Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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COMPUTING THE HAUSDORFF DISTANCE BETWEEN TWO SETS OF PARAMETRIC CURVES

  • Kim, Ik-Sung (Division of Data Information Korea Maritime University) ;
  • McLean, William (School of Mathematics and Statistics The University of New South Wales)
  • Received : 2011.09.26
  • Published : 2013.10.31
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Abstract

We present an algorithm for computing the Hausdorff distance between two parametric curves in $\mathbb{R}^n$, or more generally between two sets of parametric curves in $\mathbb{R}^n$. During repeated subdivision of the parameter space, we prune subintervals that cannot contain an optimal point. Typically, our algorithm costs O(logM) operations, compared with O(M) operations for a direct, brute-force method, to achieve an accuracy of $O(M^{-1})$.

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References

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