A Topological Process Model of Trajectories-regions Based on Critical Points

The increasing pervasiveness of movement data,as a consequence of ubiquitous positioning techniques,has made researches on trajectories in the spotlight,which can facilitate and convey valuable knowledge to various kinds of studies as well as applications,such as spatio-temporal query and data mining.Despite recent research interest on trajectories switched from raw data to semantic trajectories,neither of them take into account topological invariants harbored in movements.This paper develops a topological process model of trajectories-regions based on critical points in a two-dimensional space,which distinguishes 14 basic intersection types,in point set topological theory,between trajectories and region objects by the pattern of a nested matrix,combined as sequences of intersections for describing topological correlations of trajectories-regions.The model is not only a description of topological invariants among trajectories and regions,but also the complicated topological process covering multi-trajectory and multi-region,by incorporating semantics of trajectories' behaviors.Also,constraints on trajectories' movements,brought by topological relations among regions,are discussed in the model by means of intersection linkage patterns between two adjacent intersection events.