# Application of Data Mining Techniques to Predict Luminance of Pavement Aggregate
## 2 Materials and Methods
### Luminance Coefficient under Diffused Illumination Qd  
EN 1436 defines Qd as the ratio of the luminance of a surface area under diffuse illumination in proportion to the illuminance at the surface plane. Qd is measured using the spectral distribution of illumination according to a standard illuminator representing daylight and an observation angle of 2.29\({}^{\circ}\) representing a geometry (viewing distance) of 30 m. It is worth mentioning that the maximum luminance that can be obtained for a given area, when the surroundings have a constant luminance L, is 318 \(\text{mcd}\cdot\text{m}^{-2}\text{lx}^{-1}\). In contrast, a value of approximately Qd = 52 \(\text{mcd}\cdot\text{m}^{-2}\text{lx}^{-1}\) is attributed to \"black\" pavements (for example: mastic asphalt) [13]. This type of luminance coefficient determines daytime visibility.  
Road lighting creates a contrast between the luminance of a person, vehicle or object and the luminance of the immediate background, which is usually the road surface or its edges. Luminance contrast is a measure of the difference between the luminance of an object and the luminance of the background. Objects on the road are visible if they contrast with the road surface. Threshold contrast is the minimum contrast at which an observer can see an object against its surroundings. Luminance contrast is positive if the object is brighter than its background and negative if the object is darker than its background [38].  
Surface reflection is strong in situations corresponding to driving into the sun. The ordinary reflection is strong in situations corresponding to driving with the sun shining from the back. Adequate light for a standard road configuration when confronted with dry and wet surface conditions is evaluated by optimizing the lighting distribution function [39].  
The average luminance expressed by the Qo coefficient, although still used, is a parameter that is difficult to measure using the small space of a portable instrument. Therefore, since the 1990s, Qd has aimed to characterize the reflectivity of road markings in daylight or under road lighting. Portable devices are available and are used widely for road marking, and can also be applied to road surfaces. However, no portable instrument is available for measuring the specular coefficient. In this study, the luminance coefficient  
Figure 1: The geometry of the luminance coefficient: \(\alpha\) (viewing angle), \(\beta\) (angle between the plane of incidence of light and the viewing plane), \(\gamma\) (angle of incidence of light), and \(\delta\) (angle between the viewing plane and the axis of the road on which the luminance coefficient q of the road surface is located depending on the viewing point P [38]).  
Qd takes into account the effect of specular reflection, but to a lesser extent than Qo. Therefore, the Qd parameter can be considered a reasonable approximation of the Qo value for determining the illuminance required for road lighting design. The Qd coefficient is also relevant under weak daylight or twilight lighting conditions. In these cases, the human sense of vision is very sensitive to the contrast that results from dark objects against the surface of the road [39].  
The normalized luminance coefficient Qd for a pavement associated with an r-table can be determined by laboratory methods from a cut pavement sample under field conditions using a reflectometer, or by modern digital image analysis techniques [40].