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Facial images change appearance due to multiple factors such as different poses, lighting variations, and facial expressions. Tensors are higher order extensions of vectors and matrices, which make it possible to analyze different appearance factors of facial variation. Using higher order tensors, we can construct a multilinear structure and model the multiple factors of face variation. In particular, among the appearance factors, the factor of a person's identity modeled by a tensor structure can be used for face recognition. However, this tensor-based face recognition creates difficulty in factorizing the unknown parameters of a new test image and solving for the person-identity parameter. In this paper, to break this limitation of applying the tensor-based methods to face recognition, we propose a novel tensor approach based on an individual-modeling method and nonlinear mappings. The proposed method does not require the problematic tensor factorization and is more efficient than the traditional TensorFaces method with respect to computation and memory. We set up the problem of solving for the unknown factors as a least squares problem with a quadratic equality constraint and solve it using numerical optimization techniques. We show that an individual-multilinear approach reduces the order of the tensor so that it makes face-recognition tasks computationally efficient as well as analytically simpler. We also show that nonlinear kernel mappings can be applied to this optimization problem and provide more accuracy to face-recognition systems than linear mappings. In this paper, we show that the proposed method, individual kernel TensorFaces, produces the better discrimination power for classification. The novelty in our approach as compared to previous work is that the Individual Kernel TensorFaces method does not require estimating any factor of a new test image for face recognition. In addition, we do not need to have any a priori knowledge of or assumption abou- - t the factors of a test image when using the proposed method. We can apply individual kernel TensorFaces even if the factors of a test image are absent from the training set. Based on various experiments on the Carnegie Mellon University Pose, Illumination, and Expression database, we demonstrate that the proposed method produces reliable results for face recognition.
Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on (Volume:37 , Issue: 5 )
Date of Publication: Oct. 2007