Measuring the Irregularity of Vector-Valued Morphological Operators Using Wasserstein Metric

Mathematical morphology is a useful theory of nonlinear operators widely used for image processing and analysis. Despite the successful application morphological binary gray-scale images, extending them to vector-valued images not straightforward because there are no unambiguous orderings vectors. Among many approaches multivalued mathematical morphology, those based on total orders particularly promising. Morphological do produce so-called false-colors. On downside, they often introduce irregularities in output image. Although irregularity issue has rigorous formulation, we aware an efficient method quantify it. In this paper, propose operator using Wasserstein metric. The metric yields minimal transport cost transforming input into We illustrate by examples how