Grouping/degrouping point process, a point process driven by geometrical and topological properties of a partition in regions

In the context of image segmentation, we introduce a new kind of point process, called grouping/degrouping point process (GDPP) that aims to aggregate regions from an initial partition of the image according to geometrical and topological criteria. The initial partition, produced by a low-level region-based segmentation process, is represented using a topological map that represents all the geometrical information and topological features of the image partition. Points in the process are localized in regions and newly defined energies of the partition allow to take into account geometrical and topological features like the number of holes or the area of contact between regions. The simulation of the point population is driven by birth and death moves used in a Reversible Jump Markov Chain Monte Carlo method. We propose special birth and death moves using the adjacency relation between regions. Experiments are provided on a sample partition that show the effects of the different potentials. In a 3D medical image, a GDPP based application is provided to segment brain tumor. The results are compared to a region merging approach and to a reference segmentation proposed by an expert. This approach emphasizes the ability of the GDPP to solve real world segmentation problem.