Computing robustness and persistence for images Journal Article


Author(s): Bendich, Paul; Edelsbrunner, Herbert; Kerber, Michael
Article Title: Computing robustness and persistence for images
Affiliation IST Austria
Abstract: We are interested in 3-dimensional images given as arrays of voxels with intensity values. Extending these values to acontinuous function, we study the robustness of homology classes in its level and interlevel sets, that is, the amount of perturbationneeded to destroy these classes. The structure of the homology classes and their robustness, over all level and interlevel sets, can bevisualized by a triangular diagram of dots obtained by computing the extended persistence of the function. We give a fast hierarchicalalgorithm using the dual complexes of oct-tree approximations of the function. In addition, we show that for balanced oct-trees, thedual complexes are geometrically realized in $R^3$ and can thus be used to construct level and interlevel sets. We apply these tools tostudy 3-dimensional images of plant root systems.
Journal Title: IEEE Transactions of Visualization and Computer Graphics
Volume: 16
Issue 6
Date Range: October 24 - 29, 2010
Conference Location: Salt Lake City, Utah, USA
ISSN: 1077-2626
Publisher: IEEE  
Date Published: 2010-11-01
Start Page: 1251
End Page: 1260
Sponsor: This research is partially supported by the National Science Foundation (NSF) under grant DBI-0820624 and the Defense Advanced Research Projects Agency (DARPA) under grants HR0011-05-0057 and HR0011-09-0065.
URL:
DOI: 10.1109/TVCG.2010.139
Open access: yes (repository)
IST Austria Authors
  1. Michael Kerber
    21 Kerber
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