Multilinear Projection for Face Recognition via Canonical Decomposition

Abstract

This paper introduces a new multilinear projection algorithm for appearance-based recognition in a tensor framework. The multilinear projection simultaneously maps an unlabeled image from the pixel space into multiple causal factors underlying image formation, including illumination, imaging, and scene structure. For facial recognition, the most relevant aspect of scene structure is the specific person whose face has been imaged. Our new multilinear projection algorithm, which is based on the canonical decomposition of tensors, is superior to a previously proposed multilinear projection algorithm that is based on an M-mode SVD. To develop our algorithm, we extend and formalize the definition of the mode-m product, the mode-m identity tensor, and the mode-m pseudo-inverse tensor. We demonstrate our multilinear projection in the context of facial image recognition and compare its results in simultaneously inferring the identity, view, illumination, etc., coefficient vectors of an unlabeled test image with those obtained using multilinear projection based on M-mode SVD, as well as the results obtained using a set of multiple linear projections. Finally, a practical strategy for biometric systems is discussed in which an uncooperative subject can be enrolled using a small number of training images and then recognized in unconstrained test images.