Elementary morphological operations on the spherical CIELab quantale

Abstract

Mathematical morphology is a theory with applications in image and signal processing and analysis. This paper presents a quantale-based approach to color morphology based on the CIELab color space with spherical coordinates. The novel morphological operations take into account the perceptual difference between color elements by using a distance-based ordering scheme. Furthermore, the novel approach allows the use of non-flat structuring elements. Although the paper focuses on dilations and erosions, many other morphological operations can be obtained by combining these two elementary operations. An illustrative example reveals that non-flat dilations and erosions may preserve more features of a natural color image than their corresponding flat operations.