number of coefficients.

Introduction

Linear discriminant analysis (LDA) is a well-known feature extraction and data representation technique widely used in the areas of pattern recognition for feature extraction and dimension reduction. The objective of LDA is to find the optimal projection so that the ratio of the determinants of the between-class and the within-class scatter matrices of the projected samples reaches its maximum. However, concatenating 2D matrices into 1D vectors leads to very high dimensional nature of image vector, where it is difficult to evaluate the scatter matrices accurately due to its large size and the relatively small number of training samples. Furthermore, the within-class scatter matrix is always singular, making the direct implementation of LDA algorithm an intractable task.

To overcome these problems, a new technique called 2DLDA [1] was recently proposed, which directly computes eigenvectors of the so called scatter matrices without matrix-to-vector conversion. Because the size of the scatter matrices is equal to the width of the images, which is quite small compared to the size of the scatter matrices in LDA, 2DLDA evaluates the scatter matrices more accurately and computes the corresponding eigen vectors more efficiently. It was reported in Ref. [1] that the recognition accuracy on several databases was higher using 2DLDA than other PCA and LDA-based algorithms.

However, the main drawback of 2DLDA is that it needs more coefficients for image representation than conventional PCA- and LDA-based schemes. For an image size of $112 \times 92$ , the commonly used image size in face recognition, the number of coefficients used by 2DLDA for classification is $112 \times d$ , where $d$ is set to no less than 5 for satisfactory accuracy.

In this paper, we first indicate that 2DLDA is essentially working in the row-direction of images, and then propose an alternative 2DLDA which works in the column direction of images. By simultaneously combining row and column directions, we develop two-directional 2DLDA, i.e. (2D)²LDA, for efficient representation and recognition. Experimental results on ORL and Yale database shows that the proposed method obtains same or even better recognition accuracy than 2DLDA, while the number of coefficients needed by the former for image representation is much smaller than that of the latter.

Section snippets

Overview of 2DLDA approach

2DLDA is an effective feature extraction and discrimination approach [1] in face recognition. Formally, it can briefly be formulated as follows: Suppose ${A_{k}}_{k = 1}^{N}$ are the training images, which contain $C$ classes, and the $i$ th class $C_{i}$ has $n_{i}$ samples $(\sum_{i = 1}^{C} n_{i} = N)$ . 2DLDA attempts to seek a set of optimal discriminating vectors to form a transform $X_{d} = {x_{1}, x_{2}, \dots, x_{d}}$ by maximizing the 2D Fisher criterion denoted as $J (X) = \frac{X^{T} G_{b} X}{X^{T} G_{w} X} .$ In Eq. (1), T denotes matrix transpose, $G_{b}$ and $G_{w}$ , respectively, are

Experimental results

In this section, we experimentally evaluate our proposed alternative-2DLDA and (2D)²LDA methods with PCA [3], 2DPCA [4], alternative-2DPCA [2], (2D)²PCA [2] and 2DLDA [1] methods, on two well-known face databases: ORL and Yale. While the ORL database is used to test the performance of the face recognition algorithms under the condition of minor variation of scaling and rotation, the Yale database is used to examine the performance of the algorithms under the condition of varied facial

Conclusion

In this paper, an efficient face representation and recognition method called (2D)²LDA is proposed. The main difference between (2D)²LDA and existing 2DLDA is that the latter only works in the row direction of face images, while the former works simultaneously in the row and the column directions of face images. The major advantage of the proposed method is that it requires fewer number of coefficients and least computing time for face image representation and recognition unlike standard PCA,

References (4)

L. Ming et al.
2D-LDA: a statistical linear discriminant analysis for image matrix
Pattern Recognition Lett.
(2005)
D. Zhang, Z.-H. Zhou, (2D)2PCA: 2-directional 2-dimensional PCA for efficient face representation and recognition, J....

There are more references available in the full text version of this article.

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