# Sparse Indoor Camera Positioning with Fiducial Markers
## 4 Experiments
### Complete Floor Dataset  
This experiment deals with a more complex environment consisting of an entire floor within a building. The floor layout includes four interconnected corridors and a large central hall, a nexus for all corridors (see Figure 5b). This setup incorporates 22 fixed cameras, all strategically positioned along the ceiling, with no overlap between their fields of view. We employed 50 ArUco markers [34] to cover the area, obtaining 10 different groups using our moving camera. An overview summarizing the datasets used in this work, including the complete floor configuration, can be found in Table 1.  
As in the previous case, two variations of the datasets were generated, labeled A and B. In dataset A, the fixed cameras were oriented to face directly downward, while in dataset B, they were angled slightly to provide a different view of the floor layout. Similar to the work carried out on the previous dataset, we conducted ablation studies on these datasets to assess how different combinations of optimization terms affect the reconstruction accuracy. These results are summarized in Table 3.  
As evidenced by the results, just as in previous datasets, relying solely on the reprojection error term (\(E_{rp}\)) leads to suboptimal outcomes compared to our method, including additional optimization terms. Applying all optimization terms achieves the most robust and consistent results, yielding superior outcomes in dataset B. This enhancement underscores the importance of integrating multiple constraints to effectively address the  
Figure 5: **Corridor and complete floor datasets**. Representations of camera positions and orientations are depicted using blue, orange, and purple pyramids. (**a**) Corridor datasets. (**b**) Complete floor datasets.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{4}{c}{**Complete Floor**} \\ \cline{2-5}  & \multicolumn{2}{c}{**Dataset A**} & \multicolumn{2}{c}{**Dataset B**} \\ \hline
**Method** & \(E_{t}\) **(cm)** \(\downarrow\) & \(E_{t}\) **(\%)** \(\downarrow\) & \(E_{t}\) **(cm)** \(\downarrow\) & \(E_{t}\) **(\%)** \(\downarrow\) \\ \hline \(E_{rp}\) & 156.79 \(\pm\) 70.16 & 1.264 & 133.01 \(\pm\) 60.42 & 1.073 \\ \(E_{rp}+E_{cc}\) & 61.92 \(\pm\) 19.87 & 0.499 & 87.11 \(\pm\) 36.56 & 0.703 \\ \(E_{rp}+E_{cm}\) & 63.47 \(\pm\) 25.40 & 0.512 & 65.30 \(\pm\) 31.38 & 0.527 \\ \(E_{rp}+E_{cc}+E_{cm}\) & 62.27 \(\pm\) 20.25 & 0.502 & 65.79 \(\pm\) 31.43 & 0.531 \\ \(E_{rp}+E_{cp}\) & 46.62 \(\pm\) 11.96 & 0.376 & 28.61 \(\pm\) 11.26 & 0.231 \\ \(E_{rp}+E_{cp}+E_{cc}\) & 34.27 \(\pm\) 8.47 & 0.276 & 24.11 \(\pm\) 9.21 & 0.194 \\ \(E_{rp}+E_{cp}+E_{cm}\) & 25.96 \(\pm\) 6.67 & 0.209 & 24.90 \(\pm\) 9.51 & 0.201 \\ \hline \(E_{rp}+E_{cp}+E_{cc}+E_{cm}\) & 26.97 \(\pm\) 7.58 & 0.218 & 23.64 \(\pm\) 9.27 & 0.191 \\ \hline \hline \end{tabular}
\end{table}
Table 3: **Results using the complete floor datasets**. The term \(E_{rp}\) refers to the baseline, the term \(E_{cp}\) refers to the usage of control points, \(E_{cc}\) refers to the enforcement of cameras being at the same plane, and \(E_{cm}\) applies the same principle to the markers. \(E_{t}\) denotes the translational errors, expressed in cm and as a percentage with respect to the running distance.  
complexities of pose estimation in expansive environments. Finally, we achieved an error of approximately 27 cm and 24 cm for datasets A and B of the complete floor, respectively.