A Geometric Framework for Detection of Critical Points in a Trajectory Using Convex Hulls

Abstract

Large volumes of trajectory-based data require development of appropriate data manipulation mechanisms that will offer efficient computational solutions. In particular, identification of meaningful geometric points of such trajectories is still an open research issue. Detection of these critical points implies to identify self-intersecting, turning and curvature points so that specific geometric characteristics that are worth identifying could be denoted. This research introduces an approach called Trajectory Critical Point detection using Convex Hull (TCP-CH) to identify a minimum number of critical points. The results can be applied to large trajectory data sets in order to reduce storage costs and complexity for further data mining and analysis. The main principles of the TCP-CH algorithm include computing: convex areas, convex hull curvatures, turning points, and intersecting points. The experimental validation applied to Geolife trajectory dataset reveals that the proposed framework can identify most of intersecting points in reasonable computing time. Finally, comparison of the proposed algorithm with other methods, such as turning function shows that our approach performs relatively well when considering the overall detection quality and computing time.

A Spatio-Temporal Entropy-based Framework for the Detection of Trajectories Similarity

“…The geometric parameters considered include curvature, turning and self-intersection points. They are detected by the application of a convex hull structure as introduced in our previous work [58]. More precisely, these three geometric parameters can be defined as follows:…”

“…Among different parameters that can be considered for qualifying a self-intersecting point, the time and distance covered by the self-intersecting part of the trajectory between passing through twice can be mentioned. Trajectory Critical Points are detected by the application of a Convex-Hull algorithm (TCP-CH) that has been applied to detect the main geometric characteristics, that is, curvature, turning and intersection points as introduced in our previous work [58]. Prior to the application of the TCP-CH algorithm, noisy points are removed by the application of a Kalman filter whose objective is to smooth the successive positions by recursively correcting error values often generated by GPS positioning errors.…”

“…Prior to the application of the TCP-CH algorithm, noisy points are removed by the application of a Kalman filter whose objective is to smooth the successive positions by recursively correcting error values often generated by GPS positioning errors. Curvature and turning points are identified by the TCP-CH algorithm in such a way that starting and ending points of the convex hulls are selected as turning points, while for each convex hull the curvature point is the one located at the maximum distance from the connecting line of two turning points [58].…”

“…Convex hulls have been derived for the 326 trajectories and by application of an algorithm introduced in our previous work [58]; a total number of 7498 convex hulls were obtained. Convex hulls are particularly useful when detecting light differences between similar trajectories according for instance to their origin and destination.…”

“…hull the curvature point is the one located at the maximum distance from the connecting line of two turning points [58].…”