Topological analysis of voxelized objects by discrete geodesic Reeb graph

We introduce here the concept of discrete level sets (DLS) that can be constructed on a voxelized surface with the assurance of certain topological properties. This eventually aids in construction of discrete geodesic Reeb graph (DGRG) on a voxelized object, for topological analysis. Under various transformations like rotation and topology-constrained anisotropic deformation, a DGRG remains invariant to typical topological features like loops or cycles, which eventually helps in identifying 'handles' in the underlying object. Experiments on different datasets show promising results on the practical usefulness of DLS and DGRG towards extraction of high-level topological features of arbitrary voxel sets.