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Communication Dans Un Congrès Année : 2022

Morphological counterpart of Ornstein-Uhlenbeck semigroups and PDEs

Jesús Angulo

Résumé

Morphological semigroups and corresponding Partial Dierential Equations are equivalent respectively to Hopf-Lax semigroups and the Cauchy problem of a family of first-order Hamilton-Jacobi equations. They are related to Maslov idempotent analysis too. The Ornstein-Uhlenbeck operator and Ornstein-Uhlenbeck semigroup play the role of the Laplacian and the heat kernel semigroup if the Lebesgue measure is replaced by the standard Gaussian measure. In this paper we revisit some contributions on the idempotent analogue of the semigroups associated with the Ornstein-Uhlenbeck semigroup, which are based on a Maslov measure, as well as the associated rst-order Hamilton-Jacobi equation. We study the relevance of the corresponding semigroups in the context of morphological erosions and dilations.
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Dates et versions

hal-03759586 , version 1 (24-08-2022)

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Jesús Angulo. Morphological counterpart of Ornstein-Uhlenbeck semigroups and PDEs. International Conference on Discrete Geometry and Mathematical Morphology DGMM 2022: Discrete Geometry and Mathematical Morphology, Baudrier, É., Naegel, B., Krähenbühl, A., Tajine, M. (eds), Oct 2022, Strasbourg, France. pp.169-181, ⟨10.1007/978-3-031-19897-7_14⟩. ⟨hal-03759586⟩
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