|Author||Agarwal, Pankaj K. ♦ Har-Peled, Sariel ♦ Sharir, Micha ♦ Wang, Yusu|
|Subject Domain (in DDC)||Computer science, information & general works ♦ Data processing & computer science|
|Subject Keyword||Fast Algorithm ♦ Several Variant ♦ Standard Approach ♦ Efficient Approximation Algorithm ♦ Point Set ♦ Robust Variant ♦ Possible Translation ♦ Standard Setting ♦ Second Part ♦ Minimum Rms ♦ Hausdorff Distance ♦ Summed Hausdorff Distance ♦ First Part ♦ Deterministic Efficient Dynamic Data Structure ♦ Approximation Algorithm|
|Description||In Proc. 19th Annu. ACM Sympos. Comput. Geom
We study the shape matching problem under the Hausdorff distance and its variants. In the first part of the paper, we consider two sets of balls in, , and wish to find a translation that minimizes the Hausdorff distance between, the set of all balls in shifted by, and. We consider several variants of this problem. First, we extend the notion of Hausdorff distance from sets of points to sets of balls, so that each ball has to be matched with the nearest ball in the other set. We also consider the problem in the standard setting, by computing the Hausdorff distance between the unions of the two sets (as point sets). Second, we consider either all possible translations (as is the standard approach), or consider only translations that keep the balls of disjoint from those of. We propose several exact and approximation algorithms for these problems. In the second part of the paper, we note that the Hausdorff distance is sensitive to outliers, and thus consider two more robust variants—the root-meansquare (rms) and the summed Hausdorff distance. We propose efficient approximation algorithms for computing the minimum rms and the minimum summed Hausdorff distances under translation, between two point sets in. In order to obtain a fast algorithm for the summed Hausdorff distance, we propose a deterministic efficient dynamic data structure for maintaining an-approximation of the-median of a set of points in, under insertions and deletions. 1
|Educational Role||Student ♦ Teacher|
|Age Range||above 22 year|
|Education Level||UG and PG ♦ Career/Technical Study|
|Learning Resource Type||Article|
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