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Mathematical Morphology for Real-Valued Images on Riemannian Manifolds

Abstract : This paper introduces mathematical morphology for real-valued images whose support space is a Riemannian manifold. The starting point consists in replacing the Euclidean distance in the canonic quadratic structuring function by the Riemannian distance. Besides the definition of Riemannian dilation/erosion and Riemannian opening/closing, their properties are explored. We generalize also some theoretical results on Lasry-Lions regularization for Cartan-Hadamard manifolds. Theoretical connections with previous works on adaptive morphology and on manifold shape are considered. Various useful image manifolds are formalized, with an example using real-valued 3D surfaces.
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Submitted on : Monday, June 17, 2013 - 10:07:02 AM
Last modification on : Wednesday, November 17, 2021 - 12:27:09 PM

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Jesus Angulo, Santiago Velasco-Forero. Mathematical Morphology for Real-Valued Images on Riemannian Manifolds. 11th International Symposium, ISMM 2013, May 2013, Uppsala, Sweden. pp.279-291, ⟨10.1007/978-3-642-38294-9_24⟩. ⟨hal-00834667⟩



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