Image set classification by symmetric positive semi-definite matrices

Representing images and videos by covariance descriptors and leveraging the inherent manifold structure of Symmetric Positive Definite (SPD) matrices leads to enhanced performances in various visual recognition tasks. However, when covariance descriptors are used to represent image sets, the result is often rank-deficient. Thus, most existing approaches adhere to blind perturbation with predefined regularizers just to be able to employ inference tools. To overcome this problem, we introduce novel similarity measures specifically designed for rank-deficient covariance descriptors, i.e., symmetric positive semi-definite matrices. In particular, we derive positive definite kernels that can be decomposed into the kernels on the cone of SPD matrices and kernels on the Grassmann manifolds. Our experiments evidence that, our method achieves superior results for image set classification on various recognition tasks including hand gesture classification, face recognition from video sequences, and dynamic scene categorization.