On The Algorithms Of Face Recognition

Face recognition, an important sub-field of computer vision and pattern recognition, has been extensively studied mainly due to its theoretical and practical significance. Although the face recognition has gained great progress, it includes still a lot of unsolved difficult problems. Hence, face recognition requires a further study for practical applications. This paper simply discusses the current research focus such as PCA, LDA and Bayesian methods, and proposes some improved methods for face recognition.(1) PCA is one of the most important algorithms for dimension reduction, in which the original space is approximated by several principal components of all features so that mean square error (MSE) is minimized. Usually, PCA methods require that an image matrix is arranged into a high dimensional vector that will produce a very high dimensional covariance matrix which leads to two limits, extremely high computational complexity and very large storage space. Compared with the classical PCA,2DPCA directly uses two-dimensional images matrix to calculate a smaller (lower) covariance matrix, which decreases the computation load and saves the storage space. Although 2DPCA promotes the development of face recognition, some information contained in the high dimensional covariance matrix, which can help to improve face recognition rate, is lost by lower dimensional covariance matrix. To exploit more discriminant information, we propose a vertically symmetrical variation 2DPCA (S2DPCA) algorithm for face recognition. The experiments on face databases show that S2DPCA reduces the computational complexity comparing with PCA, and improves the face recognition rate comparing with PCA and 2DPCA.(2) However, because S2DPCA has higher degree of freedom than 2DPCA, it is more sensitive to small sample size. To further improve the performance of the S2DPCA, an efficient algorithm of face feature extraction is proposed on basis of the weighted variation of 2DPCA (WV2DPCA), in which the face space is elaborately divided into three parts:the part above the eyebrows, one between eyebrows and the nasal tip, and that below nasal tip. WV2DPCA extracts the features from each sub-image matrix. According to taking the different roles of three sub-images in face recognition, a common weight is assigned to each sub-image. Finally, the classification is performed by the weighted nearest neighbor method. The WV2DPCA has three advantages that include alleviating the bad effect of small sample size, increasing face recognition rate, and decreasing the computational complexity.(3) The main drawback in WV2DPCA is the strategy how to assign appropriate weights to the sub-images. However, weights used in WV2DPCA are roughly estimated according to different samples, and may be inaccurate. To overcome this drawback, an adaptive weighted variation 2DPCA (AWV2DPCA) for face recognition is developed. In AWV2DPCA, each face image is divided into several sub-images, and all the sub-images of the same position are defined as a sub-image set. AWV2DPCA extracts the features associated with each of sub-image sets, and adaptively estimates the weight corresponding to each of sub-image sets according to the similarity of features, and performs the classification by the weighted nearest neighbor method.(4) The traditional Bayesian algorithms for face recognition assume that the samples meet the Gaussian distribution. In fact, the distributions of samples are very complicated. To adapt to the complicated distributions of samples, a face recognition algorithm based on the binary image is proposed in the light of the Bayesian principle. In this algorithm, the images binarization is firstly performed, and the class conditional probability is calculated under the assumption that the sample feature variables are mutually independent each other, and finally posterior probability is calculated by Bayesian formula. The above simple method decreases the computational complexity.To further enhance the face recognition rate, a face recognition algorithm of binary image is proposed by the smallest Bayesian risk method, which estimates the loss function according to the similarity of the samples, then evaluates the smallest risk by Bayesian formula, and finally determines that they belong to which class. This algorithm increases the gaps between classes and improves face recognition rate.(5) It is well-known that the line discriminant analysis (LDA) applied to high-dimensional face recognition often suffers from two problems, small sample size (SSS) and close-to-class overlap. To overcome these problems, a LDA-based face recognition algorithm with regularization parameters is proposed, which resolves the SSS problem by regularization parameters and redefined within-class scatter matrices, and prevents from the overlap of edge classes through weighting between-class scatter matrices. Extensive experimental results show the proposed LDA algorithm can solve the above two problems and outperforms traditional methods such as eigenfaces and Fisherfaces by controlling the regularization parameters. On the basis of the above method, an algorithm of feature extraction in face image space is proposed. This algorithm decomposes the eigenfeature space into two subspaces, principal component subspace and null subspace, and regularizes two subspaces with the eigen-feature spectrum model to alleviate the instability, overfitting or poor generalization. The experiments on ORL face database show that our method, which uses fewer features, can achieve higher recognition rate than other approaches, such as FLDA, BML, and DSL.