Gromov‐Hausdorff Stable Signatures for Shapes using Persistence

  title={Gromov‐Hausdorff Stable Signatures for Shapes using Persistence},
  author={F. Chazal and D. Cohen-Steiner and L. Guibas and F. M{\'e}moli and S. Oudot},
  journal={Computer Graphics Forum},
  • F. Chazal, D. Cohen-Steiner, +2 authors S. Oudot
  • Published 2009
  • Mathematics, Computer Science
  • Computer Graphics Forum
  • We introduce a family of signatures for finite metric spaces, possibly endowed with real valued functions, based on the persistence diagrams of suitable filtrations built on top of these spaces. We prove the stability of our signatures under Gromov‐Hausdorff perturbations of the spaces. We also extend these results to metric spaces equipped with measures. Our signatures are well‐suited for the study of unstructured point cloud data, which we illustrate through an application in shape… CONTINUE READING
    187 Citations

    Topics from this paper

    Persistence stability for geometric complexes
    • 155
    • PDF
    A Distance Between Filtered Spaces Via Tripods
    • 10
    • PDF
    Stable Signatures for Dynamic Metric Spaces via Zigzag Persistent Homology
    • 9
    The Persistence Space in Multidimensional Persistent Homology
    • 23
    The ultrametric Gromov-Wasserstein distance
    • 1
    • PDF
    A Primer on Persistent Homology of Finite Metric Spaces
    • 2
    • PDF
    Persistent Homotopy Groups of Metric Spaces
    • PDF
    Some Properties of Gromov–Hausdorff Distances
    • F. Mémoli
    • Mathematics, Computer Science
    • Discret. Comput. Geom.
    • 2012
    • 35
    • PDF


    Stability of persistence diagrams
    • 819
    • PDF
    Proximity of persistence modules and their diagrams
    • 333
    • PDF
    On the use of Gromov-Hausdorff Distances for Shape Comparison
    • 147
    • PDF
    Persistence barcodes for shapes
    • 158
    • PDF
    Topological Persistence and Simplification
    • 941
    • PDF
    A Gromov-Hausdorff Framework with Diffusion Geometry for Topologically-Robust Non-rigid Shape Matching
    • 284
    • PDF
    Gromov-Hausdorff distances in Euclidean spaces
    • F. Mémoli
    • Mathematics, Computer Science
    • 2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops
    • 2008
    • 66
    • PDF
    Stability in multidimensional Size Theory
    • 7
    • PDF