Morphology on Categorical Distributions

Abstract Mathematical morphology (MM) is an indispensable tool for post-processing. Several extensions of MM to categorical images, such as multi-class segmentations, have been proposed. However, none provide satisfactory definitions on probabilistic representations images. The distribution a natural choice representing uncertainty about Extending distributions problematic because categories are inherently unordered. Without ranking categories, we cannot use the standard framework based supremum and infimum. Ranking impractical problematic. Instead, consider representation operations that emphasize single category. In this work, review compare previous approaches. We propose two approaches distributions: operating Dirichlet over parameters directly distributions. “protected” variant latter demonstrate proposed by fixing misclassifications modeling annotator bias.