Foreground Segmentation via Background Modeling on Riemannian Manifolds

Statistical modeling in color space is a widely used approach for background modeling to foreground segmentation. Nevertheless, sometimes computing such statistics directly on image values is not enough to achieve a good discrimination. Thus the image may be converted into a more information rich form, such as a tensor field, in which can be encoded color and gradients. In this paper, we exploit the theoretically well-founded differential geometrical properties of the Riemannian manifold where tensors lie. We propose a novel and efficient approach for foreground segmentation on tensor field based on data modeling by means of Gaussians mixtures (GMM) directly in the tensor domain. We introduced a Expectation Maximization (EM) algorithm to estimate the mixture parameters, and are proposed two algorithms based on an online K-means approximation of EM, in order to speed up the process. Theoretic analysis and experimental evaluations demonstrate the promise and effectiveness of the proposed framework.