New Approach for Multi-Valued Mathematical Morphology Computation

Abstract

Mathematical Morphology (MM) is a useful tool for spatial image processing. It is based on an infimum operator (min) and a supremum operator (max) applied in local neighborhoods to detect pixel extremes. The MM was initially defined for mono-band images in which each pixel image is a scalar value and it is easy to find pixels extremes by the infimum and the supremum operators. However, in the case of multi-band images, where each pixel image is represented by a vector, establishing an order between image pixels in local neighborhoods by the infimum and supremum operators is not trivial. Many works discussed the feasibility to extend the MM to multi-band images but they did not lead to any consensual definition of the multi-valued mathematical morphology. Nevertheless, these existing works agree that the definition of the MM for multi-band images is based on the notion of vector ordering. In this paper, we propose a multi-valued MM operators computing by introducing a new vector ordering algorithm that allows extending the scalar MM to multi-band images. The proposed multi-valued morphological operations were tested in the experimental phase for the morphological descriptors computation. The obtained results based on use of the proposed vector ordering algorithm for the multi-valued MM computing improve the classification rates.