Texture segmentation using independent-scale component-wise Riemannian-covariance Gaussian mixture model in KL measure based multi-scale nonlinear structure tensor space

This paper proposes a novel texture segmentation approach using independent-scale component-wise Riemannian-covariance Gaussian mixture model (ICRGMM) in Kullback-Leibler (KL) measure based multi-scale nonlinear structure tensor (MSNST) space. We use the independent-scale distribution and full-covariance structure to replace the covariant-scale distribution and 1D-variance structure used in our previous research. To construct the optimal full-covariance structure, we define the full-covariance on KL, Euclidean, log-Euclidean, and Riemannian gradient mappings, and compare their performances. The comparison experiments demonstrate that the Riemannian gradient mapping leads to its optimum properties over other choices when constructing the full-covariance. To estimate and update the statistical parameters more accurately, the component-wise expectation-maximization for mixtures (CEM²) algorithm is proposed instead of the originally used K-means algorithm. The superiority of the proposed ICRGMM has been demonstrated based on texture clustering and Graph Cuts based texture segmentation using a large number of synthesis texture images and real natural scene textured images, and further analyzed in terms of error ratio and modified F-measure, respectively.