Computing robustness and persistence for images.

Published

Journal Article

We are interested in 3-dimensional images given as arrays of voxels with intensity values. Extending these values to a continuous function, we study the robustness of homology classes in its level and interlevel sets, that is, the amount of perturbation needed to destroy these classes. The structure of the homology classes and their robustness, over all level and interlevel sets, can be visualized by a triangular diagram of dots obtained by computing the extended persistence of the function. We give a fast hierarchical algorithm using the dual complexes of oct-tree approximations of the function. In addition, we show that for balanced oct-trees, the dual complexes are geometrically realized in R³ and can thus be used to construct level and interlevel sets. We apply these tools to study 3-dimensional images of plant root systems.

Full Text

Duke Authors

Cited Authors

  • Bendich, P; Edelsbrunner, H; Kerber, M

Published Date

  • November 2010

Published In

Volume / Issue

  • 16 / 6

Start / End Page

  • 1251 - 1260

PubMed ID

  • 20975165

Pubmed Central ID

  • 20975165

Electronic International Standard Serial Number (EISSN)

  • 1941-0506

International Standard Serial Number (ISSN)

  • 1077-2626

Digital Object Identifier (DOI)

  • 10.1109/tvcg.2010.139

Language

  • eng