# Fusing Appearance and Prior Cues for Road Detection
## 2 Proposed Algorithm
### Preprocessing of the Input Image
#### 2.1.3 Illuminant Invariant Transformation  
Color information is a powerful cue for appearance based road detection methods. However, these methods usually fail since the color of the road varies significantly depending on the acquisition conditions. Especially, shadows and highlights appearing in the road images have the greatest impact since they often lead to false road detection. To solve this problem, illuminant invariant information is needed to provide robustness to lighting conditions. In this paper, we follow the photometric invariant approach proposed in [25].  
Under PLN (Planckian light source, Lambertian surfaces, and narrowband imaging sensors) assumptions, the input image is converted to an illuminant invariant space denoted by \(\mathcal{I}\). For the pixel \(i\) in the input image, \(\mathcal{I}_{i}\) is defined as follows:  
\[\mathcal{I}_{i}=r_{i}\times\cos\theta+b_{i}\times\sin\theta, \tag{2}\]  
\[r_{i}=\log\left(R_{i}/G_{i}\right), \tag{3}\]  
\[b_{i}=\log\left(B_{i}/G_{i}\right), \tag{4}\]  
where \(r_{i}\) and \(b_{i}\) are the corresponding log-chromaticity values using the \(G\) channel for normalization, with \(R_{i}\), \(G_{i}\), and \(B_{i}\) representing the stand RGB color channels of the image after morphological processing. Then, as shown in Figure 2, a set of color surfaces of a given chromaticity value imaged under different lighting conditions are projected onto a straight line in the log-chromaticity space. After that, sets of color surfaces with different chromaticity values form parallel lines. In addition, these straight lines define an orthogonal axis \(\ell_{\theta}\), where surfaces under different illuminations are represented by the same point. Movements along \(\ell_{\theta}\) imply changing the chromaticity value of the surface, which are independent of illumination.  
Finally, following this approach, a shadow-free and highlight-free grayscale image is obtained, which is invariant under different lighting conditions. It is important to mention that converting RGB images requires knowledge of \(\theta\), i.e., the illuminant invariant angle, which is an intrinsic parameter of the camera and can be calibrated by entropy-minimization. The value of the \(\theta\) used in our experiments is 48.7\({}^{\circ}\). Results of the illuminant invariant transformation are shown in Figure 1.  
Unfortunately, lots of detail information will be decimated in the process of derivation. [PERSON] et al. [35] argued that HSV color space provides diversified pixel information which can be efficiently exploited to detect road surfaces where HSV means hue, saturation and value channels in color images. Motivated by this, we use a log-chromaticity space to provide a high invariance to shadows  
Figure 2: Illuminant invariant transformation.  
and highlights, then we use the HSV color space to recover detail information and provide a high discriminative power. Specifically, experimental results show that the best performance is obtained when we combine the log-chromaticity space and the S (saturation) channel in the HSV color space.