Computing the Fréchet distance between simple polygons in polynomial time
Proceedings of the twenty-second annual symposium on Computational geometry
On-line data reduction and the quality of history in moving objects databases
MobiDE '06 Proceedings of the 5th ACM international workshop on Data engineering for wireless and mobile access
Fréchet distance for curves, revisited
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Dynamics-aware similarity of moving objects trajectories
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
Computing the Fréchet distance between simple polygons
Computational Geometry: Theory and Applications
Exact algorithms for partial curve matching via the Fréchet distance
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Approximating the Fréchet distance for realistic curves in near linear time
Proceedings of the twenty-sixth annual symposium on Computational geometry
Geodesic Fréchet distance inside a simple polygon
ACM Transactions on Algorithms (TALG)
Polyline approach for approximating Hausdorff distance between planar free-form curves
Computer-Aided Design
Link distance and shortest path problems in the plane
Computational Geometry: Theory and Applications
Mining trajectory corridors using fréchet distance and meshing grids
PAKDD'10 Proceedings of the 14th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining - Volume Part I
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
A GPU approach to subtrajectory clustering using the Fréchet distance
Proceedings of the 20th International Conference on Advances in Geographic Information Systems
Computational Geometry: Theory and Applications
Implicitization of curves and (hyper)surfaces using predicted support
Theoretical Computer Science
Measuring similarity between curves on 2-manifolds via homotopy area
Proceedings of the twenty-ninth annual symposium on Computational geometry
| Hi-index | 0.00 |
The Hausdorff distance is a very natural and straightforward distance measure for comparing geometric shapes like curves or other compact sets. Unfortunately, it is not an appropriate distance measure in some cases. For this reason, the Fréchet distance has been investigated for measuring the resemblance of geometric shapes which avoids the drawbacks of the Hausdorff distance. Unfortunately, it is much harder to compute. Here we investigate under which conditions the two distance measures approximately coincide, i.e., the pathological cases for the Hausdorff distance cannot occur. We show that for closed convex curves both distance measures are the same. Furthermore, they are within a constant factor of each other for so-called κ-straight curves, i.e., curves where the arc length between any two points on the curve is at most a constant κ times their Euclidean distance. Therefore, algorithms for computing the Hausdorff distance can be used in these cases to get exact or approximate computations of the Fréchet distance, as well.