A graph-anisotropic approach to 3-D data segmentation

In this paper, we present a general framework for the segmentation of surfaces represented by 3-D scattered data. The method we present is based on a contextual anisotropic diffusion scheme. Contextual information at each data point involves the selection of optimal directions, locally representing the shape. Over the set of points, graph based representations are well adapted to gather this kind of information in a single compact description. Thus, we introduce two structures respectively denoted minimal and maximal escarpment trees. Our segmentation process is tightly bound to these structures. It proceeds in two stages. The first stage corresponds to the exploration of the maximal escarpment tree and the detection of atomic regions. Then, the second stage permits the progressive merging of emergent regions over the minimal escarpment tree, subject to implicit conditions on the presence of singularities. The sequence of these two treatments has proven to be effective, it corresponds to a new an original approach of segmentation.