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.

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Lattice computing models such as the morphological neural networks and fuzzy neurocomputing models are becoming increasingly important with the advent of granular computing. In particular, the morphological perceptron with competitive learning (MP/CL), introduced by Sussner and Esmi, exhibited satisfactory classification results in some well known classification problems. On the downside, the MP/CL is subject to overfitting in which the network learns singular characteristics from the training data. In this paper, we propose a learning strategy based on a certain genetic algorithm to circumvent the overfitting problem of MP/CL. Computational experiments revealed that the novel model can achieve similar classification results but using a smaller number of hidden neurons.