## 5 Summary and Discussion  
This study presents a novel approach for scaling non-metric 3D point clouds using monocular depth or disparity estimation, combined with achieving extrinsic camera calibration from a single image in the railway context. As demonstrated, direct metric estimation using neural networks fails in achieving the accuracy required to reliably assess vegetation encroachment into the structural gauge. To address this, we developed a method for scale estimation and extended it to compute reliable extrinsic calibration. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{4}{c}{**Average Chamfer Distance**} \\ \cline{2-5}
**Scene** & \multirow{2}{*}{**Benchmark**} & \multicolumn{3}{c}{**Result**} \\ \cline{3-5}  & & **UniDepth** & **Depth Pro** & **MiDaS** \\ \hline
13\_station\_ohlsdorf\_13.1 & 1.68 m & 2.62 m & 3.09 m & **0.81 m** \\
14\_signals\_station\_14.1 & 1.46 m & 3.73 m & **1.16 m** & 3.75 m \\
19\_vegetation\_curve\_19.1 & **2.68 m** & 4.61 m & 4.98 m & 5.85 m \\ Average & **1.94 m** & 3.65 m & 3.07 m & 3.47 m \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average Chamfer distances obtained from calibration under significantly violated preliminary conditions. Figure 12: Additional experiments evaluating the impact of segmentation and preliminary parameter violations on the overall system. (**a**) Comparison of calibration accuracy between using the segmentation model InternImage and ground truth data; (**b**) Average Chamfer distances obtained from calibration under significantly violated preliminary conditions. The proposed method is based on high-quality rail segmentation. By adapting the InternImage segmentation model, pretrained on the CityScapes dataset, to the Railsem19 dataset, we achieve rail segmentation that delivers scaling performance comparable to using ground truth segmentation. This segmentation enables scale estimation by measuring the rail gauge in the point cloud and aligning it with the standard European gauge of 1.435 m. Additionally, the point cloud is rotated to align the rails with the _x_-axis and detect the _ego_-track, enabling precise extrinsic calibration from a single image. Our evaluation shows that the method reduces the average Chamfer distance from the benchmark value of 2.01 m to 0.41 m, when the preliminary conditions are met. Even when calibration is performed only at the beginning of a scene, the Chamfer distance remains low at 0.42 m. In both scenarios, our method outperforms the benchmark across all evaluated scenes. When environmental conditions vary significantly, such as transitioning between outdoor and underground environments, and the scaling factor is averaged, the method achieves a Chamfer distance of 0.71 m. Although one scene (2 %) in this challenging case did not outperform the benchmark, the deterioration was low (0.13 m), and the overall reconstruction quality remained high. Additionally, in this context, we demonstrated that both Depth Pro and MiDaS backbones outperformed the benchmark in this particular scene, and that individual scaling outperformed the benchmark in all scenes where these backbones exhibited deterioration. The system computes extrinsic calibration with an average error of 0.16 m and 5.17\({}^{\circ}\), aligning the scaled point cloud with a coordinate system that facilitates structural gauge inspection by closely resembling real-world spatial dimensions. In this system, equivalent to OSDaR23, the ground lies in the _x_-_y_ plane, the _x_-axis aligns with the direction of motion, and the _z_-axis represents height, similar to the center-rear-axis coordinate frame used in the automotive domain. To the best of our knowledge, no extrinsic calibration method has been published that aligns with this coordinate system and relies solely on single monocular images without additional sensors, making this approach a new benchmark in the field.