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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Communication dans un congrès
Cris L. Luengo Hendriks, Gunilla Borgefors, and Robin Strand. 11th International Symposium, ISMM 2013, May 2013, Uppsala, Sweden. Springer, 7883, pp.279-291, 2013, Lecture Notes in Computer Science. <10.1007/978-3-642-38294-9_24>
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https://hal-mines-paristech.archives-ouvertes.fr/hal-00834667
Contributeur : Doriane Ibarra <>
Soumis le : lundi 17 juin 2013 - 10:07:02
Dernière modification le : mercredi 13 septembre 2017 - 01:03:01

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Jesus Angulo, Santiago Velasco-Forero. Mathematical Morphology for Real-Valued Images on Riemannian Manifolds. Cris L. Luengo Hendriks, Gunilla Borgefors, and Robin Strand. 11th International Symposium, ISMM 2013, May 2013, Uppsala, Sweden. Springer, 7883, pp.279-291, 2013, Lecture Notes in Computer Science. <10.1007/978-3-642-38294-9_24>. <hal-00834667>

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