# Vehicle Collision Prediction under Reduced Visibility Conditions
## 2 Related Work
### Research on Human Factors  
Two human factors can be considered for traffic safety namely the perception-reaction time (PRT) and the visibility due to weather conditions. They are introduced and compared as follows.  
PRT or \"break reaction time\" is an important human factor, which changes under complex traffic conditions. [PERSON] et al. stated that \"the perception-reaction time for a driver is often broken down into the four components that are assumed to make up the perception reaction time. These are referred to as the PIEV time or process\". PIEV is short for perception, intellection, emotion, and volition [15], which are defined as follows:  
Figure 1: A typical three-layer back-propagation neural network.  
* Perception is \"the time to see or discern an object or event\".
* Intellection is \"the time to understand the implications of the object's presence or event\".
* Emotion is \"the time to decide how to react\".
* Vollition is \"the time to initiate the action, for example, the time to engage the brakes\".  
In 1998, [PERSON] et al. compared Mazda's algorithm and Honda's algorithm for braking critical distance, then the authors proposed a modified algorithm which considered human factors [16]. In 2010, [PERSON] et al. designed a three layer back-propagation neural network to evaluate the PRT from sensing data [17]. In 2012, [PERSON] et al. proposed the probability density function of PRT, and classified it into three categories, namely fast, medium, and slow [18]. In 2015, [PERSON] et al. proposed a quantitative model to describe the relationship between visibility and PRT during daytime fog. Then, the dehazing of images was performed using visibility enhancement algorithms in a Head Up Display [19].  
Visibility has two definitions. One is the meteorological visibility: \"the distance at which the contrast of a black object is attenuated by 95%\", and the other one is the target visibility: \"it rates to what extent a target is detected in a scene, when an observer looks at it\" [19]. Meteorological visibility can be estimated by detection of atmospheric light extinction from weather stations or visibility cameras, and the range is in kilometer level [20]. Target visibility can be estimated by camera equipped in a vehicle, and the range is in meter level [21]. In this work, we use target visibility, because the information for meteorological visibility cannot represent visibility on the reads if the weather stations are not close enough to traffic stations [22]. [PERSON] et al. analyzed the relationship between visibility and driver behavior using inductive loop data, then found that driver speeds are much lower in fog than in clear visibility, but following distances decrease in fog. Especially in the visibility range between 40 m and 120 m, free-driving speeds are too high to allow for a successful stop for a stationary object [23]. [PERSON] et al. also found the relationship between visibility and PRT during daytime fog [19]. Most work focus on how to detect and enhance vision under low visibility, such as in fog [24]. However, we do not speculate on how to convert foggy images into clear ones for some target visibility. This work focuses on \"how to improve performance of rear-end CWS under poor visibility conditions.\" Based on the research work mentioned above (mainly [19]), it is concluded that target visibility can affect driver speed, following distances, and the PRT.