Computing Robustness and Persistence for Images

@article{Bendich2010ComputingRA,
  title={Computing Robustness and Persistence for Images},
  author={Paul Bendich and H. Edelsbrunner and M. Kerber},
  journal={IEEE Transactions on Visualization and Computer Graphics},
  year={2010},
  volume={16},
  pages={1251-1260}
}
  • Paul Bendich, H. Edelsbrunner, M. Kerber
  • Published 2010
  • Computer Science, Medicine
  • IEEE Transactions on Visualization and Computer Graphics
  • 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… CONTINUE READING
    70 Citations
    Memory-Efficient Computation of Persistent Homology for 3D Images Using Discrete Morse Theory
    • 20
    • PDF
    Persistent Homology in Image Processing
    • 9
    Stable Morse Decompositions for Piecewise Constant Vector Fields on Surfaces
    • A. Szymczak
    • Mathematics, Computer Science
    • Comput. Graph. Forum
    • 2011
    • 17
    • PDF
    Persistent Homology – State of the art and challenges
    • 5
    • PDF
    Persistent Homology Computation with a Twist
    • 87
    • PDF
    Objective-oriented Persistent Homology
    • 3
    • PDF
    Approximation algorithms for Vietoris-Rips and Čech filtrations
    • PDF
    A Study of Monodromy in the Computation of Multidimensional Persistence
    • 6
    • PDF
    A point calculus for interlevel set homology
    • 6
    • PDF

    References

    SHOWING 1-10 OF 31 REFERENCES
    Topology Based Selection and Curation of Level Sets
    • 21
    • PDF
    Homology and Robustness of Level and Interlevel Sets
    • 38
    • PDF
    Persistence Diagrams of Cortical Surface Data
    • 105
    • PDF
    On the Local Behavior of Spaces of Natural Images
    • 421
    • PDF
    Contour trees and small seed sets for isosurface traversal
    • 369
    • PDF
    A topological approach to simplification of three-dimensional scalar functions
    • 78
    • PDF
    Provably good mesh generation
    • 304
    • PDF
    A survey of the marching cubes algorithm
    • 429
    • PDF
    Quantifying Transversality by Measuring the Robustness of Intersections
    • 32
    • PDF