Classification approach based on the product of riemannian manifolds from Gaussian parametrization space
This paper presents a novel framework for visual content classification using jointly local mean vectors and covariance matrices of pixel level input features. We consider local mean and covariance as realizations of a bivariate Riemannian Gaussian density lying on a product of submanifolds. We first introduce the generalized Mahalanobis distance and then we propose a formal definition of our product-spaces Gaussian distribution on Rm × SPD(m). This definition enables us to provide a mixture model from a mixture of a finite number of Riemannian Gaussian distributions to obtain a tractable descriptor. Mixture parameters are estimated from training data by exploiting an iterative Expectation-Maximization (EM) algorithm. Experiments in a texture classification task are conducted to evaluate this extended modeling on several color texture databases, namely popular Vistex, 167-Vistex and CUReT. These experiments show that our new mixture model competes with state-of-the-art on the experimented datasets.