为隐式曲面设计高效精确的刚性保持正则化方法
As-Rigid-As-Possible Regularization for Implicit Surfaces
- 通过采样点计算隐式曲面的刚性保持能量
- 在采样点上实现精确的微分计算，效率高
- 适用于神经形状处理，优于现有方法
隐式曲面表示因在机器学习中的应用而重新受到关注。优化中常见正则化项用于惩罚表面偏离原始形状的偏差。流行的逐段刚性最小化（ARAP）能量在真实变形行为与高效计算之间取得良好平衡，尤其适用于分段线性网格。本文提出一种基于表面采样点计算变形函数ARAP能量的方法，利用隐式表示获取每个采样点的微分信息，评估在每个采样点上是精确且高效的（数值精度范围内）。我们展示了该方法在多个神经形状处理任务中的通用性，并与文献中的其他方法进行了性质对比。
原文摘要 · Abstract (English)
Implicit surface representations have regained popularity because of their use in machine learning. A common component in optimization is regularization, penalizing the deviation of the surface from its original shape. The popular as-rigid-aspossible (ARAP) energy strikes a good compromise between realistic deformation behavior and efficient computation, at least for piecewise linear meshes. We develop an approach for computing the ARAP energy of a deformation function based on point sampling of the surface. The implicit representation is exploited to provide differentials in each sample. The evaluation is efficient and exact in each sample (up to numerical precision). We demonstrate the general applicability of the method to neural shape processing in several applications and contrast its properties with alternatives from the literature.
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