| Title: |
Homotopy Measures for Representative Trajectories |
| Authors: |
Chambers, Erin W.; Kostitsyna, Irina; Löffler, Maarten; Staals, Frank; Sub Computational Geometry; Computational Geometry |
| Publication Year: |
2016 |
| Subject Terms: |
trajectory analysis; representative trajectory; homotopy area |
| Description: |
An important task in trajectory analysis is defining a meaningful representative for a cluster of similar trajectories. Formally defining and computing such a representative r is a challenging problem. We propose and discuss two new definitions, both of which use only the geometry of the input trajectories. The definitions are based on the homotopy area as a measure of similarity between two curves, which is a minimum area swept by all possible deformations of one curve into the other. In the first definition we wish to minimize the maximum homotopy area between r and any input trajectory, whereas in the second definition we wish to minimize the sum of the homotopy areas between r and the input trajectories. For both definitions computing an optimal representative is NP-hard. However, for the case of minimizing the sum of the homotopy areas, an optimal representative can be found efficiently in a natural class of restricted inputs, namely, when the arrangement of trajectories forms a directed acyclic graph. |
| Document Type: |
book part |
| File Description: |
text/plain |
| Language: |
English |
| Relation: |
https://dspace.library.uu.nl/handle/1874/350862 |
| Availability: |
https://dspace.library.uu.nl/handle/1874/350862 |
| Rights: |
info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.5AEB44B8 |
| Database: |
BASE |