一种基于阈值化的算子分裂方法用于曲率正则化的曲面重建
A Thresholding Based Operator-Splitting Method for Curvature-Regularized Surface Reconstruction
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中文总结 AI 辅助
该研究针对点云曲面重建问题，提出结合曲率正则化、算子分裂与阈值动力学的方法，用指示函数表示曲面并分解优化问题，高效实现了尖角与凹特征的准确重建。
中文摘要 AI 辅助
从点云进行曲面重建是计算几何中的基础问题，广泛应用于计算机图形学、医学成像和制造业。本文提出一种求解曲率正则化曲面重建模型的高效方法。为避免传统水平集方法中重新初始化带来的计算成本，我们用指示函数表示重建曲面；通过引入辅助变量，将原优化问题重新表述为初值问题的稳态解计算。随后开发算子分裂方法，将所得问题分解为两个易处理的子问题，其中一个可通过迭代阈值化高效求解。该方法结合了曲率正则化、算子分裂和阈值动力学的优势，数值实验表明其计算效率高，能准确重建尖角和凹特征。
英文摘要
Surface reconstruction from point clouds is a fundamental problem in computational geometry with broad applications in computer graphics, medical imaging, and manufacturing. In this paper, we propose an efficient method for solving a curvature-regularized surface reconstruction model. To avoid the computational cost associated with reinitialization in traditional level set methods, we represent the reconstructed surface by an indicator function. By introducing an auxiliary variable, we reformulate the original optimization problem as the computation of the steady-state solution of an initial value problem. We then develop an operator-splitting method to decompose the resulting problem into two tractable subproblems, one of which can be efficiently solved by iterative thresholding. The proposed approach combines the advantages of curvature regularization, operator splitting, and threshold dynamics. Numerical experiments show that the proposed method is computationally efficient and can accurately reconstruct sharp corners and concave features.
发表机构
- Hong Kong Baptist University（香港浸会大学）
- The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））
- Shenzhen International Center for Industrial and Applied Mathematics, Shenzhen Research Institute of Big Data（深圳大数据研究院工业与应用数学国际中心）
- Shenzhen Loop Area Institute（深圳河套学院）
- Beijing Normal-Hong Kong Baptist University（北京-香港浸会大学联合国际学院）
- Guangzhou Nanfang College（广州南方学院）
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