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TVCG
2010

Computing Robustness and Persistence for Images

11 years 6 months ago
Computing Robustness and Persistence for Images
—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.
Paul Bendich, Herbert Edelsbrunner, Michael Kerber
Added 31 Jan 2011
Updated 31 Jan 2011
Type Journal
Year 2010
Where TVCG
Authors Paul Bendich, Herbert Edelsbrunner, Michael Kerber
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