Supervised morphology for structure tensor-valued images based on symmetric divergence kernels

Mathematical morphology is a nonlinear image processing methodology based on computing min/max operators in local neighbourhoods. In the case of tensor-valued images, the space of SPD matrices should be endowed with a partial ordering and a complete lattice structure. Structure tensor describes robustly the local orientation and anisotropy of image features. Formulation of mathematical morphology operators dealing with structure tensor images is relevant for texture filtering and segmentation. This paper introduces tensor-valued mathematical morphology based on a supervised partial ordering, where the ordering mapping is formulated by means of positive definite kernels and solved by machine learning algorithms. More precisely, we focus on symmetric divergences for SPD matrices and associated kernels.