## 1 Introduction  
With the aim of making every facet of citizens' lives easy, various technologies and solutions have been studied for intelligent transportation system (ITS) applications in recent years. The aim of an ITS is to provide users with traffic information that enables them to make safer and smarter use of transportation networks. Among many ITS technologies, vision-based vehicle detection has played a vital role in many applications, such as traffic control, traffic surveillance, and autonomous driving. Compared to other sensors such as lidar and radar [1; 2; 3], camera-based sensors are more preferable owing to such benefits as easy installation, low-cost maintenance, and high flexibility. Furthermore, the emergence of parallel computing, including multicore processing and graphical processing units, has allowed the pursuit of the real-time implementation of vision-based vehicle detection methods. To detect on-road vehicles, most vehicle detection methods use vehicle appearances as the main features [4]. In the absence of details regarding vehicle appearance, detecting vehicles at nighttime is more challenging than in the daytime. In the daytime, vehicle detection is based on the color, shape, shadow, corners, and edges of vehicles [5]. On the other hand, at night, the abovementioned features are not visible because of the low contrast and luminosity of nighttime images. Under dark conditions, the most salient features are light sources, and vehicle headlights or taillights become important characteristics that can be used for identifying vehicles. Depending on the purpose of the specific system, a vehicle detection algorithm may be constructed based on headlights or taillights only or both headlights and taillights. For instance, traffic surveillance systems only detect oncoming vehicles(headlights), whereas advanced driver-assistance systems monitor preceding vehicles (taillights) or both preceding and oncoming vehicles (taillights and headlights). For nighttime vehicle detection, most existing studies execute two main steps: vehicle light identification followed by vehicle light pairing. Various methods have been proposed to identify headlights in a captured image. Most of the methods first segment the image to find bright blobs that may be headlights. By using a fixed or adaptive threshold, a set of pixels of bright spots whose gray intensity values are higher than the threshold is retrieved. Then, to classify whether a bright blob is a headlight, rule-based or machine-learning-based methods are applied, the former of which are the most commonly used. In studies on rule-based methods [6; 7], rules are constructed based on prior knowledge and statistical laws of contrast, position, size, and shape to classify headlights and other objects. The difficulty concerning rule-based methods is that the rules should be defined carefully and cover all scenarios to obtain highly accurate results. Alternatively, machine-learning-based methods have been researched recently because of their good discrimination and superior adaptability. In [8; 9], a support vector machine (SVM) is applied to classify headlights and nuisance lights (reflections). Additionally, the Adaboost classifier and Haar features are combined to discriminate headlights from non-headlights in [10; 11]. Unlike headlights, the dominant color of taillights is red; the redness of rear lights can be easily filtered out using color spaces. In [12], a set of thresholds for filtering red color in taillights is directly derived from automotive regulations and adapted for real-world conditions in the hue-saturation-value (HSV) color space. A Y'UV color space [13] is used to extract potential taillight candidates in an image. In [14], the mean of red intensity of vehicle taillight are used to verify whether an extracted bright blob is a vehicle. After identifying vehicle lights, the light pairing process is conducted, since a vehicle is indicated by a pair of vehicle lights. This process can be performed by finding the similarity between two vehicle lights.