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Approximating Convex Shapes With Respect to Symmetric Difference Under Homotheties

Authors Juyoung Yon, Sang Won Bae, Siu-Wing Cheng, Otfried Cheong, Bryan T. Wilkinson

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Keywords
  • shape matching
  • convexity
  • symmetric difference
  • homotheties

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Abstract

The symmetric difference is a robust operator for measuring the error of approximating one shape by another.  Given two convex shapes P and C, we study the problem of minimizing the volume of their symmetric difference under all possible scalings and translations of C. We prove that the problem can be solved by convex programming.  We also present a combinatorial algorithm for convex polygons in the plane that runs in O((m+n) log^3(m+n)) expected time, where n and m denote the number of vertices of P and C, respectively.

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Juyoung Yon, Sang Won Bae, Siu-Wing Cheng, Otfried Cheong, and Bryan T. Wilkinson. Approximating Convex Shapes With Respect to Symmetric Difference Under Homotheties. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 63:1-63:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.SoCG.2016.63

Author Details

Juyoung Yon
Sang Won Bae
Siu-Wing Cheng
Otfried Cheong
Bryan T. Wilkinson

References

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