Efficient Detection of Patterns in 2D Trajectories of Moving Points

Abstract

Moving point object data can be analyzed through the discovery of patterns in trajectories. We consider the computational efficiency of detecting four such spatio-temporal patterns, namely flock, leadership, convergence, and encounter, as defined by Laube et al., Finding REMO-detecting relative motion patterns in geospatial lifelines, 201-214, (2004). These patterns are large enough subgroups of the moving point objects that exhibit similar movement in the sense of direction, heading for the same location, and/or proximity. By the use of techniques from computational geometry, including approximation algorithms, we improve the running time bounds of existing algorithms to detect these patterns.

Decentralized Monitoring of Moving Objects in a Transportation Network Augmented with Checkpoints

“…The term 'trajectory' in this paper refers specifically to a 'set of n moving point objects whose locations are known at t consecutive time steps [emphasis added]' [8], as opposed to the more general definition of a trajectory as 'polyline in threedimensional space (two-dimensional geography, plus time), represented as a sequence of points (x, y, t)' [9]. This latter definition would also include movement data from checkpoints.…”

Implementing a qualitative calculus to analyse moving point objects

“…Longley et al (2005, p. 70) argue that any representation is discrete, stating that "the world is infinitely complex, but computer systems are finite". To date, by far the most common way to store a trajectory, is as a set of spatial locations at consecutive time steps (Orlando et al 2007, Turchin 1998, Yu et al 2004, Yu & Kim 2006, Gudmundsson, van Kreveld & Speckmann 2007) which we will term fixes, according to . Obviously, such a discrete set of fixes conflicts with the assumption of spatial and temporal continuity underlying QTC.…”

Decentralized Movement Pattern Detection amongst Mobile Geosensor Nodes

“…As such, the definition is quite restrictive. Current work by the authors is looking at relaxing these constraints, and discussion of the options has already appeared in the literature [3].…”

“…They are the spatiotemporal "trace" left behind by the behavior of moving entities [2]. Examples of movement patterns include flocking as in a "mob" of sheep [3], leading and following found in group dynamics [4,5], or converging and diverging of pedestrians in crowding scenarios [6,7]. Figure 1 illustrates the movement pattern of a prototypical "flock".…”