Bayesian Covariance Representation with Global Informative Prior for 3D Action Recognition

For the merits of high-order statistics and Riemannian geometry, covariance matrix has become a generic feature representation for action recognition. An independent action can be represented by an empirical statistics over all of its pose samples. Two major problems of covariance include the following: (1) it is prone to be singular so that actions fail to be represented properly, and (2) it is short of global action/pose-aware information so that expressive and discriminative power is limited. In this article, we propose a novel Bayesian covariance representation by a prior regularization method to solve the preceding problems. Specifically, covariance is viewed as a parametric maximum likelihood estimate of Gaussian distribution over local poses from an independent action. Then, a Global Informative Prior (GIP) is generated over global poses with sufficient statistics to regularize covariance. In this way, (1) singularity is greatly relieved due to sufficient statistics, (2) global pose information of GIP makes Bayesian covariance theoretically equivalent to a saliency weighting covariance over global action poses so that discriminative characteristics of actions can be represented more clearly. Experimental results show that our Bayesian covariance with GIP efficiently improves the performance of action recognition. In some databases, it outperforms the state-of-the-art variant methods that are based on kernels, temporal-order structures, and saliency weighting attentions, among others.