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.

中文翻译：

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全变差扩散及其在形状分解中的应用

摘要 形状分解的一个挑战是捕捉不同部分之间的正确边界并获得分段常数结果。基于全变分正则化的良好边缘保持性和稀疏性，本文引入了一种新的扩散模型，通过最小化带狄利克雷边界约束的加权总变分能量。通过全变差扩散模型，我们提出了一种保边形状分解优化模型，该模型可以通过每个子问题具有封闭形式解的增广拉格朗日方法进行有效求解。大量实验表明，我们的方法可以为网格和 3D 点云生成具有分段恒定部分和特征保留边界的分割结果，特别是对于具有尖锐特征的形状。此外，对于网格分割，当在普林斯顿分割基准上进行评估时，我们的结果优于通过几种现有技术获得的结果。此外，定量误差表明该算法在数值上是稳健的，并且计算成本是合理的。