Re-meshing techniques for topological analysis

A method for the extraction of the Extended Reeb Graph (ERG) from a closed 3D triangular mesh is presented. The ERG codes the relationships among critical points of the height function associated to the mesh, and it can represent isolated as well as degenerate critical points. The extraction process is based on a remeshing strategy of the original mesh, which is forced to follow contour levels. The occurrence and configuration of flat areas in the re-triangulated model identify critical areas of the shape, and their relationships allow the reconstruction of the global topological structure of the shape.