mlsanityData to 7 Oct 2026

Boundary Estimation from Point Clouds: Algorithms, Guarantees and Applications

arXiv 2111.03217 ↗First posted 5 Nov 2021math.NA cs.NA math.STcited by 4

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 14 of its 80 references that are in the map. First posted on arXiv 5 Nov 2021.

Builds on

14 of 80 references.

References · 14

  1. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,283
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  8. 2015Density Level Sets: Asymptotics, Inference, and Visualizationcited by 11
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  11. 2018The limit shape of convex hull peelingcited by 6
  12. 2013A Hamilton-Jacobi equation for the continuum limit of non-dominated sortingcited by 3
2 more
  1. 2020A continuum limit for the PageRank algorithmcited by 3
  2. 2020Spectral Clustering Revisited: Information Hidden in the Fiedler Vectorcited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 0; 2024: 1; 2025: 0; 2026: 1.

4 papers.

  1. 2022Hamilton-Jacobi equations on graphs with applications to semi-supervised learning and data depthcited by 7
  2. 2022Eikonal depth: an optimal control approach to statistical depthscited by 1
  3. 2024Boundary Detection Algorithm Inspired by Locally Linear Embeddingcited by 0
  4. 2026Gaussian Linear Functional Manifold Method for Massive Point Cloud Datacited by 0