## 3 Methodology
### LiDAR-Camera Processing Pipeline
#### 3.1.2 Depth Normalization and Mapping  
LiDAR-color normalization refers to the process of mapping LiDAR data, often height or intensity values from a point cloud, to color values for visualization purposes [27]. Since LiDAR data consist of points in 3D space, typically represented as [**x, y, z, i**] and sometimes intensity, it lacks direct color information. To visualize these points meaningfully in 2D or 3D maps, it is essential to normalize certain attributes, such as height z or intensity, and map them to color values. This process helps in creating colorized point clouds or height maps where different heights or intensities are represented by different colors [28; 29]. In addition, the normalization process involves scaling the attribute values into a specific range, from 0 to 255, to ensure that the color representation is accurate and meaningful. By doing this, the visual output becomes more intuitive, allowing for easy interpretation of the data based on color changes. This normalization is performed using the following equation:  
\[z_{normalized}=\frac{(z-z_{min})}{(z_{max}-z_{min})}x(c_{max}-c_{min})+c_{min} \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c} \hline
**Pipeline** & **Fusion Strategy** & **Region Type** & **Estimating Distances** \\ \hline CoRDE & Full Region & Entire Region & Minimum value in the region \\ \hline CeRDE & Central point & \(n\times n\) region around the center point & Minimum in \(n\times n\) region \\ \hline GCRDE & Grid + Central point & \(n\times n\) regions around grid cell centers & The most frequent depth group \\ \hline \end{tabular}
\end{table}
Table 1: Comparison of the depth estimation pipelines and their estimation strategies.  
where \(z_{min}\) and \(z_{max}\) represent the minimum and maximum elevation values, while \(c_{min}\) and \(c_{max}\) define the range of colors used in the mapping. By applying this transformation, LiDAR data can be visualized effectively in applications such as colorized point clouds and height maps, improving data interpretation and analysis.  
Figure 2 illustrates the pixel color range from 0 to 255. A pixel value of 0 corresponds to 0 m, while a pixel value of 255 represents 255 m. The transparent sparse depth map consists of \(x\), \(y\), and \(z\) points, where the \(z\) values are derived using this scale. After extracting the pixel from the transparent sparse depth map, Equation (2) is applied to calculate the distance corresponding to each pixel. Since there are no pixel colors representing intermediate values, the margin of error relative to the actual value is \(\pm\)1 m.  
Figure 3a presents transparent Sparse Depth Images, generated using Equation (1). The pixel colors represent different distance ranges. Black pixels indicate the closest points. Gray pixels represent slightly farther distances, followed by light gray pixels, which are even more distant. An even lighter shade of gray signifies points that are significantly farther away. Finally, white pixels denote the farthest distances. The transparent sparse depth map becomes unclear when projected onto the RGB image. To enhance clarity, the depth map was colorized for better visualization, as shown in Figure 3b. In this paper, the results are presented in color.