Medial Axis Isoperimetric Profiles
Name
medial_isoperimetric.pdf
Description
Accepted version
Size
1.81 MB
Format
Unknown
Checksum (MD5)
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Author(s)
Zhang, Paul
DeFord, Daryl
Solomon, Justin
Date Issued
2020
Journal
Computer Graphics Forum
Publisher
Wiley
Version
Author's final manuscript
Abstract
© 2020 The Author(s) Computer Graphics Forum © 2020 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. Recently proposed as a stable means of evaluating geometric compactness, the isoperimetric profile of a planar domain measures the minimum perimeter needed to inscribe a shape with prescribed area varying from 0 to the area of the domain. While this profile has proven valuable for evaluating properties of geographic partitions, existing algorithms for its computation rely on aggressive approximations and are still computationally expensive. In this paper, we propose a practical means of approximating the isoperimetric profile and show that for domains satisfying a “thick neck” condition, our approximation is exact. For more general domains, we show that our bound is still exact within a conservative regime and is otherwise an upper bound. Our method is based on a traversal of the medial axis which produces efficient and robust results. We compare our technique with the state-of-the-art approximation to the isoperimetric profile on a variety of domains and show significantly tighter bounds than were previously achievable.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1111/CGF.14064
