2D Topological Map Isomorphism for Multi-Label Simple Transformation Definition

Guillaume Damiand (1) , Tristan Roussillon (1) , Christine Solnon (1)

1 M2DisCo - Geometry Processing and Constrained Optimization

A 2D topological map allows one to fully describe the topol-ogy of a labeled image. In this paper we introduce new tools for compar-ing the topology of two labeled images. First we define 2D topological map isomorphism. We show that isomorphic topological maps correspond to homeomorphic embeddings in the plane and we give a polynomial-time algorithm for deciding of topological map isomorphism. Then we use this notion to give a generic definition of multi-label simple transformation as a set of transformations of labels of pixels which does not modify the topology of the labeled image. We illustrate the interest of multi-label simple transformation by generating look-up tables of small transforma-tions preserving the topology.

Mots clés: Combinatorial maps; 2D topological maps isomorphism; labeled image; simple points; simple sets

Domaines: Algorithme et structure de données [cs.DS]; Traitement des images [eess.IV]

Guillaume Damiand, Tristan Roussillon, Christine Solnon. 2D Topological Map Isomorphism for Multi-Label Simple Transformation Definition. 18th International Conference on Discrete Geometry for Computer Imagery, Sep 2014, Siena, Italy. pp.39-50, ⟨10.1007/978-3-319-09955-2_4⟩. ⟨hal-01078001⟩