, Volume 38, Issue 1, pp 59–90 | Cite as

Combinatorial and Experimental Methods for Approximate Point Pattern Matching

  • Martin Gavrilov
  • Piotr Indyk
  • Rajeev  Motwani
  • Suresh Venkatasubramanian


Point pattern matching is an important problem in computational geometry, with applications in areas like computer vision, object recognition, molecular modeling, and image registration. Traditionally, it has been studied in an exact formulation, where the input point sets are given with arbitrary precision. This leads to algorithms that typically have running times of the order of high-degree polynomials, and require robust calculations of intersection points of high-degree surfaces. We study approximate point pattern matching, with the goal of developing algorithms that are more efficient and more practical than exact algorithms. Our work is motivated by the observation that in practice, data sets that form instances of pattern matching problems are noisy, and so approximate formulations are more appropriate. We present new and efficient algorithms for approximate point pattern matching in two and three dimensions, based on approximate combinatorial distance bounds on sets of points, and via the use of methods from combinatorial pattern matching. We also present an average-case analysis and a detailed empirical study of our methods.


Grid Cell Pattern Match Computational Geometry Hausdorff Distance Basic Alignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Department of Computer Science, Stanford University, Stanford, CA 94306-9010USA
  2. 2.AT&T; Labs — Research, 180 Park Avenue, Florham Park, NJ 07932USA

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