# Vehicle Speed Estimation Based on 3D ConvNets and Non-Local Blocks
## 1 Introduction  
Intelligent transportation systems (ITS) are of practical importance and interest for traffic regulators and supervisors. They provide support for government departments in traffic management, commuting improvement, traffic congestion relief, traffic accident prevention, etc. A critical component of traffic management practice and a popular topic in ITS research is vehicle speed estimation [1], which is widely applied to identify traffic congestion or other events of interest. In this paper, we focus on the average vehicle speed estimation problem, which is defined as the average speed of all the vehicles in a scene. One family of approaches to vehicle speed estimation is based on additional specialized hardware. Three commonly used devices are induction-coil loop detectors, laser detectors, and radar detectors [2]. They all have shortcomings in practice. The inductive loop detector method requires installing a loop detector in the ground. The installation process is complex and can adversely affect road condition (accelerate asphalt deterioration) [3]. Laser detectors and radar detectors do not cause these problems, yet they need frequent and expensive maintenance. Furthermore, radar detectors need to be meticulously positioned in consideration of installation angle. Another family of approaches to vehicle speed estimation is based on surveillance camera information. Nowadays, high-resolution digital cameras are ubiquitous, which provide economic and accessible sources of data. However, it is a challenging problem to extract relevant informationon traffic form video footage [4]. A conventional practice for information extraction is to install two cameras in specifically chosen locations and process the data collected by the two cameras with particularly designed algorithms. In contrast, monocular cameras are not currently in extensive use for traffic information extraction. However, there are two primary benefits in using single monocular cameras. First, monocular cameras are standard infrastructure for most of the established surveillance camera systems. Thus, it does not require substantial investment in infrastructure. Second, monocular cameras have wider coverage compared to two-camera systems. In particular, monocular cameras can simultaneously monitor multiple lanes. One existing monocular camera-based method to vehicle speed estimation utilizes the technique of **Camera Calibration**[1; 5; 6]. In short, this method obtains the algorithm-generated scale and calculates the speed based on the vehicle trajectories acquired by a two-stage process including detection and tracking. The camera calibration process require the input of the intrinsic and extrinsic parameters. Due to different camera models, shooting angles and installation positions, camera calibration is required for each camera. Some camera calibration-based methods need the multiple manual measurements on the road [5; 7; 8]. Some algorithms have limitations in camera placement [1; 5; 9; 10]. Besides, the accuracy of the speed estimate heavily relies on the accuracy of algorithms for detection and tracking. A variety of suboptimal environments (illumination variation, motion blur, background clutter and overlapping, etc.) could result in problems in vehicle detection and tracking, including detection missing, false detection, tracking loss, etc. [11]. When the vehicle detection or tracking is subpar, the error of speed estimation will be significant. More detailed analyses are presented in Section 2.1. As an attempt to ameliorate the aforementioned limitations of camera calibration- based methods, we propose an automatic approach to average vehicle speed estimation based on video footage. Figure 1 is a schematic illustration of our method. The inputs: RGB images and optical flow from a short video. The outputs: the average speed of the vehicles in the video. The input images only need to be standardized and scaled. RoI (Region of Interest) in images can be defined to do average vehicle speed estimation on a single lane.