Comparing Images Using the Hausdorff Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stability of Persistence Diagrams
Discrete & Computational Geometry
Size functions for 3D shape retrieval
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Analysis of Two-Dimensional Non-Rigid Shapes
International Journal of Computer Vision
Numerical Geometry of Non-Rigid Shapes
Numerical Geometry of Non-Rigid Shapes
Extending Persistence Using Poincaré and Lefschetz Duality
Foundations of Computational Mathematics
Foundations of Computational Mathematics
Alexander duality for functions: the persistent behavior of land and water and shore
Proceedings of the twenty-eighth annual symposium on Computational geometry
A study of monodromy in the computation of multidimensional persistence
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Comparing shapes through multi-scale approximations of the matching distance
Computer Vision and Image Understanding
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Persistent homology provides shapes descriptors called persistence diagrams. We use persistence diagrams to address the problem of shape comparison based on partial similarity. We show that two shapes having a common sub-part in general present a common persistence sub-diagram. Hence, the partial Hausdorff distance between persistence diagrams measures partial similarity between shapes. The approach is supported by experiments on 2D and 3D data sets.