发表机构
TU Berlin（柏林工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对隐式曲面提出了基于点采样的尽可能刚性（ARAP）能量计算方法，将其应用于神经形状处理，通过与现有方法对比验证了该方法的通用性与优势。
AI 中文摘要
隐式曲面表示因在机器学习中的应用而重新受到关注。优化中的常见组成部分是正则化，用于惩罚曲面与其原始形状的偏差。流行的尽可能刚性（ARAP）能量在现实变形行为与高效计算之间取得了良好的平衡，至少对于分段线性网格而言是如此。我们开发了一种基于曲面点采样计算变形函数ARAP能量的方法，利用隐式表示为每个采样点提供微分，该方法在每个采样点的计算高效且精确（数值精度范围内）。我们在多个应用中展示了该方法对神经形状处理的通用性，并将其特性与文献中的替代方法进行了对比。
英文摘要
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.
Journal refComputer Graphics forum, Volume 25 (2026), Number 5
