Topological modeling of illuminated surfaces using Reeb graph

We present a feature-based object representation for topological modeling of three-dimensional illuminated surfaces. The proposed approach encodes an object into the Reeb graph concept from computational topology. This skeletal structure is based on the generalized height function in the light direction defined on the illuminated surface. In this paper, the topological properties of the proposed representation are analyzed in the Morse theoretic framework, and its close relationship to the shading problem is also highlighted. Some numerical simulations with synthetic and real 3D data are provided to demonstrate the potential of object singularities in topological modeling.