Computing the Hausdorff distance between two sets of parametric curves
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We present an algorithm for computing the Hausdorff distancebetween two parametric curves in Rn, or more generally betweentwo sets of parametric curves in Rn. During repeated subdivision of theparameter space, we prune subintervals that cannot contain an optimalpoint. Typically, our algorithm costs O(logM) operations, compared withO(M) operations for a direct, brute-force method, to achieve an accuracyof O(M−1).
Abstract
We present an algorithm for computing the Hausdorff distancebetween two parametric curves in Rn, or more generally betweentwo sets of parametric curves in Rn. During repeated subdivision of theparameter space, we prune subintervals that cannot contain an optimalpoint. Typically, our algorithm costs O(logM) operations, compared withO(M) operations for a direct, brute-force method, to achieve an accuracyof O(M−1).
참고문헌 (6)
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- E. Belogay, "Calculating the Hausdorff distance between curves", Inform. Process. Lett, 64(1), pp.17~22 (1997)
- M. Bouts, "Comparing images using the Hausdorff distance", ~ (2006)
- R. P. Brent, "Algorithms for Minimization without Derivatives" (1973), Prentice–Hall
- G. Rote, "Computing the minimum Hausdorff distance between two point sets on a line under translation", Inform. Process. Lett, 38(3), pp.123~127 (1991)
- L. Scharf, "Computing the Hausdorff distance between sets of curves", pp.2003