Article

Homotopy-preserving medial axis simplification

Authors:

Dinesh ManochaAuthors Info & Claims

SPM '05: Proceedings of the 2005 ACM symposium on Solid and physical modeling

Pages 39 - 50

https://doi.org/10.1145/1060244.1060250

Published: 13 June 2005 Publication History

Abstract

We present a novel algorithm to compute a simplified medial axis of a polyhedron. Our simplification algorithm tends to remove unstable features of Blum's medial axis. Moreover, our algorithm preserves the topological structure of the original medial axis and ensures that the simplified medial axis has the same homotopy type as Blum's medial axis. We use the separation angle formed by connecting a point on the medial axis to closest points on the boundary as a measure of the stability of the medial axis at the point. The medial axis is decomposed into its parts that are the sheets, seams and junctions. We present a stability measure of each part of the medial axis based on separation angles and examine the relation between the stability measures of adjacent parts. Our simplification algorithm uses iterative pruning of the parts based on efficient local tests. We have applied the algorithm to compute a simplified medial axis of complex models with tens of thousands of triangles and complex topologies.

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Cited By

Huang QKraemer PThery SBechmann D(2024)Dynamic Skeletonization via Variational Medial Axis SamplingSIGGRAPH Asia 2024 Conference Papers10.1145/3680528.3687678(1-11)Online publication date: 3-Dec-2024
https://dl.acm.org/doi/10.1145/3680528.3687678
Li BYe YYao JYang YXie WGe M(2024)A detail-preserving method for medial mesh computation in triangular meshesGraphical Models10.1016/j.gmod.2024.101236136(101236)Online publication date: Dec-2024
https://doi.org/10.1016/j.gmod.2024.101236
Zhang SXu GWu HGu RQi LPang Y(2024)Medial hex-meshing: high-quality all-hexahedral mesh generation based on medial meshEngineering with Computers10.1007/s00366-023-01925-540:4(2537-2557)Online publication date: 10-Jan-2024
https://doi.org/10.1007/s00366-023-01925-5
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Homotopy-preserving medial axis simplification
1. Computing methodologies
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2. Theory of computation
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cover image ACM Conferences

SPM '05: Proceedings of the 2005 ACM symposium on Solid and physical modeling

June 2005

287 pages

ISBN:1595930159

DOI:10.1145/1060244

Program Chairs:
Leif Kobbelt
RWTH Aachen University, Germany
,
Vadim Shapiro
University of Wisconsin--Madison, USA

Copyright © 2005 ACM.

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Published: 13 June 2005

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SPM05: 2005 ACM Symposium on Solid and Physical Modeling

June 13 - 15, 2005

Massachusetts, Cambridge

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Cited By

Huang QKraemer PThery SBechmann D(2024)Dynamic Skeletonization via Variational Medial Axis SamplingSIGGRAPH Asia 2024 Conference Papers10.1145/3680528.3687678(1-11)Online publication date: 3-Dec-2024
https://dl.acm.org/doi/10.1145/3680528.3687678
Li BYe YYao JYang YXie WGe M(2024)A detail-preserving method for medial mesh computation in triangular meshesGraphical Models10.1016/j.gmod.2024.101236136(101236)Online publication date: Dec-2024
https://doi.org/10.1016/j.gmod.2024.101236
Zhang SXu GWu HGu RQi LPang Y(2024)Medial hex-meshing: high-quality all-hexahedral mesh generation based on medial meshEngineering with Computers10.1007/s00366-023-01925-540:4(2537-2557)Online publication date: 10-Jan-2024
https://doi.org/10.1007/s00366-023-01925-5
Rong PJu T(2023)Variational Pruning of Medial Axes of Planar ShapesComputer Graphics Forum10.1111/cgf.1490242:5Online publication date: 10-Aug-2023
https://doi.org/10.1111/cgf.14902
Selbach LKowalski TGerwert KBuchin MMosig A(2021)Shape decomposition algorithms for laser capture microdissectionAlgorithms for Molecular Biology10.1186/s13015-021-00193-616:1Online publication date: 8-Jul-2021
https://doi.org/10.1186/s13015-021-00193-6
Lee YBaek JKim YPark F(2021)IMAT: The Iterative Medial Axis TransformComputer Graphics Forum10.1111/cgf.1426640:6(162-181)Online publication date: 8-Apr-2021
https://doi.org/10.1111/cgf.14266
Bai XYe LZhu JZhu LKomura T(2020)Skeleton Filter: A Self-Symmetric Filter for Skeletonization in Noisy Text ImagesIEEE Transactions on Image Processing10.1109/TIP.2019.294456029(1815-1826)Online publication date: 1-Jan-2020
https://dl.acm.org/doi/10.1109/TIP.2019.2944560
Rasche C(2020)Rapid region analysis for classificationIET Image Processing10.1049/iet-ipr.2019.027314:10(2110-2120)Online publication date: Jul-2020
https://doi.org/10.1049/iet-ipr.2019.0273
Chu YHou FWang WLi L(2019)Topology Preserving Simplification of Medial Axes in 3D ModelsComputer Graphics Forum10.1111/cgf.1386438:7(607-616)Online publication date: 14-Nov-2019
https://doi.org/10.1111/cgf.13864
Durix BChambon SLeonard KMari JMorin G(2019)The Propagated Skeleton: A Robust Detail-Preserving ApproachDiscrete Geometry for Computer Imagery10.1007/978-3-030-14085-4_27(343-354)Online publication date: 23-Feb-2019
https://doi.org/10.1007/978-3-030-14085-4_27
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