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
Object recognition by computer: the role of geometric constraints
Object recognition by computer: the role of geometric constraints
Approximate matching of polygonal shapes (extended abstract)
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Recognizing solid objects by alignment with an image
International Journal of Computer Vision
Polygonal shape recognition using string-matching techniques
Pattern Recognition
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
A survey of image registration techniques
ACM Computing Surveys (CSUR)
On enclosing k points by a circle
Information Processing Letters
Statistical Approaches to Feature-Based Object Recognition
International Journal of Computer Vision
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
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Approximate Geometric Pattern Matching Under Rigid Motions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Parametric search made practical
Proceedings of the eighteenth annual symposium on Computational geometry
Digital Image Processing
Handbook of Fingerprint Recognition
Handbook of Fingerprint Recognition
Model-based image matching using location (pattern, recognition)
Model-based image matching using location (pattern, recognition)
Crossing Numbers and Hard Erdös Problems in Discrete Geometry
Combinatorics, Probability and Computing
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Comparing random starts local search with key feature matching
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
Global Localization of Vehicles Using Local Pole Patterns
Proceedings of the 31st DAGM Symposium on Pattern Recognition
Vehicle localization by matching triangulated point patterns
Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Noisy colored point set matching
Discrete Applied Mathematics
Hi-index | 0.01 |
This paper presents simple and deterministic algorithms for 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. The match may be of two types: exact and approximate. If an exact matching exists, then each point in Q coincides with the corresponding point in P under some translation and/or rotation. For an approximate match, some translation and/or rotation may be allowed such that each point in Q lies in a predefined @e-neighborhood region around some point in P. The proposed algorithm for the exact matching needs O(n^2) space and O(n^2logn) preprocessing time. The existence of a match for a given query set Q can be checked in O(k@alogn) time in the worst-case, where @a is the maximum number of equidistant pairs of point in P. For a set of n points, @a may be O(n^4^/^3) in the worst-case. Some applications of the partial point set pattern matching are then illustrated. Experimental results on random point sets and some fingerprint databases show that, in practice, the computation time is much smaller than the worst-case requirement. The algorithm is then extended for checking the exact match of a set of k line segments in the query set with a k-subset of n line segments in the sample set under rigid motion in O(knlogn) time. Next, a simple version of the approximate matching problem is studied where one point of Q exactly matches with a point of P, and each of the other points of Q lie in the @e-neighborhood of some point of P. The worst-case time and space complexities of the proposed algorithm are O(n^2k^2logn) and O(n), respectively. The proposed algorithms will find many applications to fingerprint matching, image registration, and object recognition.