Math @ Duke

Publications [#302434] of Paul L Bendich
Papers Published
 with Bendich, P; Edelsbrunner, H; Kerber, M, Computing robustness and persistence for images.,
IEEE Transactions on Visualization and Computer Graphics, vol. 16 no. 6
(2010),
pp. 12511260, ISSN 10772626 [doi]
(last updated on 2017/12/13)
Abstract: We are interested in 3dimensional 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 octtree approximations of the function. In addition, we show that for balanced octtrees, 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 3dimensional images of plant root systems.


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