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曲线有向的（移动）点配置：一个代表沿曲线有向的距离，另一个代表与曲线有向的有符号正交距离线。弯曲的直线表示关注运动的方向。例如，它可以像在高速公路上行驶时那样是笔直的，或者可以像在十字路口或回旋处时那样是弯曲的。受点演算的启发，曲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。我们将此表示称为时间点上的点描述符优先静态（PDP _S）表示，并将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弯曲运动，研究了一些基本的微观分析交通示例。最后，我们讨论了工作的一些扩展，以突出PDP在识别可用于GIS，自动驾驶车辆，运动分析和步态分析中使用的运动模式的实际好处。