An optimal algorithm for geometrical congruence
Journal of Algorithms
Congruence, similarity and symmetries of geometric objects
Discrete & Computational Geometry - ACM Symposium on Computational Geometry, Waterloo
Approximate matching of polygonal shapes (extended abstract)
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Invariant Descriptors for 3D Object Recognition and Pose
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part I
On enclosing k points by a circle
Information Processing Letters
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
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
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Crossing Numbers and Hard Erdös Problems in Discrete Geometry
Combinatorics, Probability and Computing
Hi-index | 0.00 |
This paper presents a simple algorithm for the partial point set pattern matching in 2D. Given a set P of n points, called sample set, and a query set Q of k points (n ≥ k), the problem is to find a matching of Q with a subset of P under rigid motion. In other words, whether each point in Q is matched with corresponding point in P under translation and/or rotation. The proposed algorithm requires O(n2) space and O(n2logn) preprocessing time, and the worst case query time complexity is O(kαlogn), where α is the maximum number of equidistant pairs of points. For a set of n points, α may be O(n4/3) in the worst case. Experimental results on random point sets and fingerprint databases show that it needs much less time in actual practice. The algorithm is then extended for checking the existence of a matching among two sets of line segments under rigid motion in O(knlogn) time, and locating a query polygon among a set of sample polygons in O(kn) time under rigid motion.