## 2 Data and Methods
### LiDAR Feature Extraction
\[\textbf{Cov}=\frac{1}{k+1}\sum_{i=0}^{k}\left(\textbf{X}_{i}-\overline{ \textbf{X}}\right)\left(\textbf{X}_{i}-\overline{\textbf{X}}\right)^{T} \tag{6}\]  
In this equation, \(\textbf{X}_{i}\) is the \(i\)th neighbour and \(\overline{\textbf{X}}\) is the geometric centre of the neighbourhood determined by,  
\[\overline{\textbf{X}}=\frac{1}{k+1}\sum_{i=0}^{k}\textbf{X}_{i} \tag{7}\]  
After the covariance matrix was computed, eigenvalues (\(w\)) and eigenvectors (\(v\)) were determined. The direction along which the dataset had the maximum variation is indicated by the eigenvector with the largest eigenvalue. These were used for eigenvalues-based feature extraction. First, the eigenvalues, and correspondingly the eigenvectors, were sorted in ascending order as \(\lambda_{1}>\lambda_{2}>\lambda_{3}\). In order to perform accurate feature extraction, it had to be ensured that the vectors were normalized between 0 and 1 and that the eigenvalues were greater than 0 [38]. The calculated eigenvalue based features were linearity \(L_{\lambda}\), planarity \(P_{\lambda}\), sphericity \(S_{\lambda}\), omnivariance \(O_{\lambda}\), anisotropy \(A_{\lambda}\), eigenentropy \(E_{\lambda}\), sum of eigenvalues \(\sum_{\lambda}\) and change of curvature \(C_{\lambda}\). \[L_{\lambda}=\frac{\lambda_{1}-\lambda_{2}}{\lambda_{1}} \tag{8}\]  
Figure 2:0  
Figure 2:1  
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Figure 2:6  
The 3D features calculated for each point \(P(i)\) were reduced to the gridded horizontal plane in order to be combined with the features calculated from the satellite images. Each tile covered by LiDAR point clouds was divided into 1 m \(\times\) 1 m cells in \((x,y)\). Due to one or more \(P(i)\) points falling within the same cell, the feature value of each cell is represented by the average value of these points. All gridded LiDAR features can be used directly, but the absolute height requires post-processing to be performed. The elevations derived from LiDAR data represent geographic elevations as absolute heights, in contrast with other features that are characterized by statistical relationships. To determine the distance between objects and the ground in this study, the digital elevation model was subtracted from the height values of points in the point cloud. Finally, the LiDAR feature extraction was completed by clipping the features based on satellite images. Figure 3 illustrates the rendering of the generated features in blue and red colour for low- and high-impact feature values. In general, these features provide insight into the geometry of objects in the point cloud and their relation with the surrounding objects. For instance, anisotropy represents the uniformity of a point cloud, while linearity can be defined as a measure of linear attributes. Furthermore, absolute height provides a distinction between the roads and other objects above [39]. Together, these features complete the geometric relation between the road and its neighbouring object which is not properly handled in the satellite-only segmentation solutions. Figure 2:7 Illustration of gridded feature samples from LiDAR data.