# Sparse Indoor Camera Positioning with Fiducial Markers
## 4 Experiments
### Comparison with Other Works  
In this section, we assess how our proposed method stands in comparison to established techniques within the field, including the approaches by [PERSON] et al. [5] and the MarkerMapper system [4], which are both adept at handling camera field overlaps. Additionally, we extend our comparison to state-of-the-art structures from motion (SFM) implementations such as OpenDroneMap [28], Pix4D [29], and COLMAP [30], as well as the Gaussian splatting approach PolyCam [32]. Despite numerous attempts, these methods failed to produce complete reconstructions due to insufficient camera overlaps and a lack of distinctive key points for reliable matching, except for the MarkerMapper [4] and [PERSON] et al. [5] methods, which successfully operated within some datasets. The datasets used for this evaluation, collectively referred to as dense, were introduced by [PERSON] et al. [5] and tested the capacity to manage overlapping views. These datasets include artificial and real scenarios, representing a single corridor, an entire floor, and multiple floors. In these scenarios, fixed cameras are positioned on the ceilings, while Aruco [34] fiducial markers are placed on the floor. Similar to our work, these datasets demonstrate various camera arrangements as different configurations. On the other hand, the datasets introduced in our study, labeled as sparse, are specifically designed to assess the efficacy of methods in positioning fixed cameras with no overlap. However, there are no existing methods with publicly available code that can be evaluated using our proposed datasets. Consequently, we cannot compare our results on these datasets with any other existing method. Table 6 presents the results of our comparative analysis. The symbol '\(\times\)' indicates that a method was inapplicable, while the symbol '\(-\)' denotes that specific error data were unavailable due to a lack of ground truth. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Methods**} \\ \cline{3-8}  & & \multicolumn{3}{c}{**MarkerMapper [4]\({}^{\dagger}\)**} & **[PERSON] et al. [5]\({}^{\dagger}\)** & **Our Method** \\ \hline
**Datasets** & **Variant** & \(\mathbf{E_{t}}\) **(cm)**\(\downarrow\) & \(\mathbf{E_{r}}\) (\({}^{\circ}\))\(\downarrow\) & \(\mathbf{E_{t}}\) **(cm)**\(\downarrow\) & \(\mathbf{E_{r}}\) (\({}^{\circ}\))\(\downarrow\) & \(\mathbf{E_{t}}\)**(cm)**\(\downarrow\) & \(\mathbf{E_{r}}\) (\({}^{\circ}\))\(\downarrow\) \\ \hline (Dense) Syn. corridor & A & 0.36 & 0.004 & 0.66 & 0.052 & 0.39 & 0.063 \\  & B & 36.37 & 0.018 & 0.41 & 0.063 & 1.08 & 0.056 \\ (Dense) Syn. duplex 1 st room & A & 0.13 & 0.003 & 0.19 & 0.021 & 0.05 & 0.004 \\  & B & 0.54 & 0.004 & 0.18 & 0.053 & 0.23 & 0.004 \\ (Dense) Syn. duplex 1 st floor & A & 1.19 & 0.003 & 0.49 & 0.157 & 0.31 & 0.092 \\  & B & 4.09 & 0.022 & 2.69 & 0.241 & 0.88 & 0.087 \\ (Dense) Syn. duplex 2 floors & A & 18.19 & 0.090 & 2.04 & 0.050 & 4.95 & 0.131 \\  & B & 14.94 & 0.670 & 7.35 & 0.552 & 9.68 & 0.168 \\ (Dense) Corridor & A & \(\times\) & \(-\) & 1.22 & \(-\) & 3.39 & \(-\) \\  & B & \(\times\) & \(-\) & 0.84 & \(-\) & 2.11 & \(-\) \\ (Dense) Complete floor & A & \(\times\) & \(-\) & 14.82 & \(-\) & 5.22 & \(-\) \\  & B & \(\times\) & \(-\) & 15.72 & \(-\) & 4.88 & \(-\) \\ (Sparse) Corridor & A & \(\times\) & \(-\) & \(\times\) & \(-\) & 5.09 & \(-\) \\  & B & \(\times\) & \(-\) & \(\times\) & \(-\) & 2.84 & \(-\) \\ (Sparse) Complete Floor & A & \(\times\) & \(-\) & \(\times\) & \(-\) & 26.97 & \(-\) \\  & B & \(\times\) & \(-\) & \(\times\) & \(-\) & 23.64 & \(-\) \\ (Sparse) Entire Building & & \(\times\) & \(-\) & \(\times\) & \(-\) & 41.96 & \(-\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: **Comparison with other works**. Lower values for both \(\mathbf{E_{t}}\) and \(\mathbf{E_{r}}\) represent better reconstruction. MarkerMapper was the only method capable of obtaining coherent results.