Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Robot vision
Congruence, similarity and symmetries of geometric objects
Discrete & Computational Geometry - ACM Symposium on Computational Geometry, Waterloo
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
An efficiently computable metric for comparing polygonal shapes
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Voronoi diagrams based on convex distance functions
SCG '85 Proceedings of the first annual symposium on Computational geometry
An Efficiently Computable Metric for Comparing Polygonal Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Approximate matching of polygonal shapes (extended abstract)
SCG '91 Proceedings of the seventh 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
Applications of parametric searching in geometric optimization
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Approximate decision algorithms for point set congruence
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Matching shapes with a reference point
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Improvements on bottleneck matching and related problems using geometry
Proceedings of the twelfth annual symposium on Computational geometry
Sampling of Images for Efficient Model-Based Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Efficient and small representation of line arrangements with applications
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Phase-independent rhythmic analysis of genome-wide expression patterns
Proceedings of the sixth annual international conference on Computational biology
Comparing Images Using the Hausdorff Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
Similarity Clustering of Dimensions for an Enhanced Visualization of Multidimensional Data
INFOVIS '98 Proceedings of the 1998 IEEE Symposium on Information Visualization
Content based retrieval of VRML objects: an iterative and interactive approach
Proceedings of the sixth Eurographics workshop on Multimedia 2001
A Maximum Entropy Algorithm for Rhythmic Analysis of Genome-Wide Expression Patterns
CSB '02 Proceedings of the IEEE Computer Society Conference on Bioinformatics
Coarse grained gather and scatter operations with applications
Journal of Parallel and Distributed Computing
Information Processing Letters
NURBS curve shape modification and fairness evaluation for computer aided aesthetic design
ISCGAV'07 Proceedings of the 7th WSEAS International Conference on Signal Processing, Computational Geometry & Artificial Vision
Efficient shape recognition method using novel metric for complex polygonal shapes
MobiMedia '06 Proceedings of the 2nd international conference on Mobile multimedia communications
Approximate input sensitive algorithms for point pattern matching
Pattern Recognition
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Approximate one-to-one point pattern matching
Journal of Discrete Algorithms
Non-crossing matchings of points with geometric objects
Computational Geometry: Theory and Applications
A memetic algorithm for efficient solution of 2D and 3D shape matching problems
AI'12 Proceedings of the 25th Australasian joint conference on Advances in Artificial Intelligence
Fast and exact network trajectory similarity computation: a case-study on bicycle corridor planning
Proceedings of the 2nd ACM SIGKDD International Workshop on Urban Computing
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We consider the problem of computing a translation that minimizes the Hausdorff distance between two sets of points. For points in @@@@1 in the worst case there are ⊖(mn) translations at which the Hausdorff distance is a local minimum, where m is the number of points in one set and n is the number in the other. For points in @@@@2 there are ⊖(mn(m + n)) such local minima. We show how to compute the minimal Hausdorff distance in time &Ogr;(mn log mn) for points in @@@@1 and in time &Ogr;(m2n2&agr;(mn)) for points in @@@@2. The results for the one-dimensional case are applied to the problem of comparing polygons under general affine transformations, where we extend the recent results of Arkin et al on polygon resemblance under rigid body motion. The two-dimensional case is closely related to the problem of finding an approximate congruence between two points sets under translation in the plane, as considered by Alt et al.