Congruence, similarity and symmetries of geometric objects
Discrete & Computational Geometry - ACM Symposium on Computational Geometry, Waterloo
Approximate decision algorithms for point set congruence
Computational Geometry: Theory and Applications
RAPID: randomized pharmacophore identification for drug design
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Approximate congruence in nearly linear time
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Point matching under non-uniform distortions
Discrete Applied Mathematics - Special issue: Computational molecular biology series issue IV
The skip quadtree: a simple dynamic data structure for multidimensional data
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
GIScience '08 Proceedings of the 5th international conference on Geographic Information Science
Example-based synthesis of 3D object arrangements
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
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Let A and B be two colored point sets in R2, with |A| ≤ |B|. We propose a process for determining matches, in terms of the bottleneck distance, between A and subsets of B under color preserving rigid motion, assuming that the position of all colored points in both sets contains a certain amount of "noise". The process consists of two main stages: a lossless filtering algorithm and a matching algorithm. The first algorithm determines a number of candidate zones which are regions that contain a subset S of B such that A may match one or more subsets B′ of S. We use a compressed quadtree to have easy access to the subsets of B related to candidate zones and store geometric information that is used by the lossless filtering algorithm in each quadtree node. The second algorithm solves the colored point set matching problem: we generate all, up to a certain equivalence, possible motions that bring A close to some subset B′ of every S and seek for a matching between sets A and B&prime. To detect these possible matchings we use a bipartite matching algorithm that uses Skip Quadtrees for neighborhood queries. We have implemented the proposed algorithms and report results that show the efficiency of our approach.