A topological tree of shapes

Nicolas Passat (1) , Yukiko Kenmochi (2)

1 CRESTIC - Centre de Recherche en Sciences et Technologies de l'Information et de la Communication - EA 3804
2 Equipe Image - Laboratoire GREYC - UMR6072

In this article, we enrich the framework of morphological hierarchies with new acyclic graphs and trees. These structures lie at the convergence of hierarchical models and topological descriptors. We define them in the context of digital grey-level imaging. We discuss their links with component-trees, trees of shapes and adjacency trees. This analysis leads to new notions, including a notion of topological tree of shapes.

Domaines: Traitement des images [eess.IV]; Topologie géométrique [math.GT]

Nicolas Passat, Yukiko Kenmochi. A topological tree of shapes. International Conference on Discrete Geometry and Mathematical Morphology (DGMM), Oct 2022, Strasbourg, France. pp.221-235, ⟨10.1007/978-3-031-19897-7_18⟩. ⟨hal-03707130v2⟩