Building the topological tree of shapes from the tree of shapes

Julien Mendes Forte (1, 2) , Nicolas Passat (3) , Yukiko Kenmochi (1, 2)

1 GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen
2 Equipe Image - Laboratoire GREYC - UMR6072
3 CRESTIC - Centre de Recherche en Sciences et Technologies de l'Information et de la Communication - EA 3804

The topological tree of shapes was recently introduced as a new hierarchical structure within the family of morphological trees. Morphological trees are efficient models for image processing and analysis. For such applications, it is of paramount importance that these structures be built and manipulated with optimal complexity. In this article, we focus on the construction of the topological tree of shapes. We propose an algorithm for building the topological tree of shapes from the tree of shapes. In particular, a cornerstone of this algorithm is the construction of the complete tree of shapes, another recently introduced tree unifying both the tree of shapes and the topological tree of shapes. We also discuss the cost of the computation of these structures.

Mots clés: Morphological trees; Tree of shapes; Topological tree of shapes; Complete tree of shapes; Algorithmics

Domaines: Informatique [cs]

Julien Mendes Forte, Nicolas Passat, Yukiko Kenmochi. Building the topological tree of shapes from the tree of shapes. International Conference on Discrete Geometry and Mathematical Morphology (DGMM), 2024, Florence, Italy. pp.271-285, ⟨10.1007/978-3-031-57793-2_21⟩. ⟨hal-04363684⟩