Partha Bhowmick: Topological Analysis of Voxelized Objects

Topological Analysis of Voxel Sets

Algorithm

Piyush Kanti Bhunre and Partha Bhowmick, Topological Analysis of Voxelized Objects by Discrete Geodesic Reeb Graph, Journal of Computer and System Sciences, 2017 [in press].

Contribution

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.

An example

See the figure below.
Left—A voxel set of an object with four 'handles' along with level sets at regular distances 0, 5, 10,... from a source voxel s.
Middle—DGRG of the object, where v₀ corresponds to the source voxel.
Right—DGRG embedded within the real model.
Notice how the embedded DGRG represents the geometry and shape of the underlying object. Here the object is fairly complicated, containing multiple 'handles', and our technique is capable of extracting the geometry and topology of the object.