# Robust Registration of Medical Images in the Presence of Spatially-Varying Noise
## 3 Results
### Evaluation of the Proposed Algorithms on Retina Images  
So far, we have provided evidence for the superior performance of EMD-based registration methods for the registration of MR images compared to intensity-based methods. Here, we evaluate the proposed approach on retina images and in the presence of additive spatially varying intensity distortion. Retina images are frequently used in the diagnosis of various ophthalmological disorders. These images are often taken at different times. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Similarity** & **Method** & **Convergence \%** & **T-RMSE** & **I-RMSE** \\ \hline \multirow{3}{*}{SSD} & Intensity-based & 61.33\% & 2.393 \(\pm\) 0.375 & 0.075 \(\pm\) 0.008 \\  & LR-EMD & 80\% & 2.088 \(\pm\) 0.309 & 0.073 \(\pm\) 0.008 \\  & AFR-EMD & **90\%** & **1.927 \(\pm\) 0.206** & **0.067 \(\pm\) 0.007** \\ \hline \multirow{3}{*}{CC} & Intensity-based & 76\% & 2.167 \(\pm\) 0.341 & 0.069 \(\pm\) 0.007 \\  & LR-EMD & **100\%** & 2.032 \(\pm\) 0.323 & 0.069 \(\pm\) 0.008 \\  & AFR-EMD & **100\%** & **1.777 \(\pm\) 0.213** & **0.062 \(\pm\) 0.007** \\ \hline \multirow{3}{*}{RC} & Intensity-based & 96\% & 1.331 \(\pm\) 0.142 & 0.048 \(\pm\) 0.003 \\  & LR-EMD & 97.33\% & 1.544 \(\pm\) 0.357 & 0.053 \(\pm\) 0.009 \\  & AFR-EMD & **100\%** & **1.217 \(\pm\) 0.153** & **0.043 \(\pm\) 0.003** \\ \hline \multirow{3}{*}{MI} & Intensity-based & 53\% & 2.205 \(\pm\) 0.516 & 0.062 \(\pm\) 0.009 \\  & LR-EMD & **100\%** & 1.299 \(\pm\) 0.325 & 0.042 \(\pm\) 0.008 \\ \cline{1-1}  & AFR-EMD & **100\%** & **1.054 \(\pm\) 0.266** & **0.035 \(\pm\) 0.007** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the quantitative performance measures. The measures for the best-performing algorithms are highlighted in bold. Figure 8: Target and reference images from IBSR MR dataset and registered images using our two methods and intensity-based hierarchical algorithm. Hence image registration has a crucial role in the accurate comparison of the longitudinal retina images. However, these images are often distorted via a non-uniform background or spatially varying intensity noise. Previous studies have explored the application of vascular structures and landmarks in the registration of these noisy images [48; 49]. However, the registration performance still remains far from perfect. Here, we investigate the application of LR-EMD and AFR-EMD in the registration of retina images. Here, we used category S of the Fundus Image Registration (FIRE) Dataset [47] to evaluate the proposed approaches. The two main challenges of this dataset are strong non-uniform spatially varying intensity distortion and outlier regions appearing in one image but not the other. In this dataset, the registration accuracy is quantified by the ten extracted anatomical landmarks. Hence, the error between landmarks in the reference and registered images as Mean Registration Error (MRE) is used to measure image registration performance. Figure 9 presents the registration performance of the proposed approaches in each case for different similarity measures. Table 2 also shows the average MRE for comparison of different similarity measures. It can be seen that the proposed approaches improve the performance of different similarity measures, especially for three measures of SSD, CC, and MI. These measures are not robust in the presence of spatially varying intensity distortion. The EMD based method results in improvement and robustness of these similarity measures. In addition to the Fundus Image Registration (FIRE) Dataset, we used retina images in [50] taken two years apart (Figure 10A top panel) and visually evaluated the performance \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Average MRE**} \\ \hline
**Similarity Measure** & **Intensity-Based** & **LR-EMD** & **AFR-EMD** \\ \hline SSD & 106.19 & 26.27 & 25.6 \\ \hline CC & 106.19 & 26.27 & 25.6 \\ \hline RC & 22.97 & 15.7 & 18.06 \\ \hline MI & 76.27 & 18.18 & 19.85 \\ \hline \hline \end{tabular}
\end{table}