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Open AccessArticle

Adaptive Metrics for Adaptive Samples

by 1,2,† and 1,3,*,†
1
Department of Computer Science and Engineering, University of Connecticut, Storrs, CT 06269, USA
2
Swift Health Systems Inc., Irvine, CA 92617, USA
3
Department of Computer Science, North Carolina State University, Raleigh, NC 27695, USA
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Algorithms 2020, 13(8), 200; https://doi.org/10.3390/a13080200
Received: 1 July 2020 / Revised: 31 July 2020 / Accepted: 3 August 2020 / Published: 18 August 2020
(This article belongs to the Special Issue Topological Data Analysis)
We generalize the local-feature size definition of adaptive sampling used in surface reconstruction to relate it to an alternative metric on Euclidean space. In the new metric, adaptive samples become uniform samples, making it simpler both to give adaptive sampling versions of homological inference results and to prove topological guarantees using the critical points theory of distance functions. This ultimately leads to an algorithm for homology inference from samples whose spacing depends on their distance to a discrete representation of the complement space. View Full-Text
Keywords: surface reconstruction; homology inference; adaptive sampling; topological data analysis surface reconstruction; homology inference; adaptive sampling; topological data analysis
MDPI and ACS Style

Cavanna, N.J.; Sheehy, D.R. Adaptive Metrics for Adaptive Samples. Algorithms 2020, 13, 200.

AMA Style

Cavanna NJ, Sheehy DR. Adaptive Metrics for Adaptive Samples. Algorithms. 2020; 13(8):200.

Chicago/Turabian Style

Cavanna, Nicholas J.; Sheehy, Donald R. 2020. "Adaptive Metrics for Adaptive Samples" Algorithms 13, no. 8: 200.

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