# 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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