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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.

Keywords

Adjacent Cell Volume Function Translation Vector Deterministic Algorithm Combinatorial Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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