Bi-2DPCA: A Fast Face Coding Method for Recognition
Jian Wu Yang, Yong Xu, Jing-yu Yang · InTech eBooks · 2010
In this paper, two-dimensional principal component analysis (2DPCA) is first re-examined and its two properties are revealed. 2DPCA can eliminate the correlation between column vectors of image and compact the image energy onto a small number of column vectors (these vectors are used for image representation). In other words, 2DPCA realizes an optimal compression in horizontal direction. These properties are desirable and provide some theoretical supports for 2DPCA-based image representation. However, 2DPCA does not consider the correlation in vertical direction. This leads to a relative lower compression rate compared to PCA. Bi-2DPCA technique is developed to overcome the weakness of 2DPCA. Basically, Bi2DPCA is to perform 2DPCA twice sequentially, i.e., a first compression in horizontal direction followed by a second one in vertical direction. In this way, the correlations in both directions are eliminated and, the image energy is compacted into the up-left corner of image. The elements in this corner are chosen as features. So, Bi-2DPCA needs fewer coefficients than 2DPCA for image representation. This results in lower storage requirements and a remarkable speedup in classification. Actually, Bi-2DPCA based representation is not only economical in storage but also effective for discrimination. Our experiments on FERET database show Bi-2DPCA is comparable with 2DPCA. In addition, the theoretical justification for Bi-2DPCA based image representation is provided. This representation mechanism is sequentially optimal in the sense of minimal mean-square error. In comparison, ST-KLT lacks this justification and is shown to be suboptimal in theory. That is, the mean-square error (MSE) of ST-KLT is always larger than that of Bi-2DPCA. Besides, we also show that the MSEs of the image-data dependent coding methods such as Bi-2DPCA and ST-KLT are much less than the image-data independent method like 2D-DCT. Our experiments indicate that the significant MSE difference between two methods does affect their recognition performances and, the image-data dependent methods are more suitable for representing faces for recognition purpose. The insignificant MSE difference, however, almost has no effect on the recognition results. In contrast to PCA, the most prominent advantage of Bi-2DPCA is its low computational complexity. Actually, Bi-2DPCA has lower computation requirement than PCA on almost all aspects involved, including the construction of covariance matrices, calculating the eigenvectors of these covariance matrices, and image transformation. This characteristic makes Bi-2DPCA faster than PCA in both training and testing processes. It should be mentioned that the speed advantage of Bi-2DPCA would become more remarkable with the increase of database scale and training sample size. Besides, our experiments on the FERET database also demonstrate that Bi-2DPCA is comparable with PCA in recognition performance.