# 2D/3D Multimode Medical Image Registration Based on Normalized Cross-Correlation
## 3 Experiments and Results
### Experimental Evaluation Criteria  
In this paper, the difference between the images after registration is selected for qualitative analysis, and repeated registration experiments are carried out. Furthermore, the mean absolute error (MAE) [52], target registration error (MTRE) [53], and iteration time are selected for quantitative analysis. The registration is considered successful when the errors of rotation and translation parameters are less than 5. _MSE_ is represented by Equation (10), and _MAE_ is represented by Equation (11). \[MSE=\frac{1}{dim}\sum_{i=1}^{dim}\left(T_{reg}(i)-T_{truth}(i)\right)\ ^{2} \tag{10}\]  
\[MAE=\frac{1}{dim}\sum_{i=1}^{dim}\left|T_{reg}(i)-T_{truth}(i)\right| \tag{11}\]  
The original normalized cross-correlation (NCC) algorithm is used as the registration experimental control group to verify the effectiveness and accuracy of the normalized cross-correlation algorithm with the Sobel operator (NCCS) and the normalized cross-correlation algorithm with the LOG operator (NCCL). The experiments are divided into two categories. The first one is to register the original single-resolution image directly. The second is to use a multiresolution strategy for registration. The Powell optimization algorithm's one-dimensional search accuracy in the experiment is set to 0.01. The algorithm's overall iterative accuracy is set to 0.001, and the maximum number of iterations is set to 1000. For the original resolution image registration, three groups of experiments are set up, and the rigid body transformation parameters are arranged according to the order \(\left(\alpha,\beta,\theta,t_{x},t_{y},t_{z}\right)\). The first three parameters are rotation along the X-, Y-, and Z-axes. The last three parameters are translation along the X-, Y-, and Z-axes. The true values of the first group of experimental reference images are set to  
Figure 4: Schematic diagram of projection coordinate system. (\(-\)3,4,2,5,5,5). The second group of experimental reference images is set to (\(-\)3,4,2,10,10,10). Finally, the third group of experimental reference images is set to (5,6,7,8,9,10). In the experiment, the initial value is optimized by (0,0,0,0,0). As shown in Figure 5, the DRR image projected by CT at the initial value is shown. The reference images of the three groups of experiments are shown in Figure 6a-c and correspond to the reference images of experiment 1, experiment 2, and experiment 3, respectively. The results of the first group of experiments are shown in Figure 7. The second group of experimental results is shown in Figure 8, and the third group of experiments is shown in Figure 9. NCCS represents normalized cross-correlation based on the Sobel operator. NCCL represents normalized cross-correlation based on the LOG operator, and NCC represents normalized cross-correlation. Each result display chart is divided into two rows and three columns for comparative analysis of registration results. The first line represents the DRR image generated by CT projection after registration. The second line represents the difference between the reference image and the registered DRR image. The  
Figure 5: DRR image at the initial value. Figure 6: Experimental reference images. (**a**) Experiment 1 reference image; (**b**) experiment 2 reference image; (**c**) experiment 3 reference image. first column corresponds to the normalized cross-correlation based on the Sobel operator from top to bottom. The second column corresponds to the normalized cross-correlation based on the LOG operator. The third column corresponds to the original normalized cross-correlation. The different images of the three experiments show that the difference image is the smoothest when NCC based on the LOG operator is used as the similarity measure. The difference between the registration result and the reference image is the smallest; NCC's registration effect based on the Sobel operator is the second. The difference between the original NCC algorithm and the reference image is the largest. The NCC based on the LOG operator is the largest.