GPU-based centroidal voronoi tessellation using local search on thinnest digital surface

Voronoi tessellation is a classical geometric problem with different variants and nature of constraints. Centroidal Voronoi tessellation (CVT) is one such leading variant and used in many applications. Although there exists a multitude of CVT techniques for 3D objects considered as discrete volumes, e.g., as sets of voxels, there is no significant work in the literature on CVT computation for voxelized (a.k.a. 'digital') surfaces. In this paper we focus on this problem and propose a novel GPU-based algorithm for CVT computation on a digital surface. Its novelty rests on several fundamental ideas. Firstly, the digital surface is thinnest by construction; that is, while being voxelized from a triangulated surface, its every triangle is 2-minimal in topological sense. As a result, each voxel of the digital surface has the smallest possible neighborhood, which eventually limits the search space and aids in efficient computation. Secondly, as the optimization constraint, a novel formulation of Voronoi energy is used, which is easy to compute and hence leads to quick convergence of the algorithm. The GPU-based algorithm with related procedures and their complexity analysis have been discussed in detail, and related experimental results have also been furnished to adjudge the merit and usefulness of the proposed algorithm.