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

International audience; We present a new type of point process, called Grouping/Degrouping Point Process (GDPP), which aim is to select a set of regions of a volume associated to an object or a Region of Interest (ROI). These regions can be obtained from a first low-level region-based segmentation for example. Geometrical and topological information of regions as localisation, adjacency, number of holes ..., are introduced in potentials which computation is done from a population of points which fall in these regions. Thus, a population of points can iteratively converge using Simulated Annealing and therefore select an optimal set of regions. In the paper, we provide the definition of region based potentials and birth and death moves used in a Reversible Jump Monte Carlo Markov Chain method. We also propose special birth and death moves using adjacency of regions. Simulations are done on Positron Emission Tomography. They show the possibility to estimate coherent sets of regions using GDPP as these sets make sense with ROIs defined by a clinician. Implementation of the process implies manipulation of 3D regions. Topological maps have been used as they permit an efficient computation of geometrical and topological properties of 3D regions and they provide a basis that allows further developments.