article

Recursive geometry of the flow complex and topology of the flow complex filtration

Authors:

Joachim Giesen,

Matthias JohnAuthors Info & Claims

Computational Geometry: Theory and Applications, Volume 40, Issue 2

Pages 115 - 137

https://doi.org/10.1016/j.comgeo.2007.05.005

Published: 01 July 2008 Publication History

Abstract

The flow complex is a geometric structure, similar to the Delaunay tessellation, to organize a set of (weighted) points in R^k. Flow shapes are topological spaces corresponding to substructures of the flow complex. The flow complex and flow shapes have found applications in surface reconstruction, shape matching, and molecular modeling. In this article we give an algorithm for computing the flow complex of weighted points in any dimension. The algorithm reflects the recursive structure of the flow complex. On the basis of the algorithm we establish a topological similarity between flow shapes and the nerve of a corresponding ball set, namely homotopy equivalence.

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Cited By

Bauer UEdelsbrunner HCheng SDevillers O(2014)The Morse Theory of Čech and Delaunay FiltrationsProceedings of the thirtieth annual symposium on Computational geometry10.1145/2582112.2582167(484-490)Online publication date: 8-Jun-2014
https://dl.acm.org/doi/10.1145/2582112.2582167
Sadri BSingh K(2014)Flow-complex-based shape reconstruction from 3D curvesACM Transactions on Graphics10.1145/256032833:2(1-15)Online publication date: 8-Apr-2014
https://dl.acm.org/doi/10.1145/2560328
Giesen JKuehne Lda Fonseca GLewiner TPeñaranda LChan TKlein R(2013)A parallel algorithm for computing the flow complexProceedings of the twenty-ninth annual symposium on Computational geometry10.1145/2462356.2462384(57-66)Online publication date: 17-Jun-2013
https://dl.acm.org/doi/10.1145/2462356.2462384
Show More Cited By

Index Terms

Recursive geometry of the flow complex and topology of the flow complex filtration
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Computer vision representations
        Hierarchical representations
  2. Computer graphics
    1. Shape modeling
      1. Point-based models
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image Computational Geometry: Theory and Applications

Computational Geometry: Theory and Applications Volume 40, Issue 2

July, 2008

86 pages

ISSN:0925-7721

Issue’s Table of Contents

Copyright © Elsevier B.V. © 2007.

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 July 2008

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Cited By

Bauer UEdelsbrunner HCheng SDevillers O(2014)The Morse Theory of Čech and Delaunay FiltrationsProceedings of the thirtieth annual symposium on Computational geometry10.1145/2582112.2582167(484-490)Online publication date: 8-Jun-2014
https://dl.acm.org/doi/10.1145/2582112.2582167
Sadri BSingh K(2014)Flow-complex-based shape reconstruction from 3D curvesACM Transactions on Graphics10.1145/256032833:2(1-15)Online publication date: 8-Apr-2014
https://dl.acm.org/doi/10.1145/2560328
Giesen JKuehne Lda Fonseca GLewiner TPeñaranda LChan TKlein R(2013)A parallel algorithm for computing the flow complexProceedings of the twenty-ninth annual symposium on Computational geometry10.1145/2462356.2462384(57-66)Online publication date: 17-Jun-2013
https://dl.acm.org/doi/10.1145/2462356.2462384
Sadri BPolthier KAlexa MKazhdan M(2009)Manifold homotopy via the flow complexProceedings of the Symposium on Geometry Processing10.5555/1735603.1735618(1361-1370)Online publication date: 15-Jul-2009
https://dl.acm.org/doi/10.5555/1735603.1735618
Giesen JMiklos BPauly MWormser CHershberger JFogel E(2009)The scale axis transformProceedings of the twenty-fifth annual symposium on Computational geometry10.1145/1542362.1542388(106-115)Online publication date: 8-Jun-2009
https://dl.acm.org/doi/10.1145/1542362.1542388
Biasotti SDe Floriani LFalcidieno BFrosini PGiorgi DLandi CPapaleo LSpagnuolo M(2008)Describing shapes by geometrical-topological properties of real functionsACM Computing Surveys10.1145/1391729.139173140:4(1-87)Online publication date: 15-Oct-2008
https://dl.acm.org/doi/10.1145/1391729.1391731

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