Defining regions within the Combinatorial Pyramid framework

Irregular Pyramids are defined as a stack of successively reduced graphs. Each vertex of a reduced graph is associated to a set of vertices in the base level graph named its receptive field. If the initial graph is deduced from a planar sampling grid its reduced versions are planar and each receptive field is a region of the initial grid. Combinatorial Pyramids are defined as a stack of successively reduced combinatorial maps. Combinatorial maps are based on half edges named darts and the receptive field of a dart is a sequence of darts in the base level combinatorial map. We present in this paper preliminary results showing how to define regions from the receptive fields of the darts.