, Volume 50, Issue 2, pp 175–207

Improved Approximation Bounds for Planar Point Pattern Matching


DOI: 10.1007/s00453-007-9059-9

Cite this article as:
Cho, M. & Mount, D.M. Algorithmica (2008) 50: 175. doi:10.1007/s00453-007-9059-9


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 approximation ratio approaches 3 in the limit. We also investigate the performance of the algorithm by Goodrich et al. as a function of this ratio, and present nearly matching lower bounds on the approximation ratios of both algorithms.


Point pattern matching Approximation algorithms Hausdorff distance 

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of MarylandCollege ParkUSA
  2. 2.Department of Computer Science and Institute for Advanced Computer StudiesUniversity of MarylandCollege ParkUSA

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