A Proof of the Tree of Shapes in n-D
Discrete Mathematics
2022-06-13 v1 Data Structures and Algorithms
Image and Video Processing
Geometric Topology
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 G{\'e}raud 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.
Keywords
Cite
@article{arxiv.2206.05109,
title = {A Proof of the Tree of Shapes in n-D},
author = {Thierry GÉraud and Nicolas Boutry and Sébastien Crozet and Edwin Carlinet and Laurent Najman},
journal= {arXiv preprint arXiv:2206.05109},
year = {2022}
}