Topological Map: Minimal Encoding of 3d Segmented Images

Yves Bertrand (1) , Guillaume Damiand (2) , Christophe Fiorio (2)

1 SIC - SIGNAL-IMAGE-COMMUNICATION
2 ICAR - Image & Interaction

In this paper we define formally and completely the 3d topological map introduced in BertrandAl00: a model which encodes totally and minimally all the topological information of a 3d image. In particular, we focus on the problem of disconnections induced by the constructive definition based on several levels of maps. This multilevel representation is more or less a graph pyramid in sense that each level can be compute from the previous one in term of merge operations. Furthermore, algorithms extracting these maps from a segmented image have been given in BertrandAl00 and have been implemented and tested in practical applications.

Mots clés: Boundary representation; 3D Image; Labeled image; Image representation; Combinatorial map; Topological map; Topological representation

Domaines: Traitement des images [eess.IV]; Mathématique discrète [cs.DM]

Yves Bertrand, Guillaume Damiand, Christophe Fiorio. Topological Map: Minimal Encoding of 3d Segmented Images. GBR: Graph-Based Representation in Pattern Recognition, May 2001, Ischia, Italy. pp.64-73. ⟨lirmm-01168509⟩