Publication 21-CNA-016

Boundary estimation from point clouds: algorithms, guarantees and applications

Jeff Calder
Department of Mathematics
University of Minnesota
jcalder@umn.edu

Sangmin Park
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
sangminp@andrew.cmu.edu

Dejan Slepčev
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
slepcev@andrew.cmu.edu

Abstract: 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.

Get the paper in its entirety as  21-CNA-016.pdf

---

«   Back to CNA Publications