article

Comparing shapes through multi-scale approximations of the matching distance

Authors:

Barbara Di Fabio,

Grzegorz Jabłoński,

Filippo MedriAuthors Info & Claims

Computer Vision and Image Understanding, Volume 121

Pages 43 - 56

https://doi.org/10.1016/j.cviu.2013.11.004

Published: 01 April 2014 Publication History

Abstract

Two of the main ingredients of topological persistence for shape comparison are persistence diagrams and the matching distance. Persistence diagrams are signatures capturing meaningful properties of shapes, while the matching distance can be used to stably compare them. From the application viewpoint, one drawback of these tools is the computational cost for evaluating the matching distance. In this paper we introduce a new framework for the matching distance estimation: It preserves the reliability of the entire approach in comparing shapes, extremely reducing the computational cost. Theoretical results are supported by experiments on 3D-models.

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Cited By

Kim WMémoli F(2020)Spatiotemporal Persistent Homology for Dynamic Metric SpacesDiscrete & Computational Geometry10.1007/s00454-019-00168-w66:3(831-875)Online publication date: 2-Feb-2020
https://dl.acm.org/doi/10.1007/s00454-019-00168-w
Iuricich FScaramuccia SLandi CDe Floriani LChen WWeiskopf D(2016)A discrete morse-based approach to multivariate data analysisSIGGRAPH ASIA 2016 Symposium on Visualization10.1145/3002151.3002166(1-8)Online publication date: 28-Nov-2016
https://dl.acm.org/doi/10.1145/3002151.3002166
Jimenez MMedrano BMonaghan DO'Connor N(2016)Designing a Topological Algorithm for 3D Activity RecognitionProceedings of the 6th International Workshop on Computational Topology in Image Context - Volume 966710.1007/978-3-319-39441-1_18(193-203)Online publication date: 15-Jun-2016
https://dl.acm.org/doi/10.1007/978-3-319-39441-1_18
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Published In

cover image Computer Vision and Image Understanding

Computer Vision and Image Understanding Volume 121, Issue

April, 2014

119 pages

ISSN:1077-3142

Issue’s Table of Contents

Copyright © Elsevier Inc. © 2013.

Publisher

Elsevier Science Inc.

United States

Publication History

Published: 01 April 2014

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Cited By

Kim WMémoli F(2020)Spatiotemporal Persistent Homology for Dynamic Metric SpacesDiscrete & Computational Geometry10.1007/s00454-019-00168-w66:3(831-875)Online publication date: 2-Feb-2020
https://dl.acm.org/doi/10.1007/s00454-019-00168-w
Iuricich FScaramuccia SLandi CDe Floriani LChen WWeiskopf D(2016)A discrete morse-based approach to multivariate data analysisSIGGRAPH ASIA 2016 Symposium on Visualization10.1145/3002151.3002166(1-8)Online publication date: 28-Nov-2016
https://dl.acm.org/doi/10.1145/3002151.3002166
Jimenez MMedrano BMonaghan DO'Connor N(2016)Designing a Topological Algorithm for 3D Activity RecognitionProceedings of the 6th International Workshop on Computational Topology in Image Context - Volume 966710.1007/978-3-319-39441-1_18(193-203)Online publication date: 15-Jun-2016
https://dl.acm.org/doi/10.1007/978-3-319-39441-1_18
Carrière MOudot SOvsjanikov MAugsdörfer UWallner J(2015)Stable topological signatures for points on 3D shapesProceedings of the Eurographics Symposium on Geometry Processing10.1111/cgf.12692(1-12)Online publication date: 6-Jul-2015
https://dl.acm.org/doi/10.1111/cgf.12692
Rieck BLeitte H(2015)Persistent Homology for the Evaluation of Dimensionality Reduction SchemesComputer Graphics Forum10.1111/cgf.1265534:3(431-440)Online publication date: 1-Jun-2015
https://dl.acm.org/doi/10.1111/cgf.12655

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