Total variation diffusion and its application in shape decomposition

Abstract

One challenge in shape decomposition is to capture correct boundaries between different parts and get piecewise constant results. Based on the good edge-preserving and sparsity properties of total variation regularization, this paper introduces a novel diffusion model by minimizing weighted total-variation energy with Dirichlet boundary constraints. By the total variation diffusion model, we propose an edge-preserving shape decomposition optimization model, which can be solved effectively by augmented Lagrangian method with each subproblem having closed form solution. A number of experiments display that our method can produce segmentation results with piecewise constant parts and feature-preserving boundaries for both meshes and 3D point clouds, especially for shapes with sharp features. In addition, for mesh segmentation, our results compare favorably to those obtained by several existing techniques when evaluated on the Princeton Segmentation Benchmark. Furthermore, the quantitative errors show that the algorithm is robust numerically and the computational costs are reasonable.