Mathematical Morphology on the Spherical CIELab Quantale with an Application in Color Image Boundary Detection

Mathematical morphology is a theory with applications in image processing and analysis. This paper presents a quantale-based approach to color morphology based on the CIELab color space in 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 for the use of non-flat structuring elements. An illustrative example reveals that non-flat dilations and erosions may preserve more features of a color image than their corresponding flat operations. Furthermore, the novel non-flat morphological operators yielded promising results on experiments concerning the detection of the boundaries of objects on color images.