Geometric pattern matching for point sets in the plane under similarity transformations
Information Processing Letters
Approximate input sensitive algorithms for point pattern matching
Pattern Recognition
Recognition of binding patterns common to a set of protein structures
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
An efficient approximation algorithm for point pattern matching under noise
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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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.