Congruence, similarity and symmetries of geometric objects
Discrete & Computational Geometry - ACM Symposium on Computational Geometry, Waterloo
Computing the minimum Hausdorff distance for point sets under translation
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
The upper envelope of Voronoi surfaces and its applications
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Matching points into noise regions: combinatorial bounds and algorithms
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Approximate decision algorithms for point set congruence
Computational Geometry: Theory and Applications
Geometric pattern matching under Euclidean motion
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
Approximate Geometric Pattern Matching Under Rigid Motions
IEEE Transactions on Pattern Analysis and Machine Intelligence
State of the art in shape matching
Principles of visual information retrieval
Improvements on Geometric Pattern Matching Problems
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
On the parameterized complexity of d-dimensional point set pattern matching
Information Processing Letters
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Given a set A={a"1,...,a"n} of n image points and a set B={b"1,...,b"n} of n model points, the problem is to find a transformation matching (a one-to-one mapping) each point a@?A to some point b@?B such that the length of the longest edge in the matching is minimised (so-called bottleneck distance). The geometric transformations we allow are translation, rotation, reflexion and scaling. In this paper, we give (1+@e)-approximation algorithms for the case when the points are given in R^2, two of which run in O(n^3^.^5@e^4logn) and O(n^2^.^5@e^4lognlogdiam(B)d"o"p"t) time, respectively, where diam(B) is the diameter of B and d"o"p"t is the bottleneck distance in an optimal matching.