# Medical Augmented-Reality Visualizer for Surgical Training and Education in Medicine
## 3 Results
### Head-Tracking Accuracy  
To validate the head-tracking accuracy of MARVIS, several points (Figure 15) near the edges of the calibration volume were selected for calculating the reprojection error. For the image plane in the middle of the calibrated volume, one pixel of the HdTM camera image corresponds to 2.5 mm. The obtained results listed in Table 3 confirm an angular accuracy below 0.1 degree [34], which is sufficient to track the user's head viewing direction. This is used for determining the orientation of the user's viewpoint in the global coordinate system and then to enable parallax motion. The accuracy of this measurement is crucial to prevent the vergence-accommodation conflict.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{\(X_{0}\)}} & \multicolumn{3}{c}{**Marker 1**} & \multicolumn{3}{c}{**Marker 2**} & \multicolumn{3}{c}{**Marker 3**} & \multicolumn{3}{c}{**Marker 4**} \\ \hline  & \multicolumn{3}{c}{**On**} & \multicolumn{3}{c}{**On**} & \multicolumn{3}{c}{**On**} & \multicolumn{3}{c}{**On**} & \multicolumn{3}{c}{**On**} & \multicolumn{3}{c}{**On**} & \multicolumn{3}{c}{**On**} & \multicolumn{3}{c}{**On**} & \multicolumn{3}{c}{**On**} \\  & \multicolumn{3}{c}{**Camera**} & \multicolumn{3}{c}{**Projector**} & \multicolumn{3}{c}{**Camera**} & \multicolumn{3}{c}{**Projector**} & \multicolumn{3}{c}{**Camera**} & \multicolumn{3}{c}{**Projector**} & \multicolumn{3}{c}{**Camera**} & \multicolumn{3}{c}{**Projector**} & \multicolumn{3}{c}{**Camera**} & \multicolumn{3}{c}{**Projector**} \\ \hline \(Z\) & \(X\) & \(Y\) & \(X\) & \(Y\) & \(X\) & \(Y\) & \(X\) & \(Y\) & \(X\) & \(Y\) & \(X\) & \(Y\) & \(X\) & \(Y\) \\ \hline
**[mm]** & [mm]** & [mm] & [mm] & [mm] & [mm] & [mm] & [mm] & [mm] & [mm] & [mm] & [mm] & [mm] & [mm] & [mm] & [mm] & [mm] \\ \hline
55.5 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\
65.5 & \(-\)0.02 & 0.01 & \(-\)0.04 & 0.02 & 0.011 & 0.00 & 0.03 & 0.02 & \(-\)0.02 & 0.01 & 0.07 & 0.00 & 0.014 & \(-\)0.00 & 0.02 & 0.00 \\
75.5 & \(-\)0.01 & 0.02 & 0.00 & 0.03 & \(-\)0.01 & \(-\)0.02 & \(-\)0.02 & 0.02 & 0.01 & 0.02 & 0.17 & 0.00 & 0.00 & \(-\)0.01 & 0.00 & 0.00 \\
85.5 & \(-\)0.01 & 0.04 & 0.00 & \(-\)0.08 & 0.01 & 0.01 & 0.11 & 0.03 & \(-\)0.01 & \(-\)0.01 & 0.05 & \(-\)0.03 & \(-\)0.02 & \(-\)0.02 & 0.00 \\
95.5 & \(-\)0.02 & 0.05 & \(-\)0.01 & 0.03 & \(-\)0.02 & 0.01 & 0.03 & 0.04 & 0.01 & 0.01 & 0.12 & \(-\)0.01 & \(-\)0.01 & \(-\)0.02 & \(-\)0.01 & \(-\)0.05 \\
105.5 & \(-\)0.02 & 0.06 & \(-\)0.01 & \(-\)0.01 & \(-\)0.04 & 0.01 & \(-\)0.04 & 0.05 & 0.02 & \(-\)0.00 & 0.17 & \(-\)0.02 & 0.02 & \(-\)0.04 & 0.02 & \(-\)0.18 \\
112.8 & 0.01 & 0.05 & 0.00 & \(-\)0.05 & \(-\)0.01 & 0.00 & \(-\)0.02 & 0.03 & 0.00 & 0.00 & 0.11 & \(-\)0.01 & 0.00 & \(-\)0.02 & \(-\)0.02 & \(-\)0.16 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Object-tracking reprojection error at specific height (along \(Z\)-axis) above the table.  
Figure 14: Object tracking accuracy calculated for four calibration markers (1–4) at heights above the working table in the range of 55–112.5 mm imposed by mechanical limits of the lift table.