Approximating the Pathway Axis and the Persistence Diagrams for a Collection of Balls in 3-Space

@article{Yaffe2010ApproximatingTP,
  title={Approximating the Pathway Axis and the Persistence Diagrams for a Collection of Balls in 3-Space},
  author={Eitan Yaffe and Dan Halperin},
  journal={Discrete \& Computational Geometry},
  year={2010},
  volume={44},
  pages={660-685}
}
AbstractGiven a collection ℬ of balls in a three-dimensional space, we wish to explore the cavities, voids, and tunnels in the complement space of ∪ℬ. We introduce the pathway axis of ℬ as a useful subset of the medial axis of the complement of ∪ℬ and prove that it satisfies several desirable geometric properties. We present an algorithm that constructs the pathway graph of ∪ℬ, a piecewise-linear approximation of the pathway axis. At the heart of our approach is an approximation scheme that… 
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