# 2D/3D Multimode Medical Image Registration Based on Normalized Cross-Correlation
## 4 Discussion  
From the intuitive comparison of the three experiments, it can be concluded that after introducing gradient information or edge information, the registration performance of the new normalized correlation is significantly improved compared with the original normalized cross-correlation. Furthermore, from the perspective of image qualitative analysis, the improved normalized cross-correlation based on the LOG operator is better than that of the Sobel operator. Finally, we will verify the above conclusion through the quantitative statistical analysis of the registration results. From the statistical results, when CT and DRR simulated X-ray images are registered, the average values of MTRE and MAE of NCC based on the LOG operator are significantly improved compared with the original NCC. NCC's performance based on the Sobel operator is also improved compared with the original NCC in MTRE and MAE's mean value. It is smaller than the NCC based on the Sobel operator, but the gap is smaller. NCC's registration time based on the Sobel operator or LOG operator is longer than that of the original NCC. This is because the two improved algorithms need to extract image features through the Sobel operator or LOG operator while calculating the original NCC. Each iteration of the rigid body transformation parameter update needs to re-extract features. However, due to NCC calculation and feature extraction's sequential execution, unnecessary time waste can be caused. Hence, the registration time gap can be further reduced by optimizing the code. According to the results in Table 2, when the translation parameter is small and the rotation parameter reaches 40 degrees, both the original NCC and the log-based NCC cannot achieve accurate registration. In contrast, the NCC based on the Sobel operator can still achieve enough registration accuracy. However, the accuracy is slightly reduced compared with the registration experiment with a small angle. When the rotation parameter is small and the translation parameter reaches 40 mm, NCC registration based on the Sobel operator can still be achieved within acceptable accuracy compared with the original NCC and LOG operator. Compared with the original NCC experiment, the larger the difference \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **Rotation (\({}^{\circ}\))** & **Translation (mm)** \\ \hline \multirow{2}{*}{NCCS} & MAE & 0.5254 & \multirow{2}{*}{0.6491} \\  & time & & 2477.6 s \\ \hline \multirow{2}{*}{NCCL} & MAE & 0.4712 & \multirow{2}{*}{0.6250} \\  & time & & 1202.2 s \\ \hline \multirow{2}{*}{NCC} & MAE & 1.0858 & \multirow{2}{*}{1.0259} \\  & time & & 1291.6 s \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Data table of multiresolution experiment results. Figure 10: Multiresolution registration difference image. (**a**) Based on NCCS registration difference image; (**b**) based on NCCL registration difference image; (**c**) based on NCC registration difference image. between the true value point and the initial value point in the rotation parameters, the more difficult it is to approach the true value. This is because the order of rigid body transformation is rotation first and then translation. NCC is more sensitive to translation, so it is challenging to ensure rotation accuracy, limiting the translation's accuracy. The improved Sobel operator increases the algorithm's sensitivity to the rotation, thus increasing NCC's convergence range. To sum up, introducing edge information through the LOG operator or introducing angle information of the gradient vector through the Sobel operator can reduce the registration indexes MAE and MTRE of normalized cross-correlation. Both can improve registration accuracy and registration stability. The LOG operator's edge information can significantly improve the normalized cross-correlation as far as the registration accuracy is concerned.