## 3 Results
### Tumor Tracking Accuracy  
Figure 4 shows the trajectory of the tumor centroid in 3D along the left-right (L-R), anterior-posterior (A-P), and cranial-caudal (C-C) directions over the different respiratory phases for patients 1 through 4. Note that the scales of the Y-axis coordinates of the three directions are not identical. Among the three directions, the tumor generally moved the greatest in the C-C direction. The tumor coordinates tended to increase or decrease around IN 100% (# 11), the boundary between  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Diaphragm-Elevation Based Method**} & \multicolumn{3}{c}{**Proposed Method**} \\ \cline{2-7}  & **Inhale/Exhale** & **Phase** & **Accuracy** & **Inhale/Exhale** & **Phase** & **Accuracy** \\  & **Identification*** (\%)** & **Deviation*** (\#)** & **(\%)** & **Identification*** (\%)** & **Deviation*** (\#)** & **(\%)** \\ \hline Patient 1 & 68.8 & 4 & 60.4 & 100 & 1 & 97.9 \\ Patient 2 & 41.7 & 24 & 52.1 & 100 & 2 & 95.8 \\ Patient 3 & 39.6 & 18 & 47.9 & 100 & 0 & 100 \\ Patient 4 & 50 & 9 & 41.7 & 100 & 0 & 100 \\ Patient 5 & 41.7 & 24 & 20.8 & 100 & 2 & 95.8 \\ Patient 6 & 47.9 & 49 & 18.8 & 95.8 & 3 & 93.8 \\ Total & 48.3 & 21.3 & \(40.3\pm 17.0\) & 99.3 & 1.3 & \(97.2\pm 2.5\) \\ \hline \hline \end{tabular}  
* Inhale/exhale identification: the accuracy in identifying whether the phase belongs to an inhalation or exhilation;
* Phase deviation: total deviation of the identified respiratory rate from the correct respiratory rate.  
\end{table}
Table 1: The respiratory phase identification performance of the proposed method compared with the previous diaphragm elevation-based method in terms of the inhale/exhale identification, phase deviation, and accuracy.  
the inspiration and expiration. The specific values for the magnitude of the tumor movement for each patient are shown in Table 2. In the case of patient 4 with a tumor close to the diaphragm, the tumor movement was the largest, and the movement in the CC direction was 30.5 mm. Data on two of the patients (patients 5 and 6) were excluded in the tumor motion analysis because their tumors were located far from the diaphragm, that is, near the upper lung, and the magnitude of the tumor motion was approximately one pixel in size as the motion of the diaphragm had little effect on the tumor motion.  
Table 2 shows the 3D tumor tracking accuracy obtained using the proposed method in terms of the Hausdorff surface distance [36] and center-of-mass distance. The surface distance represents the distance between the outer surface of the segmented tumor (i.e., reference) and that of the reconstructed tumor, interpolated through the proposed method. The center-of-mass distance represents the distance between the center of mass of the segmented tumor and that of the reconstructed tumor. As expected, the larger the amplitude of the tumor motion, the greater the likelihood that tumor tracking errors in both metrics increase. However, for all four patients, the tumor was tracked with an accuracy of less than 1 mm, which is close to the in-plane resolution (0.97 \(\times\) 0.97 mm\({}^{2}\)) of the reconstructed 4 DCT volumes.  
Figure 4: The trajectory of the tumor centroid in 3D along left–right (L–R), anterior–posterior (A–P), and cranial–caudal (C–C) directions over the different respiratory phases for patients 1 through 4.