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On Variational and PDE-Based Methods for Accurate Distance Function Estimation

Abstract

A new variational problem for accurate approximation of the distance from the boundary of a domain is proposed and studied. It is shown that the problem can be efficiently solved by the alternating direction method of multipliers. Links between this problem and \(p\)-Laplacian diffusion are established and studied. Advantages of the proposed distance function estimation method are demonstrated by numerical experiments.

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ACKNOWLEDGMENTS

The Gargoyle mesh model is courtesy of AIM@SHAPE and the Lucy mesh model is courtesy of the Stanford Graphics Laboratory.

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Fayolle, PA., Belyaev, A.G. On Variational and PDE-Based Methods for Accurate Distance Function Estimation. Comput. Math. and Math. Phys. 59, 2009–2016 (2019). https://doi.org/10.1134/S0965542519120066

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  • DOI: https://doi.org/10.1134/S0965542519120066

Keywords:

  • distance function
  • p-Laplacian
  • variational methods