Uniqueness of the perfect fusion grid on $Z^d$

Jean Cousty (1) , Gilles Bertrand (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

Region merging methods consist of improving an initial segmentation by merging some pairs of neighboring regions. In a graph, merging two regions, separated by a set of vertices, is not straightforward. The perfect fusion graphs defined in [J. Cousty et al, "Fusion Graphs: Merging Properties and Watersheds", JMIV 2008] verify all the basic properties required by region merging algorithms as used in image segmentation. Unfortunately, the graphs which are the most frequently used in image analysis (namely, those induced by the direct and the indirect adjacency relations) are not perfect fusion graphs. The perfect fusion grid, introduced in the above mentioned reference, is an adjacency relation on Zd which can be used in image analysis, which indeed induces perfect fusion graphs and which is "between" the graphs induced by the direct and the indirect adjacencies. One of the main results of this paper is that the perfect fusion grid is the only such graph whatever the dimension d.

Domaines: Traitement des images [eess.IV]; Vision par ordinateur et reconnaissance de formes [cs.CV]

Jean Cousty, Gilles Bertrand. Uniqueness of the perfect fusion grid on $Z^d$. Journal of Mathematical Imaging and Vision, 2009, 34 (3), pp.291-306. ⟨10.1007/s10851-009-0147-0⟩. ⟨hal-00511818v2⟩