# Feature-Oriented CBCT Self-Calibration Parameter Estimator for Arbitrary Trajectories: FORCAST-EST
## 3 Results  
The results obtained from comparing the sinograms are in Table 1. The similarity index and NGI are low for the coarse estimate, but they increased significantly after refining. When using the FORCASTER algorithm with the estimated positions, the SSIM and NRMSE were comparable to the ones reported by [PERSON] et al. [10]. Similar to the results from the sinograms, the metrics evaluated on the reconstructions, shown in Table 2, showed a significant improvement in the refined estimate over the coarse one. Here, the NRMSE and Dice functions, after estimating and applying FORCASTER, were also comparable to the ones previously reported. There was no significant difference (\(p=0.56\)) between the Dice values of the two reconstructions when using the state-of-the-artalgorithms and refined estimates; however, the other metrics--NGI, SSIM, and NRMSE--were significantly better for the CMA-ES calibration. The reconstructed images are shown in Figure 6. The top row contains the reconstruction after only performing the rough estimate. There were obvious artifacts visible, which can be seen in the left column. These artifacts are regularly spaced and rotated around the center in the plane of the acquisition trajectory. Several edges were reconstructed twice with a slight offset. In the second row, the refined estimate was used for reconstruction. The radial artifacts are still there, but the double edges are now consolidated. Finally, the reconstruction without these radial artifacts is in the bottom row. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Algorithm** & **Runtime [hh:mm]** & **NGI** & **SSIM** & **NRMSE** \\ \hline Coarse Estimate & 01:06 & 0.397 * & 0.944 * & 0.2327 * \\ Refined Estimate & 01:26 & 0.753 & 0.992 & 0.0669 \\ Est. + FORCASTER & 03:28 & 0.919 * & 0.999 * & 0.0190 * \\ Est. + CMA-ES \& NGI & 05:39 & 0.983 * & 1.000 * & 0.0037 * \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results for the metrics evaluation on the CBCT sinogram. The two bottom rows used the refined estimate as the input for the FORCASTER algorithm, and this was achieved once with the NGI objective and once with the objective when based on feature points. The values marked with an * had significant (\(p<0.05\)) changes compared to the refined estimate. Figure 6: Reconstructions of the different steps of the algorithms. From top to bottom is as follows: Coarse estimate, Refined estimate and Refined estimate + CMA-ES when using the NGI objective. Figure 7 shows the sinograms for the sinusoidal trajectory. The calibrated sinograms are the forward projections of the prior CT image. Because this image does not contain the complete object, these two sinograms are missing structures in comparison to the acquired images. One easily spotted difference is in column (b) in the top right quadrant, which is missing a high-contrast object. In the sinogram obtained with estimated starting parameters, i.e., in the bottom row in column (a) and the right image in column (b), there is a distortion visible at the top (column (a)) and left edge (column (b)). This is more pronounced in the sinograms that were calibrated with FORCASTER than the ones calibrated with CMA-ES. This is a projection where the algorithm did not estimate the starting parameters close to the correct ones, and where the calibration did not succeed. This projection is shown in Figure 8 alongside the acquired image and the projection from the correctly calibrated parameters. \begin{table}
\begin{tabular}{l c c c c} \hline
**Algorithm** & **NGI** & **SSIM** & **NRMSE** & **Dice \({}^{\dagger}\)** \\ \hline Coarse estimate & 0.372 * & 0.290 * & 0.7898 * & 0.60 * \\ Refined estimate & 0.525 & 0.360 & 0.5485 & 0.96 \\ Est. + FORCASTER & 0.766 * & 0.677 * & 0.1627 * & 0.99 * \\ Est. + CMA-ES \& NGI & 0.944 * & 0.979 * & 0.0295 * & 1.00 * \\ \hline \end{tabular}
\end{table} 
Table 2: Results for the evaluation of the CBCT reconstructions. The dice \({}^{\dagger}\) was evaluated on a segmentation of the large metal object in the phantom.