# Feature-Oriented CBCT Self-Calibration Parameter Estimator for Arbitrary Trajectories: FORCAST-EST
## 4 Discussion  
This paper describes the FORCAST-EST algorithm, which is able to approximate the initial parameters for the calibration of arbitrary CBCT trajectories. Based on the literature review, this algorithm is the first estimator that uses only online calibration techniques. The results have shown that the estimated parameters are close enough to the correct parameters, such that state-of-the-art algorithms can successfully calibrate the trajectory. The  
Figure 10: Reconstructions of the continuous arc when using the proposed estimator, as well as CMA-ES with the NGI objective and the FDK algorithm from the astra toolbox. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Algorithm** & **NGI** & **SSIM** & **NRMSE** & **Dice \({}^{\dagger}\)** \\ \hline Coarse estimate & 0.353 \({}^{\star}\) & 0.360 \({}^{\star}\) & 0.3567 \({}^{\star}\) & 0.00 \({}^{\star}\) \\ Refined estimate & 0.446 & 0.418 & 0.2379 & 0.82 \\ Est. + FORCASTER & 0.510 \({}^{\star}\) & 0.473 \({}^{\star}\) & 0.2114 \({}^{\star}\) & 0.84 \\ Est. + CMA-ES \& NGI & 0.535 \({}^{\star}\) & 0.535 \({}^{\star}\) & 0.1958 \({}^{\star}\) & 0.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Metric results for the arc reconstruction. The dice \({}^{\dagger}\) was evaluated on a segmentation of the large metal object in the phantom in comparison to the segmentation of this object in the reconstructed image from the regular CBCT trajectory. Values marked with an \({}^{\star}\) had significant (\(p<0.05\)) changes compared to the refined estimate. Figure 9: Two slices out of the arc trajectory sinogram from the acquired data, as well as from the calibration with refined estimates and CMA-ES with the NGI objective. The left column is (**a**) ordered from top to bottom as follows: acquired data, and the simulated projections from the calibration with estimated starting parameters. The right columns (**b**) have the same order, also from left to right. Since there were no positional data reported by the Artis Zeego System, there was no calibration without estimated parameters conducted. reconstructed images are of comparable quality to those that have been reconstructed after calibration with close-to-accurate starting positions. The Dice score achieved by both algorithms was very high \(\geq\)0.99, which means the metal object in the center was reconstructed correctly. The CBCT calibrations also produced very high SSIM values (>0.999), such that they are very close to the reference calibration. These metric values are comparable to those previously reported for the FORCASTER calibration [10]. The estimation, therefore, does not reduce the quality of the reconstructed images. A comparison to the calibration algorithm was developed by [PERSON] et al. [17], and this was meant to be used in this paper. However, this was not possible since the calibration algorithm uses metrics that require specific objects in the measured phantom, and these were not included in the object scanned for this work. For the CBCT trajectory, the refined estimate needed about one and a half hours, while together with the CMA-ES algorithm it took five and a half hours for the calibration. As such, the estimation was less than 30% of the total runtime; furthermore, this difference was even higher for the arc calibration, where the estimation only contributed 20%. Further, in contrast to the approaches by [PERSON] et al. or [PERSON] et al. [18,19], no modification of the CBCT-Device was necessary to estimate the parameters. If the modification of the C-Arm is possible and allowed, the addition of more sensors might be the preferred option. Removing the dependency on roughly accurate starting parameters comes with the cost of a higher computation time. In the experiments, there was a steep increase in the time when compared to the calibration that had its starting parameters provided by the CBCT device. Still, every projection was optimized separately from one another, and they also independently used the calibration algorithm.