Abstract
Recently, a novel Log-Euclidean Riemannian metric [28] is proposed for statistics on symmetric positive definite (SPD) matrices. Under this metric, distances and Riemannian means take a much simpler form than the widely used affine-invariant Riemannian metric. Based on the Log-Euclidean Riemannian metric, we develop a tracking framework in this paper. In the framework, the covariance matrices of image features in the five modes are used to represent object appearance. Since a nonsingular covariance matrix is a SPD matrix lying on a connected Riemannian manifold, the Log-Euclidean Riemannian metric is used for statistics on the covariance matrices of image features. Further, we present an effective online Log-Euclidean Riemannian subspace learning algorithm which models the appearance changes of an object by incrementally learning a low-order Log-Euclidean eigenspace representation through adaptively updating the sample mean and eigenbasis. Tracking is then led by the Bayesian state inference framework in which a particle filter is used for propagating sample distributions over the time. Theoretic analysis and experimental evaluations demonstrate the promise and effectiveness of the proposed framework.