4D Time Density of Trajectories: Discovering Spatiotemporal Patterns in Movement Data

Abstract

Abstract:Modern positioning and sensor technology enable the acquisition of movement positions and attributes on an unprecedented scale. Therefore, a large amount of trajectory data can be used to analyze various movement phenomena. In cartography, a common way to visualize and explore trajectory data is to use the 3D cube (e.g., space-time cube), where trajectories are presented as a tilted 3D polyline. As larger movement datasets become available, this type of display can easily become confusing and illegible. In addition, movement datasets are often unprecedentedly massive, high-dimensional, and complex (e.g., implicit spatial and temporal relations and interactions), making it challenging to explore and analyze the spatiotemporal movement patterns in space. In this paper, we propose 4D time density as a visualization method for identifying and analyzing spatiotemporal movement patterns in large trajectory datasets. The movement range of the objects is regarded as a 3D geographical space, into which the fourth dimension, 4D time density, is incorporated. The 4D time density is derived by modeling the movement path and velocity separately. We present a time density algorithm, and demonstrate it on the simulated trajectory and a real dataset representing the movement data of aircrafts in the Hong Kong International and the Macau International Airports. Finally, we consider wider applications and further developments of time density.

Potential path volume (PPV): a geometric estimator for space use in 3D

“…For example, calculations of any of the 3D densities (e.g. [21–23]) could be limited to voxels inside the PPV only, thus reducing the overall time needed for calculation of these volumetric representations.…”

“…Others also incorporated time into their KDE methods, through development of new spatio-temporal kernels [19] or through adaptation of existing methods, such as for example an extension of Brownian bridges [20] into four dimensions [21, 22]. Outside of ecology Zou et al [23] present a 4D time density algorithm and demonstrate its use on airplane trajectories. However, all these methods come with a high computational cost and are therefore relatively underused.…”

Guest Editor’s Editorial “Cognitive Aspects of Human-Computer Interaction for GIS”

“…The article of Y. Zhou et al [20] refers to "4D Time Density of Trajectories: Discovering Spatiotemporal Patterns in Movement Data". In cartography, a common way to visualize and explore trajectory data is to use the 3D cube (e.g., space-time cube), where trajectories are presented as a tilted 3D polyline.…”

Visualization of Pedestrian Density Dynamics Using Data Extracted from Public Webcams

“…Space-time cube (STC) representation has proved to be useful means of conceptualization, analysis and visualization of spatio-temporal events [27,28] and trajectories [29]. It has been used for characterizing various urban phenomena, including crime hotspots [30], urban fires [31], and dengue fever [32], as well as for studying human activity patterns [33,34] and describing big trajectory datasets [35,36].In this paper, we build on a previous study by Hipp et al [25] and present a new method to derive high-resolution spatio-temporal pedestrian density from webcam images. Given the three-dimensional nature of the density, we propose a novel visualization using a continuous space-time cube representation, aiming at providing at-a-glance view of the dynamics of pedestrian density in space and time.…”

“…Space-time cube (STC) representation has proved to be useful means of conceptualization, analysis and visualization of spatio-temporal events [27,28] and trajectories [29]. It has been used for characterizing various urban phenomena, including crime hotspots [30], urban fires [31], and dengue fever [32], as well as for studying human activity patterns [33,34] and describing big trajectory datasets [35,36].…”