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.


Random Walk Mathematical Morphology Theoretical Viewpoint Idempotent Semiring Random Walk Simulation 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jesús Angulo
    • 1
  • Santiago Velasco-Forero
    • 2
  1. 1.CMM-Centre de Morphologie Mathématique, Mathématiques et SystèmesMINES ParisTechFrance
  2. 2.ITWM - Fraunhofer InstituteKaiserlauternGermany

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