Dynamics-aware similarity of moving objects trajectories

Abstract

This work addresses the problem of obtaining the degree of similarity between trajectories of moving objects. Typically, a Moving Objects Database (MOD) contains sequences of (location,time) points describing the motion of individual objects, however, they also have an implicit information about the velocity, which is an important attribute describing the dynamics of a particular object. Our main goal is to extend the MOD functionalities with the capability of reasoning about how similar are the trajectories of objects that, possibly, move along geographically different routes. Towards this, we use a distance function which balances the lack of temporal-awareness of the Hausdorff distance with the generality (and complexity of calculation) of the Fréchet distance. Based on the observation that, as a firstapproximation in practice, the individual segments of trajectories are assumed to have constant speed, we provide efficient algorithms for: (1) optimal matching between trajectories; and (2) approximate matching between trajectories, both under translations and rotations, where the approximate algorithm guarantees a bounded error-quality with respect to the optimal one.

Finding long and similar parts of trajectories

“…Trajcevski et al [21] use the maximum instead of the average distance at corresponding times as similarity measure. They give algorithms for optimal matching under rotations and translations.…”

Exploring movement-similarity analysis of moving objects

“…The distance measure is computed based on the area of a set of polygons formulated between intersection points of trajectories [22]. In another work, Euclidean time-Uniform distance has been introduced in optimal or approximate matching between trajectories under translation and rotation [27]. On a similar attempt an extension of Frèchet distance has been applied to support trajectory similarity join [8].…”

Efficient Similarity Join of Large Sets of Moving Object Trajectories

“…If the Hausdorff distance [2] is used, one can assert that the motion of the man and the dog are always within a distance of ε. However, this measure pertains only to the routes of the man and the dog, completely ignoring the dynamics of their representative motions [22]. As illustrated in Figure 1, the locations of the man and the dog at some time instance can be much larger than ε. Popularly, this means that the minimum length of leash is the fine measure of their distance.…”

“…• When only the first element in the triple is the MBR of a segment (line [18][19][20][21][22], the algorithm checks whether the corresponding entry in WMD is flagged complete, and if so the triple is discarded since it (and any new triple formed by further descending the R-tree) may not produce a better answer than the existing candidate. Otherwise the second node is expanded by calling the function expandElement.…”