Stochastic morphological filtering and Bellman-Maslov chains

This paper introduces a probabilistic framework for adaptive morphological dilation and erosion. More precisely our probabilistic formalization is based on using random walk simulations for a stochastic estimation of adaptive and robust morphological operators. Hence, we propose a theoretically sound morphological counterpart of Monte Carlo stochastic filtering. The approach by simulations is inefficient but particularly tailorable for introducing different kinds of adaptability. From a theoretical viewpoint, stochastic morphological operators fit into the framework of Bellman-Maslov chains, the (max, +)-counterpart of Markov chains, which the basis behind the efficient implementations using sparse matrix products.