Persistence barcodes for shapes

@article{Carlsson2004PersistenceBF,
  title={Persistence barcodes for shapes},
  author={Gunnar E. Carlsson and Afra Zomorodian and Anne D. Collins and Leonidas J. Guibas},
  journal={Int. J. Shape Model.},
  year={2004},
  volume={11},
  pages={149-188}
}
In this paper, we initiate a study of shape description and classification via the application of persistent homology to two tangential constructions on geometric objects. Our techniques combine the differentiating power of geometry with the classifying power of topology. The homology of our first construction, the tangent complex, can distinguish between topologically identical shapes with different "sharp" features, such as corners. To capture "soft" curvature-dependent features, we define a… 
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