用法向量总变差优化网格表面分割，提升噪声抑制能力。
Two Models for Surface Segmentation using the Total Variation of the Normal Vector
- 基于法向量场相似性，设计两种总变差正则化分割方法。
- 第二种方法在常曲率区域去噪效果更优，但计算成本更高。
- 引入流形牛顿法加速核心子问题，显著降低计算开销。
我们研究基于三角网格表示的表面分割问题，目标是根据法向量场与一组标签向量的相似性对表面进行划分。提出一种变分方法，并比较两种基于总变差度量的正则化策略：第一种直接惩罚分配函数的总变差，第二种则在标签空间中惩罚总变差。为求解由此产生的优化问题，采用针对本问题定制的分裂Bregman（ADMM）迭代算法。实验表明，尽管第二种方法计算代价更高，但在常曲率区域具有更强的噪声抑制能力。为进一步降低计算成本，提出了用于最耗时子问题的流形牛顿法，该子问题与球面上的黎曼质心相关，显著提升了求解效率。
原文摘要 · Abstract (English)
We consider the problem of surface segmentation, where the goal is to partition a surface represented by a triangular mesh. The segmentation is based on the similarity of the normal vector field to a given set of label vectors. We propose a variational approach and compare two different regularizers, both based on a total variation measure. The first regularizer penalizes the total variation of the assignment function directly, while the second regularizer penalizes the total variation in the label space. In order to solve the resulting optimization problems, we use variations of the split Bregman (ADMM) iteration adapted to the problem at hand. While computationally more expensive, the second regularizer yields better results in our experiments. In particular it removes noise more reliably in regions of constant curvature. In order to mitigate the computational cost, we present a manifold Newton scheme for the most expensive subproblem, which is related to the Riemannian center of mass on a sphere. This significantly improves the computational cost.
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