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# Morphological Scale-Space Operators for Images Supported on Point Clouds

Abstract : The aim of this paper is to develop the theory, and to propose an algorithm, for morphological processing of images painted on point clouds, viewed as a length metric measure space $(X,d,\mu)$. In order to extend morphological operators to process point cloud supported images, one needs to define dilation and erosion as semigroup operators on $(X,d)$. That corresponds to a supremal convolution (and infimal convolution) using admissible structuring function on $(X,d)$. From a more theoretical perspective, we introduce the notion of abstract structuring functions formulated on length metric Maslov idempotent measurable spaces, which is the appropriate setting for $(X,d)$. In practice, computation of Maslov structuring function is approached by a random walks framework to estimate heat kernel on $(X,d,\mu)$, followed by the logarithmic trick.
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https://hal-mines-paristech.archives-ouvertes.fr/hal-01108141
Contributeur : Jesus Angulo <>
Soumis le : dimanche 17 janvier 2016 - 14:39:23
Dernière modification le : jeudi 9 avril 2020 - 17:08:04
Document(s) archivé(s) le : lundi 18 avril 2016 - 10:10:59

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Jesus Angulo. Morphological Scale-Space Operators for Images Supported on Point Clouds. 5th International Conference on Scale Space and Variational Methods in Computer Vision, Jun 2015, Lège-Cap Ferret, France. ⟨10.1007/978-3-319-18461-6_7⟩. ⟨hal-01108141v3⟩

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