Natural Reeb Graphs

A high-level understanding of a 3D mesh is an essential requirement for many applications in computer graphics and vision. To obtain such a high-level understanding, Reeb graphs are a well-researched option. Reeb graphs rely on a mapping function defined on the surface of the object, which is challenging to create without any user input. To overcome this requirement, we propose a derivation of Reeb graphs, called Natural Reeb graphs. The explicit mapping function is replaced by an implicit function formed by a natural diffusion process on the surface. Natural Reeb graphs correctly capture all branches and loops of a surface, which is mandatory to provide a correct highlevel explanation. The proposed method to generate Natural Reeb graphs is designed to be executed efficiently on the graphics processing unit (GPU).