Tensor Fields for Multilinear Image Representation and Statistical Learning Models Applications

Nowadays, higher order tensors have been applied to model multi-dimensional image data for subsequent tensor decomposition, dimensionality reduction and classification tasks. In this paper, we survey recent results with the goal of highlighting the power of tensor methods as a general technique for data representation, their advantage if compared with vector counterparts and some research challenges. Hence, we firstly review the geometric theory behind tensor fields and their algebraic representation. Afterwards, subspace learning, dimensionality reduction, discriminant analysis and reconstruction problems are considered following the traditional viewpoint for tensor fields in image processing, based on generalized matrices.We show several experimental results to point out the effectiveness of multi-linear algorithms for dimensionality reduction combined with discriminant techniques for selecting tensor components for face image analysis, considering gender classification as well as reconstruction problems. Then, we return to the geometric approach for tensors and discuss opened issues in this area related to manifold learning and tensor fields, incorporation of prior information and high performance computational requirements. Finally, we offer conclusions and final remarks.