## 4 Experimental Results
### Evaluation of the Scaling  
We start by establishing a benchmark. We evaluate four recently published models that predict metric depth and are at least partially designed for outdoor scenes. These include the most recent models, UniDepth [2] (2025) and Depth Pro [21] (2024), as well as Depth Anything [20] (2024) and AdaBins [38] (2021). For UniDepth, we evaluate both the depth prediction model and the point cloud prediction model (UniDepth Points). For each recording in the dataset, we calculate the Chamfer distance, averaging first scene-wise and then across the entire dataset. The results are presented in Figure 6.  
UniDepth and Depth Pro significantly outperform Depth Anything and AdaBins across all scenes, while demonstrating comparable performance to each other. Overall, UniDepth achieves the lowest average Chamfer distance and is therefore adopted as our benchmark model. It is worth noting that with an average Chamfer distance of 1.94 m across the entire dataset, the reconstruction using UniDepth is still inadequate for the current use case. We now evaluate the scaling using three backbone depth prediction models. The first model, UniDepth, aligns with our benchmark as it is the most recent depth prediction model. This allows us to assess the potential improvement in reconstruction accuracy achieved through our calibration. The second model, DepthPro [21], demonstrates performance comparable to UniDepth and is therefore included in our evaluations. Finally, the third model, MiDaS [19], predicts disparities and hence provides relative depth. By applying our calibration, we convert MiDaS outputs into metric space and evaluate their accuracy. It is important to note that for the rail gauge measurement, the backbone model must predict rails as parallel structures in the resulting 3D point cloud. This criterion is met by all selected models, but is not sufficiently satisfied by Depth Anything or AdaBins. For each recording that matches the preliminaries, we perform calibration using InterImage segmentation. The results are then compared against the benchmark. Figure 7a illustrates the results. Our calibration method significantly reduces the average Chamfer distance using all backbones. Furthermore, Figure 7a demonstrates consistent improvements across all scenes. The averaged results are presented in Table 1. Additionally, the visual examples in Figure 8 demonstrate that scaling significantly enhances the reconstruction quality compared to LiDAR. Figure 6: Average Chamfer distances of the benchmark models across the entire OSDaR23 dataset. Generally, it would be advantageous if calibration did not need to be performed for every single recording. In practice, there are scenarios where our preliminary conditions are not met, so being able to calibrate only when these conditions are satisfied and then apply the calibration to other recordings would be highly beneficial. Given consistent intrinsic and extrinsic camera parameters across the dataset, this approach is feasible. However, dynamic factors such as auto white balance or contrast adjustments under varying lighting conditions (e.g., brighter or darker scenes) could still affect depth prediction and result in scale variations, as illustrated in Figure 8. To assess the impact of omitting individual calibration in stable ambient conditions, we calibrate only the first recording of each scene and apply this calibration to all subsequent recordings within the same scene. Figure 7 presents the results, demonstrating again improved reconstructions across all scenes. The averaged results are presented in Table 1.  
There are 24 scenes in the dataset that do not meet the preliminary requirements. These scenes often feature significantly different ambient conditions, such as transitions between overground and underground environments, which affect the scaling of the depth prediction backbone. To evaluate this effect, we average the calibration parameters from all scenes meeting the preliminary criteria and apply this averaged calibration to the entire dataset.