基于点云的边界估计：算法、保证和应用
Boundary Estimation from Point Clouds: Algorithms, Guarantees and Applications
摘要：
我们研究了从域中的样本点识别域的边界。我们引入新的估计的法向量的边界，一个点的距离边界，并测试一个点是否位于边界带。估计可以有效地计算，并且比文献中的估计更准确。我们提供了严格的误差估计的估计。此外，我们使用检测到的边界点来解决点云上的偏微分方程的边值问题。我们证明了点云上拉普拉斯方程和程函方程的误差估计。最后，我们提供了一系列的数值实验，说明我们的边界估计的性能，点云PDE的应用程序，并在图像数据集上的测试。
英文摘要：
We investigate identifying the boundary of a domain from sample points in the domain. We introduce new estimators for the normal vector to the boundary, distance of a point to the boundary, and a test for whether a point lies within a boundary strip. The estimators can be efficiently computed and are more accurate than the ones present in the literature. We provide rigorous error estimates for the estimators. Furthermore we use the detected boundary points to solve boundary-value problems for PDE on point clouds. We prove error estimates for the Laplace and eikonal equations on point clouds. Finally we provide a range of numerical experiments illustrating the performance of our boundary estimators, applications to PDE on point clouds, and tests on image data sets.
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。
