# Towards Moving Objects Behavior Analysis: Region Speed Limit Rate Measure
## 1 Introduction  
Objects that move in a region can be seen in various scenes of everyday life. For example, people and vehicles that move in a city, animals in the jungle, birds in the sky, and ships in the ocean, among others. The region in which these objects move can be segmented into subregions (cells) in order to analyze the movement of these objects in a sectorized way. The time can also be segmented into intervals. In this way, the movement of objects in a cell for a given time interval can be analyzed. Among the many aspects that can be considered and evaluated in the movement of objects [1, 2] is the speed [3, 4]. In particular, in this paper, we focus on analyzing the speed limit rate of moving objects in these cells at certain time intervals. To that end, we propose a measure that, based on the historical data of the moving objects' trajectories [5], determines the speed limit rate in each of the cells in which a region is segmented. To do this, we formally define the concepts of speed limit rate and temporal and spatial segmentation. In a review of the literature, we found a few related studies; however, they focused mainly on trajectory visualization [6, 7] and congestion analysis [8, 9]. Possibly the closest work to ours is [10]. There, the authors propose a TDW (trajectory data warehouse [11]) for storing the trajectories of vehicles. The geographical space where these trajectories occur is segmented into cells, and the speed and density of the vehicles are analyzed in each one. The relationship between these two variables (speed and density) is analyzed in certain time intervals, and the results are displayed by combining OLAP (online analytical processing) tools [12], GIS, and visualizations that include triangles that allow the analyst to compare the speed (represented in the base of the triangle) and the density (represented in the height of the triangle) of the vehicles in each cell. Our approach to the analysis of speed limit rates may be complementary to their work. On the other hand, in [13], the authors propose a TDW for the analysis of the trajectories of two types of moving objects: cars and ships. The geographical space is segmented into cells, and visualization techniques are also proposed with triangles that represent the fishing cost and the fish catches in each cell, as well as arrows that represent the flow among the cells. The segmentation of the geographical space allows the analyst to observe the evolution of traffic in a cell for a given time interval: the number of vehicles in circulation, their _speed_, their direction, and the traffic density in the cell, which is also shown by means of a color scale. In addition, they include a correlation analysis between different measures (e.g., density vs. speed) in each cell and analyze flows of moving objects among the cells. In [6], the authors propose a method for visualizing trajectories that are distinguished by types (e.g., the trajectories of cargo ships or fishing ships). The geographical space is segmented into rectangles (called compartments) or free-form polygons. To facilitate visualization, the trajectories are grouped considering their shape and their life span (average time spent of a trajectory in a region). These visualizations allow us to analyze both the movement and congestion in each region. The congestion is calculated from the _presence_ measure. Given a time interval \(ti\) and a region \(r\), the _presence_ can be characterized by (a) the total number of moving objects that visited \(r\) during \(ti\) or (b) the total number of visits (some moving objects might visit \(r\) during \(ti\) more than once), or (c) the total or average time spent in \(r\) by the moving objects. An analysis of the flow of the congestion and its spreading to other regions is presented in [14], where the flow of moving objects among adjacent regions is represented by arrows. A relevant recent review of research on trajectory analytics can be found in [15].