LIPIcs.SoCG.2016.63.pdf
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Approximating Convex Shapes With Respect to Symmetric Difference Under Homotheties
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32nd International Symposium on Computational Geometry (SoCG 2016)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Computational Geometry (SoCG) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2016-06-10
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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
https://doi.org/10.4230/LIPIcs.SoCG.2016.63
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.
Keywords
- shape matching
- convexity
- symmetric difference
- homotheties
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