ABSTRACT

In this paper, we represent (moving) point configurations along a curved directed line qualitatively by means of a system of relational symbols based on two distance descriptors: one representing distance along the curved directed line and the other representing signed orthogonal distance to the curved directed line. The curved directed line represents the direction of the movement of interest. For instance, it could be straight as in the case of driving along a highway or could be curved as in the case of an intersection or a roundabout. Inspired by the Point Calculus, the order between the points on the curved directed line is described by means of a small set of binary relations ($<,=,>$) acting upon the distance descriptors. We call this representation the Point-Descriptor-Precedence-Static (PDP_S) representation at a time point and Point-Descriptor-Precedence-Dynamic (PDP_D) representation during a time interval. To illustrate how the proposed approach can be used to represent and analyse curved movements, some basic micro-analysis traffic examples are studied. Finally, we discuss some extensions of our work to highlight the practical benefits of PDP in identifying motion patterns that could be useful in GIS, autonomous vehicles, sports analytics, and gait analysis.

摘要

在本文中，我们通过基于两个距离描述符的关系符号系统定性地表示沿弯曲有向线的（移动）点配置：一个表示沿弯曲有向线的距离，另一个表示到弯曲有向线的有符号正交距离。线。弯曲的有向线表示感兴趣的运动方向。例如，它可以像在高速公路上行驶那样是直的，也可以像在十字路口或环形交叉路口那样弯曲。受点微积分的启发，弯曲有向线上的点之间的顺序是通过一小组二元关系来描述的（$<,=,>$) 作用于距离描述符。我们称这种表示为时间点的点-描述符-优先-静态（PDP _S）表示和时间间隔内的点-描述符-优先-动态（PDP _D）表示。为了说明所提出的方法如何用于表示和分析曲线运动，我们研究了一些基本的微观分析交通示例。最后，我们讨论了我们工作的一些扩展，以强调 PDP 在识别可能在 GIS、自动驾驶汽车、运动分析和步态分析中有用的运动模式方面的实际优势。