Geometric Matching Algorithms for Two Realistic Terrains

  • Sang Duk Yoon
  • Min-Gyu Kim
  • Wanbin Son
  • Hee-Kap Ahn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9472)

Abstract

We consider a geometric matching of two realistic terrains, each of which is modeled as a piecewise-linear bivariate function. For two realistic terrains f and g where the domain of g is relatively larger than that of f, we seek to find a translated copy \(f'\) of f such that the domain of \(f'\) is a sub-domain of g and the \(L_\infty \) or the \(L_1\) distance of \(f'\) and g restricted to the domain of \(f'\) is minimized. In this paper, we show a tight bound on the number of different combinatorial structures that f and g can have under translation in their projections on the xy-plane. We give a deterministic algorithm and a randomized algorithm that compute an optimal translation of f with respect to g under \(L_\infty \) metric. We also give a deterministic algorithm that computes an optimal translation of f with respect to g under \(L_1\) metric.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Sang Duk Yoon
    • 1
  • Min-Gyu Kim
    • 1
  • Wanbin Son
    • 1
  • Hee-Kap Ahn
    • 1
  1. 1.Department of Computer Science and EngineeringPOSTECHPohangKorea

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