Congruence, similarity and symmetries of geometric objects
Discrete & Computational Geometry - ACM Symposium on Computational Geometry, Waterloo
Minimax geometric fitting of two corresponding sets of points
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Approximate decision algorithms for point set congruence
Computational Geometry: Theory and Applications
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Combinatorial and experimental results for randomized point matching algorithms
Proceedings of the twelfth annual symposium on Computational geometry
Improvements on bottleneck matching and related problems using geometry
Proceedings of the twelfth annual symposium on Computational geometry
Geometric pattern matching under Euclidean motion
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
On determining the congruence of point sets in d dimensions
Computational Geometry: Theory and Applications
Approximate Geometric Pattern Matching Under Rigid Motions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometric pattern matching: a performance study
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Geometric matching under noise: combinatorial bounds and algorithms
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Handbook of Fingerprint Recognition
Handbook of Fingerprint Recognition
Point set pattern matching in d-dimensions
Point set pattern matching in d-dimensions
On the parameterized complexity of d-dimensional point set pattern matching
Information Processing Letters
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This paper deals with the problem of approximate point set pattern matching in 2D. Given a set P of n points, called sample set, and a query setQ of k points (k≤n), the problem is to find a match of Q with a subset of P under rigid motion (rotation and/or translation) transformation such that each point in Q lies in the ε-neighborhood of a point in P. The ε-neighborhood region of a point pi∈P is an axis-parallel square having each side of length ε and pi at its centroid. We assume that the point set is well-seperated in the sense that for a given ε0, each pair of points p, p′∈P satisfy at least one of the following two conditions (i) |x(p)−x(p′)|≥ε, and (ii) |y(p)−y(p′)|≥3ε, and we propose an algorithm for the approximate matching that can find a match (if it exists) under rigid motion in O(n2k2(klogk+logn)) time. If only translation is considered then the existence of a match can be tested in O(nk2 logn) time. The salient feature of our algorithm for the rigid motion and translation is that it avoids the use of intersection of high degree curves.