Artificial Intelligence
Qualitative physics: past present and future
Readings in qualitative reasoning about physical systems
A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Similarity Measure Based on Correspondence of Visual Parts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Using Orientation Information for Qualitative Spatial Reasoning
Proceedings of the International Conference GIS - From Space to Territory: Theories and Methods of Spatio-Temporal Reasoning on Theories and Methods of Spatio-Temporal Reasoning in Geographic Space
Representing moving objects in computer-based expert systems: the overtake event example
Expert Systems with Applications: An International Journal
OTM'05 Proceedings of the 2005 OTM Confederated international conference on On the Move to Meaningful Internet Systems
Conceptual neighbourhood diagrams for representing moving objects
ER'05 Proceedings of the 24th international conference on Perspectives in Conceptual Modeling
Towards a geometric interpretation of double-cross matrix-based similarity of polylines
Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems
A Similarity Calculus for Comparing Qualitative Shape Descriptions
Proceedings of the 2009 conference on Artificial Intelligence Research and Development: Proceedings of the 12th International Conference of the Catalan Association for Artificial Intelligence
A Similarity Calculus for Comparing Qualitative Shape Descriptions
Proceedings of the 2009 conference on Artificial Intelligence Research and Development: Proceedings of the 12th International Conference of the Catalan Association for Artificial Intelligence
A Pragmatic Approach for Qualitative Shape and Qualitative Colour Similarity Matching
Proceedings of the 2010 conference on Artificial Intelligence Research and Development: Proceedings of the 13th International Conference of the Catalan Association for Artificial Intelligence
Polyline averaging using distance surfaces: A spatial hurricane climatology
Computers & Geosciences
Journal of Visual Communication and Image Representation
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We present an algorithm for polyline (and polygon) similarity testing that is based on the double-cross formalism. To determine the degree of similarity between two polylines, the algorithm first computes their generalized polygons, that consist of almost equally long line segments and that approximate the length of the given polylines within an $varepsilon$-error margin. Next, the algorithm determines the double-cross matrices of the generalized polylines and the difference between these matrices is used as a measure of dissimilarity between the given polylines. We prove termination of our algorithm and show that its sequential time complexity is bounded by $Oleft((fracmax(N_1,N_2)varepsilon)^2right)$, where $N_1$ and $N_2$ are the number of vertices of the given polylines. We apply our method to query-by-sketch, indexing of polyline databases, and classification of terrain features and show experimental results for each of these applications.