2010/11/01 by Paul Bendich, Herbert Edelsbrunner, Michael Kerber · 106 citations
Computer Science · Biochemistry, Genetics and Molecular Biology · #Topological and Geometric Data Analysis #Cell Image Analysis Techniques #Data Visualization and Analytics #Robustness (evolution) #Persistent homology #Computer science #Voxel #Algorithm #Artificial intelligence
paper · doi:10.1109/tvcg.2010.139
published in IEEE Transactions on Visualization and Computer Graphics 16(6), 1251-1260 (Institute of Electrical and Electronics Engineers)
openalex publication_date 2010/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
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.