Constrained free space diagrams: a tool for trajectory analysis

Time plays an important role in the analysis of moving object data. For many applications it is not sufficient to only compare objects at exactly the same times, or to consider only the geometry of their trajectories. We show how to leverage between these two approaches by extending a tool from curve analysis, namely the free space diagram. Our approach also allows us to take further attributes of the objects like speed or direction into account. We demonstrate the usefulness of the new tool by applying it to the problem of detecting single file movement. A single file is a set of moving entities, which are following each other, one behind the other. Our algorithm is the first one developed for detecting such movement patterns. For this application, we analyse demonstrate the performance of our tool both theoretically experimentally.