使用法线的全变分和形状牛顿方法的网格去噪与修复
Mesh Denoising and Inpainting using the Total Variation of the Normal and a Shape Newton Approach
AI总结：
本文提出一种基于单位法向量场全变分离散变体作为正则化泛函的表面网格去噪与修复新方法，采用适配的 split Bregman (ADMM) 迭代并结合非精确牛顿法进行形状优化，显著提升了计算速度，并在复杂3D几何体上验证了算法性能。
摘要：
我们提出了一种处理表面网格去噪与修复问题的新方法。这些问题的目的是去除噪声或填补缺失部分，同时保留诸如锐利边缘等重要特征。单位法向量场全变分离散变体作为正则化泛函以实现这些目标。为了求解所得问题，我们使用了一种适应于该问题的 split Bregman (ADMM) 迭代版本。全变分正则化项的新表述，以及在形状优化步骤中使用非精确牛顿法，使得与早期方法相比速度显著提升。文中包含了数值示例，展示了我们的算法在一些复杂3D几何体上的性能。
英文摘要：
We present a novel approach to denoising and inpainting problems for surface meshes. The purpose of these problems is to remove noise or fill in missing parts while preserving important features such as sharp edges. A discrete variant of the total variation of the unit normal vector field serves as a regularizing functional to achieve these goals. In order to solve the resulting problem, we use a version of the split Bregman (ADMM) iteration adapted to the problem. A new formulation of the total variation regularizer, as well as the use of an inexact Newton method for the shape optimization step, bring significant speed-up compared to earlier methods. Numerical examples are included, demonstrating the performance of our algorithm with some complex 3D geometries.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
