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WADS
2005
Springer

Improved Approximation Bounds for Planar Point Pattern Matching

13 years 9 months ago
Improved Approximation Bounds for Planar Point Pattern Matching
We analyze the performance of simple algorithms for matching two planar point sets under rigid transformations so as to minimize the directed Hausdorff distance between the sets. This is a well studied problem in computational geometry. Goodrich, Mitchell, and Orletsky presented a very simple approximation algorithm for this problem, which computes transformations based on aligning pairs of points. They showed that their algorithm achieves an approximation ratio of 4. We introduce a modification to their algorithm, which is based on aligning midpoints rather than endpoints. This modification has the same simplicity and running time as theirs, and we show that it achieves a better approximation ratio of roughly 3.14. We also analyze the approximation ratio in terms of a instance-specific parameter that is based on the ratio between diameter of the pattern set to the optimum Hausdorff distance. We show that as this ratio increases (as is common in practical applications) the approx...
Minkyoung Cho, David M. Mount
Added 28 Jun 2010
Updated 28 Jun 2010
Type Conference
Year 2005
Where WADS
Authors Minkyoung Cho, David M. Mount
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