Hausdorff Distance under Translation for Points, Disks, and Balls
نویسندگان
چکیده
Let A and B be two sets of balls in Rd, d = 2, 3. We measure similarity between A and B by computing the minimum Hausdorff distance between A+ t and B, where the minimum is taken either over all vectors t ∈ Rd or over the vectors t such that A+t and B do not intersect. These problems arise in measuring similarity between the shapes of two proteins. We propose a number of exact and approximation algorithms for these problems. Since Hausdorff distance is sensitive to out-liers, we also propose efficient approximation algorithms for computing the minimum root-mean-square (rms) Hausdorff distance, under translation, between two point sets.
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