Title :
Computing Robustness and Persistence for Images
Author :
Bendich, Paul ; Edelsbrunner, Herbert ; Kerber, Michael
Author_Institution :
IST Austria, Klosterneuburg, Austria
Abstract :
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.
Keywords :
botany; data visualisation; image processing; octrees; 3-dimensional images; balanced oct-trees; data visualization; dual complexes; extended persistence; hierarchical algorithm; homology classes; intensity values; interlevel sets; oct-tree approximations; perturbation; plant root systems; triangular diagram; Approximation algorithms; Approximation methods; Diamond-like carbon; Level set; Piecewise linear approximation; Robustness; Software algorithms; approximations; level sets; oct-trees; persistence diagrams; persistent homology; plant roots; robustness; voxel arrays; Algorithms; Computer Graphics; Imaging, Three-Dimensional; Plant Roots; Software;
Journal_Title :
Visualization and Computer Graphics, IEEE Transactions on
DOI :
10.1109/TVCG.2010.139