## 4 Results and Discussions
### Comparison of 3D Position Estimation Results
Furthermore, the proposed framework improves the performance of 3D position estimation by using the data zone of the QR code. The proposed framework uses only a monocular camera mounted on a drone for 3D position estimation without LiDAR. While the proposed framework is cost-effective, the performance of 3D position estimation may be less than using LiDAR. To solve this, we proposed the error correction method. We evaluated the 3D position estimation performance of the proposed framework, and validated the effectiveness of the error correction method using the video dataset taken in a real-world environment. We detected and decoded the QR code in the video frame for the 3D position estimation of the drone, which is the shooting point. The results of the QR code decoding test in Section 4.2 suggest that the trained segmentation model can successfully detect the QR code in the video frame. Sometimes, the QR code may not be easily readable or visible in certain lighting conditions or at certain angles. As shown in Figure 12, decoding may \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**Quad**} & \multicolumn{2}{c}{**Data Zone**} \\ \cline{2-5}  & **Mean** & **SD** & **Mean** & **SD** \\ \hline Base & 0.2040 & 0.1081 & 0.1440 & 0.1080 \\ Proposed & 0.1945 & 0.0935 & 0.1193 & 0.0744 \\ w/o DBSCAN & 0.2416 & 0.1487 & 0.1798 & 0.1494 \\ w/o Correction & 0.2022 & 0.0967 & 0.1463 & 0.1106 \\ \hline \hline \end{tabular} SD = Standard deviation.  
\end{table} 
Table 2: Results of the ablation study. Figure 11: Results of the depth estimation for the distance between the drone and the object. Bright colors mean a longer distance than dark colors. fail if noise occurs in the data zone of the QR code even if segmentation is performed well. Recently, research related to image denoising based on deep learning models has been proposed [60]. If noise that may occur outdoors is removed with such a deep learning model for denoising, the difficulty of QR code segmentation can be eased. Furthermore, if the hyperparameter of the computer vision algorithm that post-processes the result value of the segmentation model is adjusted or the improved post-processing method is applied, decoding performance of the QR code may be improved. The proposed framework uses the video frame captured along the path of the drone, rather than a single image. Accordingly, the QR code is captured at various angles and situations. As a results, the possibility that the QR code is not detected by certain lighting conditions or at certain angle can be reduced than when using a single image. After performing the QR code decoding, the estimated drone 3D positions and straight lines for the inventory were derived to estimate the inventory 3D position based on epipolar geometry. The ablation study in Section 4.3 suggests that the DBSCAN module, the error correction module, and the utilization of the data zone of the QR code are effective in estimating the inventory 3D position. The inventory 3D position estimated by epipolar geometry was corrected using the angle between the straight-line pairs used for the estimation. We performed visualization to present the relationship between the angle and the errors of the estimated inventory 3D position. As shown in Figure 13, as the value of \(sin\) between straight-line pairs increases, the error decreases; conversely, as the sine value decreases, the error increases. In other words, the sine value of the angle between straight-line pairs and the error of the estimated 3D position are inversely proportional. Visualization results suggest that the inventory 3D position estimated with all straight-line pairs can be corrected for error by using the sin value as a weight. Unlike previous studies using markers attached to shelves and grids [20], this paper proposes a novel framework for inventory management automation in all warehouses, including shelves and gridless warehouses.