Soft Color Morphology: A Fuzzy Approach for Multivariate Images

Abstract

Mathematical morphology is a framework composed by a set of well-known image processing techniques, widely used for binary and grayscale images, but less commonly used to process color or multivariate images. In this paper, we generalize fuzzy mathematical morphology to process multivariate images in such a way that overcomes the problem of defining an appropriate order among colors. We introduce the soft color erosion and the soft color dilation, which are the foundations of the rest of operators. Besides studying their theoretical properties, we analyze their behavior and compare them with the corresponding morphological operators from other frameworks that deal with color images. The soft color morphology outstands when handling images in the CIEL $${}^*a{}^*b{}^*$$ color space, where it guarantees that no colors with different chromatic values to the original ones are created. The soft color morphological operators prove to be easily customizable but also highly interpretable. Besides, they are fast operators and provide smooth outputs, more visually appealing than the crisp color transitions provided by other approaches.