Face recognition as a kronecker product equation

Various parameters influence face recognition such as expression, pose, and illumination. In contrast to matrices, tensors can be used to naturally accommodate for the different modes of variation. The multilinear singular value decomposition (MLSVD) then allows one to describe each mode with a factor matrix and the interaction between the modes with a coefficient tensor. In this paper, we show that each image in the tensor satisfying an MLSVD model can be expressed as a structured linear system called a Kronecker Product Equation (KPE). By solving a similar KPE for a new image, we can extract a feature vector that allows us to recognize the person with high performance. Additionally, more robust results can be obtained by using multiple images of the same person under different conditions, leading to a coupled KPE. Finally, our method can be used to update the database with an unknown person using only a few images instead of an image for each combination of conditions. We illustrate our method for the extended Yale Face Database B, achieving better performance than conventional methods such as Eigenfaces and other tensor-based techniques.