Approximating the Fréchet distance for realistic curves in near linear time
Proceedings of the twenty-sixth annual symposium on Computational geometry
Improved algorithms for partial curve matching
ESA'11 Proceedings of the 19th European conference on Algorithms
Jaywalking your dog: computing the Fréchet distance with shortcuts
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A GPU approach to subtrajectory clustering using the Fréchet distance
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
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This article is a survey on methods from computational geometry for comparing shapes that we developed within our work group at Freie Universität Berlin. In particular, we will present the ideas and complexity considerations for the computation of two distance measures, the Hausdorff distance and the Fréchet distance. Whereas the former is easier to compute, the latter better captures the similarity of shapes as perceived by human observers. We will consider shapes modelled by curves in the plane as well as surfaces in three-dimensional space. Especially, the Fréchet distance of surfaces seems computationally intractable and is of yet not even known to be computable. At least the decision problem is shown to be recursively enumerable.