Fundamentals of speech recognition
Fundamentals of speech recognition
Pattern matching for sets of segments
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A unified approach to content-based and fault-tolerant music recognition
IEEE Transactions on Multimedia
Fréchet distance for curves, revisited
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Similarity in (spatial, temporal and) spatio-temporal datasets
Proceedings of the 15th International Conference on Extending Database Technology
Computational Geometry: Theory and Applications
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In this paper we present approximate algorithms for matching two polygonal curves with respect to the Frechet distance. We define a discrete version of the Frechet distance as a distance measure between polygonal curves and show that this discrete version is bounded by the continuous version of the Frechet distance. For the task of matching with respect to the discrete Frechet distance, we develop an algorithm that is based on intersecting certain subsets of the transformation group under consideration. Our algorithm for matching two point sequences of lengths m and n under the group of rigid motions has a time complexity of O(m^2n^2) for matching under the discrete Frechet distance and can be modified for matching subcurves, closed curves and finding longest common subcurves. Group theoretical considerations allow us to eliminate translation components of affine transformations and to consider matching under arbitrary linear algebraic groups.