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A Proof of the Tree of Shapes in n-D

Abstract : In this paper, we prove that the self-dual morphological hierarchical structure computed on a n-D gray-level wellcomposed image u by the algorithm of Géraud et al. [1] is exactly the mathematical structure defined to be the tree of shape of u in Najman et al [2]. We recall that this algorithm is in quasi-linear time and thus considered to be optimal. The tree of shapes leads to many applications in mathematical morphology and in image processing like grain filtering, shapings, image segmentation, and so on.
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https://hal.archives-ouvertes.fr/hal-03690353
Contributor : Laurent Najman Connect in order to contact the contributor
Submitted on : Wednesday, June 8, 2022 - 10:18:22 AM
Last modification on : Friday, June 24, 2022 - 4:05:32 AM

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  • HAL Id : hal-03690353, version 1
  • ARXIV : 2206.05109

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Thierry Géraud, Nicolas Boutry, Sébastien Crozet, Edwin Carlinet, Laurent Najman. A Proof of the Tree of Shapes in n-D. 2022. ⟨hal-03690353⟩

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