Extended morphological covariance

Morphological covariance constitutes one of the traditional tools of mathematical morphology for texture characterization. However, with the advent of new texture analysis approaches in the last years (e. g. local binary patterns, MR8), it has been left relatively behind the state-of-the-art, in the light of the present challenges of this field, particularly illumination, rotation and scale invariant characterization. In this paper, we present a set of extensions for morphological covariance, that enhance its rotation and illumination invariance capacity. The proposed approach is tested using the Outex texture collection, where it exhibits a superior performance w.r.t the standard covariance operator.