SIAM Journal on Computing
An Efficiently Computable Metric for Comparing Polygonal Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fundamentals of speech recognition
Fundamentals of speech recognition
Approximating weighted shortest paths on polyhedral surfaces
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Regression analysis of multiple protein structures
RECOMB '98 Proceedings of the second annual international conference on Computational molecular biology
Efficient computation of geodesic shortest paths
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Fast time-series searching with scaling and shifting
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Partial matching of planar polylines under similarity transformations
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for geometric shortest path problems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Deformable Markov model templates for time-series pattern matching
Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining
Pattern matching for sets of segments
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Segment-based approach for subsequence searches in sequence databases
Proceedings of the 2001 ACM symposium on Applied computing
Visual Identification by Signature Tracking
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Online Algorithm for Segmenting Time Series
ICDM '01 Proceedings of the 2001 IEEE International Conference on Data Mining
Scaling up Dynamic Time Warping to Massive Dataset
PKDD '99 Proceedings of the Third European Conference on Principles of Data Mining and Knowledge Discovery
Geometric shape matching and drug design
Geometric shape matching and drug design
Journal of Algorithms
Approximately matching polygonal curves with respect to the Fréchet distance
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
On map-matching vehicle tracking data
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Computing the Fréchet distance between simple polygons in polynomial time
Proceedings of the twenty-second annual symposium on Computational geometry
Dynamics-aware similarity of moving objects trajectories
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
Exact algorithms for partial curve matching via the Fréchet distance
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Shape Matching by Random Sampling
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Assessing the uniqueness and permanence of facial actions for use in biometric applications
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans - Special issue on recent advances in biometrics
Go with the flow: the direction-based fréchet distance of polygonal curves
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
Shape matching by random sampling
Theoretical Computer Science
Of motifs and goals: mining trajectory data
Proceedings of the 20th International Conference on Advances in Geographic Information Systems
Measuring similarity between curves on 2-manifolds via homotopy area
Proceedings of the twenty-ninth annual symposium on Computational geometry
Hyperbolic harmonic brain surface registration with curvature-based landmark matching
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
Communicative modalities for mobile device interaction
International Journal of Human-Computer Studies
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The problem of curve matching appears in many application domains, like time series analysis, shape matching, speech recognition, and signature verification, among others. Curve matching has been studied extensively by computational geometers, and many measures of similarity have been examined, among them being the Fréchet distance (sometimes referred in folklore as the "dog-man" distance).A measure that is very closely related to the Fréchet distance but has never been studied in a geometric context is the Dynamic Time Warping measure (DTW), first used in the context of speech recognition. This measure is ubiquitous across different domains, a surprising fact because notions of similarity usually vary significantly depending on the application. However, this measure suffers from some drawbacks, most importantly the fact that it is defined between sequences of points rather than curves. Thus, the way in which a curve is sampled to yield such a sequence can dramatically affect the quality of the result. Some attempts have been made to generalize the DTW to continuous domains, but the resulting algorithms have exponential complexity.In this paper we propose similarity measures that attempt to capture the "spirit" of dynamic time warping while being defined over continuous domains, and present efficient algorithms for computing them. Our formulation leads to a very interesting connection with finding short paths in a combinatorial manifold defined on the input chains, and in a deeper sense relates to the way light travels in a medium of variable refractivity.