# Calibration Method of Projectional Geometry for X-ray C-arm Fluoroscopy Using Sinogram Data
## 4 Results  
In the experiments, ten parameters were computed for the geometrical calibration of X-ray projectional imaging, including the SDD, position and orientation of the phantom, and position of the isocenter. The sinogram and 2D projectional X-ray images were obtained, and the evaluation procedures were followed using the software application developed in this study.  
Three different methods were used to analyze the results. First, the accuracy of the calibration method was assessed using the angular range of the sinogram data used in the calibration. As shown in Figure 8, the calibration algorithm was executed under a variety of data size conditions, with the data set ranging from \(-\)15 to 15 to \(-\)60 to 60, increasing 10 degrees at each step. The results are presented in the orange bar graph of Figure 8, which shows that the operation with a wide range of data provided improved accuracy. If the data are wider than the angle from \(-\)40 to 40, the accuracy of the calibration was stable, and further improvement could not be detected. However, as the range of the data increased, so did the computational time for the calibration algorithm, as shown in the blue plot in Figure 8.  
Figure 7: Software application for the geometric calibration of X-ray imaging was implemented, which provides core functions for the calibration and graphical user interface.  
Second, the accuracy of the calibration method was assessed using the data intervals applied to the calibration algorithm. The calibration method was followed in several conditions with different angle intervals but with the same angular range applied to the algorithm, as shown in Figure 9. As illustrated with the orange bar graph in Figure 9, the narrower the angular interval, the smaller the error. The improvement in the error was not dramatic but gradual. Furthermore, as the angular interval widened, the calculation time decreased, which is indicated by the blue plot in Figure 9.  
We also tested the robustness of our method by projecting the 3D positions of the fiducial markers into various angles based on the rotation of the C-arm gantry and calculating the mean error between the projected fiducial positions and the centers of the fiducial markers in the sinogram projection image. Calibrations were performed under five different conditions, as shown in Figure 10, with angular ranges ranging from \(-20\) to \(20\) degrees, \(-30\) to \(30\) degrees, \(-40\) to \(40\) degrees, \(-50\) to \(50\) degrees, and \(-60\) to \(60\) degrees. Based on the results of each trial with different conditions, the 3D fiducial positions were projected into all of the projected images that belong to the sinogram. As illustrated in Figure 10, the evaluation result of the calibration with sinogram data with a range of \(-20\) to \(20\) degrees shows the worst accuracy. The accuracy improved by broadening the data range used by the calibration algorithm. Furthermore, as the angle moved away from \(0\) degrees, the projectional errors in each trial increased, and the gradient became much larger in the rotation angle outside of the range of the data used for calibration. In addition, the wider the angle range, the better the accuracy of the projectional error. Moreover, the gradient is much less for the results with a narrower data range.  
Figure 8: Graph of mean errors (orange bars) and computational time (blue plot) according to different angular ranges applied to the calibration algorithm; the interval of the data is \(0.4\) degrees for each range. The x-axis represents the angular range of the data applied to the calibration. The y-axis on the left and right give the error and computational time, respectively.