A new definition for fuzzy attributed graph homomorphism with application to structural shape recognition in brain imaging

We propose in this paper an original definition for fuzzy attributed graph homomorphism that deals with both the structural aspect and the maximization of similarity between attributes (on nodes and on arcs). A graph fuzzy homomorphism theory is developed to gather different pieces of information extracted from images, and to take full advantage of the whole graph structure, with several attached attributes. The homomorphism properties allow relevant and accurate graph mapping by evaluating graph structure deformation with fuzzy sets. Anticipated application is atlas-based labeling of brain MRI using graph homomorphism for spatial and temporal analysis of brain tumors and surrounding structures. The definitions and properties proposed in this paper are a first step towards this goal.