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SCG '94 Proceedings of the tenth annual symposium on Computational geometry
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Davenport-Schinzel sequences and their geometric applications
Geometric pattern matching under Euclidean motion
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Geometric matching under noise: combinatorial bounds and algorithms
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Journal of the ACM (JACM)
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SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
A Replacement for Voronoi Diagrams of Near Linear Size
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Locality of Corner Transformation for Multidimensional Spatial Access Methods
Electronic Notes in Theoretical Computer Science (ENTCS)
Interactive Hausdorff distance computation for general polygonal models
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Discrete Applied Mathematics
Polyline approach for approximating Hausdorff distance between planar free-form curves
Computer-Aided Design
An incremental Hausdorff distance calculation algorithm
Proceedings of the VLDB Endowment
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We study the shape matching problem under the Hausdorff distance and its variants. Specifically, we consider two sets A,B of balls in Rd, d=2,3, and wish to find a translation t that minimizes the Hausdorff distance between A+t, the set of all balls in A shifted by t, and B. 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 translates t (as is the standard approach), or consider only translations that keep the balls of A+t disjoint from those of B. We propose several exact and approximation algorithms for these problems. Since the Hausdorff distance is sensitive to outliers, we also propose efficient approximation algorithms for computing the minimum root mean-square (rms) and the minimum summed Hausdorff distance, under translation, between two point sets in Rd. In order to obtain a fast algorithm for the summed Hausdorff distance, we propose a deterministic efficient dynamic data structure for maintaining an e-approximation of the 1-median of a set of points, under insertion and deletion.