Extending morphological covariance

Mathematical morphology conversely to linear image analysis approaches specialises in capturing the spatial relations among pixels. This inherent potential has been exploited in the context of texture characterisation, with granulometry along with morphological covariance being the two main tools of the morphological arsenal for this task. However, with the advent of new and powerful texture analysis approaches in the last years (e.g. local binary patterns, MR8), they have 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 characterisation. In this paper, we present a set of extensions for morphological covariance, inspired from differential morphological profiles, that enhance its rotation and illumination invariance capacity. The proposed approach is tested extensively against the state-of-the-art, using the Outex, CUReT, KTH-TIPS, KTH-TIPS2 and ALOT databases, where it exhibits either a superior or comparable performance.