Continuation of Point Clouds via Persistence Diagrams

@article{Gameiro2016ContinuationOP,
  title={Continuation of Point Clouds via Persistence Diagrams},
  author={Marcio Gameiro and Yasuaki Hiraoka and Ippei Obayashi},
  journal={ArXiv},
  year={2016},
  volume={abs/1506.03147}
}
  • Marcio Gameiro, Yasuaki Hiraoka, Ippei Obayashi
  • Published in ArXiv 2016
  • Mathematics, Computer Science
  • Abstract In this paper, we present a mathematical and algorithmic framework for the continuation of point clouds by persistence diagrams. A key property used in the method is that the persistence map, which assigns a persistence diagram to a point cloud, is differentiable. This allows us to apply the Newton–Raphson continuation method in this setting. Given an original point cloud P , its persistence diagram D , and a target persistence diagram D ′ , we gradually move from D to D ′ , by… CONTINUE READING

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