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Efficient Hausdorff Distance Computation for Planar Curves  

Kim, Yong-Joon (서울대학교 전기컴퓨터공학부)
Oh, Young-Taek (서울대학교 전기컴퓨터공학부)
Kim, Myung-Soo (서울대학교 컴퓨터공학부)
Publication Information
Korean Journal of Computational Design and Engineering / v.15, no.2, 2010 , pp. 115-123 More about this Journal
Abstract
We present an efficient algorithm for computing the Hausdorff distance between two planar curves. The algorithm is based on an efficient trimming technique that eliminates the curve domains that make no contribution to the final Hausdorff distance. The input curves are first approximated with biarcs within a given error bound in a pre-processing step. Using the biarc approximation, the distance map of an input curve is then approximated and stored into the graphics hardware depth-buffer by rendering the distance maps (represented as circular cones) of the biarcs. We repeat the same procedure for the other input curve. By sampling points on each input curve and reading the distance from the other curve (stored in the hardware depth-buffer), we can easily estimate a lower bound of the Hausdorff distance. Based on the lower bound, the algorithm eliminates redundant curve segments where the exact Hausdorff distance can never be obtained. Finally, we employ a multivariate equation solver to compute the Hausdorff distance efficiently using the remaining curve segments only.
Keywords
Hausdorff distance; biarc approximation; distance map; depth buffer; trimming; solution of multivariate equation;
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