Categorified Reeb Graphs

@article{Silva2016CategorifiedRG,
  title={Categorified Reeb Graphs},
  author={V. D. Silva and E. Munch and Amit Patel},
  journal={Discrete & Computational Geometry},
  year={2016},
  volume={55},
  pages={854-906}
}
  • V. D. Silva, E. Munch, Amit Patel
  • Published 2016
  • Computer Science, Mathematics
  • Discrete & Computational Geometry
  • The Reeb graph is a construction which originated in Morse theory to study a real-valued function defined on a topological space. More recently, it has been used in various applications to study noisy data which creates a desire to define a measure of similarity between these structures. Here, we exploit the fact that the category of Reeb graphs is equivalent to the category of a particular class of cosheaf. Using this equivalency, we can define an ‘interleaving’ distance between Reeb graphs… CONTINUE READING
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