research-article

Voxel cores: efficient, robust, and provably good approximation of 3D medial axes

Authors:

David Letscher,

Tao JuAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 37, Issue 4

Article No.: 44, Pages 1 - 13

https://doi.org/10.1145/3197517.3201396

Published: 30 July 2018 Publication History

Abstract

We present a novel algorithm for computing the medial axes of 3D shapes. We make the observation that the medial axis of a voxel shape can be simply yet faithfully approximated by the interior Voronoi diagram of the boundary vertices, which we call the voxel core. We further show that voxel cores can approximate the medial axes of any smooth shape with homotopy equivalence and geometric convergence. These insights motivate an algorithm that is simple, efficient, numerically stable, and equipped with theoretical guarantees. Compared with existing voxel-based methods, our method inherits their simplicity but is more scalable and can process significantly larger inputs. Compared with sampling-based methods that offer similar theoretical guarantees, our method produces visually comparable results but more robustly captures the topology of the input shape.

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Cited By

Guo MWang BMatusik W(2024)Medial Skeletal Diagram: A Generalized Medial Axis Approach for Compact 3D Shape RepresentationACM Transactions on Graphics10.1145/368796443:6(1-23)Online publication date: 19-Nov-2024
https://doi.org/10.1145/3687964
Wang NHuang HSong SWang BWang WGuo X(2024)MATTopo: Topology-preserving Medial Axis Transform with Restricted Power DiagramACM Transactions on Graphics10.1145/368776343:6(1-16)Online publication date: 19-Nov-2024
https://doi.org/10.1145/3687763
Wang ZDou ZXu RLin CLiu YLong XXin SKomura TYuan XWang W(2024)Coverage Axis++: Efficient Inner Point Selection for 3D Shape SkeletonizationComputer Graphics Forum10.1111/cgf.1514343:5Online publication date: 31-Jul-2024
https://doi.org/10.1111/cgf.15143
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Index Terms

Voxel cores: efficient, robust, and provably good approximation of 3D medial axes
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Shape analysis

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 37, Issue 4

August 2018

1670 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/3197517

Issue’s Table of Contents

Copyright © 2018 ACM.

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Publication History

Published: 30 July 2018

Published in TOG Volume 37, Issue 4

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Cited By

Guo MWang BMatusik W(2024)Medial Skeletal Diagram: A Generalized Medial Axis Approach for Compact 3D Shape RepresentationACM Transactions on Graphics10.1145/368796443:6(1-23)Online publication date: 19-Nov-2024
https://doi.org/10.1145/3687964
Wang NHuang HSong SWang BWang WGuo X(2024)MATTopo: Topology-preserving Medial Axis Transform with Restricted Power DiagramACM Transactions on Graphics10.1145/368776343:6(1-16)Online publication date: 19-Nov-2024
https://doi.org/10.1145/3687763
Wang ZDou ZXu RLin CLiu YLong XXin SKomura TYuan XWang W(2024)Coverage Axis++: Efficient Inner Point Selection for 3D Shape SkeletonizationComputer Graphics Forum10.1111/cgf.1514343:5Online publication date: 31-Jul-2024
https://doi.org/10.1111/cgf.15143
Gaggion NFerrante EPaniagua BVicory J(2024)Fitting Skeletal Models via Graph-Based Learning2024 IEEE International Symposium on Biomedical Imaging (ISBI)10.1109/ISBI56570.2024.10635871(1-4)Online publication date: 27-May-2024
https://doi.org/10.1109/ISBI56570.2024.10635871
Chu YWang W(2023)Out‐of‐core Extraction of Curve Skeletons for Large Volumetric ModelsComputer Graphics Forum10.1111/cgf.1465241:7(1-12)Online publication date: 20-Mar-2023
https://doi.org/10.1111/cgf.14652
Chu YWang WLi L(2023)Robustly Extracting Concise 3D Curve Skeletons by Enhancing the Capture of Prominent FeaturesIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2022.316196229:8(3472-3488)Online publication date: 1-Aug-2023
https://doi.org/10.1109/TVCG.2022.3161962
Gratacós GChakrabarti AJu T(2023)Tree Recovery by Dynamic ProgrammingIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2023.329986845:12(15870-15882)Online publication date: Dec-2023
https://doi.org/10.1109/TPAMI.2023.3299868
Khargonkar NPaniagua BVicory J(2023)Skeletal Point Representations with Geometric Deep Learning2023 IEEE 20th International Symposium on Biomedical Imaging (ISBI)10.1109/ISBI53787.2023.10230505(1-5)Online publication date: 18-Apr-2023
https://doi.org/10.1109/ISBI53787.2023.10230505
Clémot MDigne J(2023)Neural skeleton: Implicit neural representation away from the surfaceComputers & Graphics10.1016/j.cag.2023.06.012114(368-378)Online publication date: Aug-2023
https://doi.org/10.1016/j.cag.2023.06.012
Sharma RKallmann M(2023)Spatially distributed lane planning for navigation in 3D environmentsComputer Animation and Virtual Worlds10.1002/cav.216234:3-4Online publication date: 16-May-2023
https://doi.org/10.1002/cav.2162
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