Boundary Estimation from Point Clouds: Algorithms, Guarantees and Applications

Jeff Calder, Sangmin Park, Dejan Slepčev

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish (US)
Article number56
JournalJournal of Scientific Computing
Issue number2
StatePublished - Aug 2022

Bibliographical note

Funding Information:
JC was supported by NSF grant DMS 1944925, the Alfred P. Sloan Foundation, and a McKnight Presidential Fellowship. SP and DS were supported by NSF grant DMS 1814991.

Funding Information:
The authors would like to thank Eddie Aamari for valuable comments, and the anonymous referees for their helpful suggestions. The authors are also grateful to CNA of CMU, IMA of Univ. of Minnesota, and Simons Institute at UC Berkeley for hospitality.

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • Boundary detection
  • Distance to boundary
  • Meshfree methods
  • PDE on point clouds


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