# Optical Flow Odometry with Panoramic Image Based on Spherical Congruence Projection
## 4 Experiments and Discussion
### Comparative Experimental Results
In the SCP-Image dataset, the alignment of the panoramic image's optical axis with the motion direction causes feature points to undergo rapid shifts when they move from the polar region to the equatorial region, causing significant changes in the degree of distortion. The proposed SCP-VIO leverages the consistency of distortion across the panoramic image in the spherical structure, ensuring that the projected subregions retain uniform distortion, greatly enhancing the accuracy of optical flow tracking. Figure 11 illustrates the comparison of trajectories in the SCP-Image dataset. In summary, SCP-VIO efficiently improves the accuracy of the odometry based on panoramic images compared to conventional odometry methods. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**VIO-Method** & **Index** & \begin{tabular}{c} **ID01** \\ **CI** \\ \end{tabular} & \begin{tabular}{c} **ID02** \\ **CI** \\ \end{tabular} & \begin{tabular}{c} **ID03** \\ **CI** \\ \end{tabular} & \begin{tabular}{c} **ID04** \\ **CI** \\ \end{tabular} \\ \hline \multirow{3}{*}{\begin{tabular}{c} SCP \\ -VIO \\ \end{tabular} } & RPEt (\%) & [1.629,1.971] & [1.272,1.423] & [2.028,2.232] & [0.052,0.161] \\  & RPEt (deg/m) & [1.033,1.121] & [0.531,0.606] & [0.458,0.523] & [0.450,0.505] \\  & ATE (m) & [0.963,0.982] & [0.325,0.344] & [0.372,0.393] & [0.213,0.223] \\ \hline \multirow{3}{*}{\begin{tabular}{c} LF \\ -VIO \\ \end{tabular} } & RPEt (\%) & [2.550,2.837] & [1.278,1.455] & [1.092,1.222] & [0.916,0.982] \\  & RPEt (deg/m) & [1.162,1.263] & [0.458,0.515] & [0.466,0.510] & [0.421,0.536] \\  & ATE (m) & [0.935,0.996] & [0.376,0.398] & [0.261,0.276] & [0.304,0.321] \\ \hline \multirow{3}{*}{\begin{tabular}{c} VINS \\ -MONO \\ \end{tabular} } & RPEt (\%) & [3.524,3.923] & [1.557,1.761] & [2.205,2.397] & [1.492,1.625] \\  & RPEt (deg/m) & [1.364,1.545] & [0.421,0.606] & [0.406,0.451] & [0.491,0.550] \\  & ATE (m) & [1.300,1.377] & [0.501,0.533] & [0.690,0.729] & [0.406,0.423] \\ \hline \multirow{3}{*}{VIO Method} & \multirow{3}{*}{Index} & ID05 & ID06 & ID07 & ID08 \\  & & CI & CI & CI & CI \\ \hline \multirow{3}{*}{\begin{tabular}{c} SCP \\ -VIO \\ \end{tabular} } & RPEt (\%) & [1.112,1.222] & [1.042,1.174] & [1.060,1.149] & [1.169,1.307] \\  & RPEt (deg/m) & [0.400,0.455] & [0.637,0.774] & [0.482,0.533] & [5.422,6.509] \\  & ATE (m) & [0.192,0.204] & [0.108,0.120] & [0.187,0.199] & [0.178,0.193] \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} LF \\ -VIO \\ \end{tabular} } & RPEt (\%) & [1.326,1.478] & [1.081,1.219] & [1.069,1.150] & [1.231,1.374] \\  & RPEt (deg/m) & [0.393,0.442] & [0.563,0.682] & [0.478,0.524] & [5.381,6.451] \\  & ATE (m) & [0.261,0.281] & [0.108,0.120] & [0.201,0.214] & [0.246,0.259] \\ \hline \multirow{3}{*}{
\begin{tabular}{c} VINS \\ -MONO \\ \end{tabular} } & RPEt (\%) & [1.612,1.793] & [3.271,3.813] & [5.132,5.809] & [3.119,3.627] \\  & RPEt (deg/m) & [0.434,0.479] & [0.442,0.512] & [0.482,0.529] & [5.581,6.750] \\ \cline{1-1}  & ATE (m) & [0.347,0.370] & [1.437,1.496] & [2.795,2.910] & [0.448,0.481] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The confidence interval of RMSE on PAL-VIO dataset. To evaluate the robustness of SCP-VIO under sensor noise, we conducted further experiments. Table 5 presents the odometry accuracy of SCP-VIO, LF-VIO, and VINS-MONO under varying levels of Gaussian noise (\(\sigma=10,25,50\)). The results show that SCP-VIO consistently achieved better robustness than the other methods across all noise levels. For instance, at \(\sigma=50\), SCP-VIO maintained a lower RPE of 2.829% and ATE of 1.067 m, whereas LF-VIO and VINS-MONO exhibited much larger errors. The performance gap became more significant under stronger noise, which indicates the advantage of our robust flow tracking strategy and spherical image representation. Furthermore, VINS-MONO failed to provide usable estimates under \(\sigma=25\) and \(\sigma=50\), suggesting that monocular tracking is highly vulnerable in noisy conditions. Figure 11: The trajectories for SCP-VIO, LF-VIO, and VINS-MONO in the self-built SCP-Image dataset.