# Accurate Landmark Localization for Medical Images Using Perturbations
## 4 Results
### Quantitative Performance Comparison with Existing Studies
Figure 4b shows MRE curves for the ISBI 2015 test1 dataset. As Table 4 illustrates, the edge perturbation depicted with red line leads other perturbations. MRE curves on Figure 5 are shown according to different epochs. Between the 20 th and 50 th epochs, the network performance has improved dramatically. After the 500 th epoch, the network performance has improved slightly. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{\(\boldsymbol{PE_{all}}\) **(pxl)**} & \multicolumn{3}{c}{**EDR (\%)**} \\ \cline{2-7}  & **Median** & **Mean \(\pm\) SD** & **\textgreater{}2 mm** & **\textgreater{}2.5 mm** & **\textgreater{}3 mm** & **\textgreater{}4 mm** \\ \hline [PERSON] [15] & n/a & \(16.7\pm\text{n/a}\) & 26.32\% & 19.79\% & 14.81\% & 8.53\% \\ \hline [PERSON] [32] & n/a & \(16.91\pm\text{n/a}\) & 23.82\% & 18.60\% & 14.21\% & 8.88\% \\ \hline [PERSON] [41] & n/a & n/a & 24.63\% & 19.08\% & 15.68\% & 11.75\% \\ \hline [PERSON] [29] & n/a & n/a & 17.50\% & 13.60\% & 10.70\% & 9.40\% \\ \hline [PERSON] [35] & n/a & \(11.7\pm\text{n/a}\) & 13.33\% & **7.33\%** & **4.46\%** & **1.65**\% \\ \hline [PERSON] [11] & n/a & \(11.81\pm\text{n/a}\) & 13.80\% & 8.80\% & 5.60\% & 2.30\% \\ \hline Edge detection perturbator (U-net) & 8.90 & \(11.78\pm 12.37\) & 14.42\% & 8.77\% & 5.65\% & 2.28\% \\ \hline Edge detection perturbator (Attention U-net) & **8.86** & \(\mathbf{11.48\pm 11.08}\) & \(\mathbf{13.26\%}\) & 7.89\% & 4.91\% & 1.79\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Quantitative comparison with existing methods on the ISBI 2015 dataset (test1). Figure 4: MRE curves according to different perturbations. (**a**) Digital Hand Atlas dataset (U-Net). (**b**) ISBI 2015 test1 dataset (U-Net). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{\(\boldsymbol{PE_{all}}\) **(pxl)**} & \multicolumn{3}{c}{**EDR (\%)**} \\ \cline{2-7}  & **Median** & **Mean \(\pm\) SD** & **\textgreater{}2 mm** & **\textgreater{}2.5 mm** & **\textgreater{}3 mm** & **\textgreater{}4 mm** \\ \hline [PERSON] [15] & n/a & \(19.20\pm\text{n/a}\) & 33.89\% & 28.00\% & 22.37\% & 12.57\% \\ \hline [PERSON] [32] & n/a & \(20.58\pm\text{n/a}\) & 32.41\% & 25.84\% & 19.84\% & 12.32\% \\ \hline [PERSON] [41] & n/a & n/a & 32.32\% & 25.84\% & 20.89\% & 15.37\% \\ \hline [PERSON] [29] & n/a & n/a & 27.60\% & 23.85\% & 20.35\% & 14.10\% \\ \hline [PERSON] [35] & n/a & \(14.80\pm\text{n/a}\) & 24.95\% & 17.16\% & 11.47\% & 4.95\% \\ \hline [PERSON] [11] & n/a & \(\mathbf{14.45\pm\text{n/a}}\) & **24.11\%** & **16.64**\% & **10.74**\% & **4.27**\% \\ \hline Edge detection perturbator (U-net) & 10.71 & 14.82 \(\pm\) 13.45 & 25.58\% & 17.74\% & 11.53\% & 5.42\% \\ \hline Edge detection perturbator (Attention U-net) & **9.96** & \(15.30\pm\mathbf{12.65}\) & 25.21\% & 18.05\% & 12.95\% & 6.79\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Quantitative comparison with existing methods on the ISBI 2015 dataset (test2). Figure 6 show the landmarks on the original image by overlapping the ground truths (red dots) and the predictions (blue dots) for the Digital Hand Atlas and ISBI datasets, respectively. The figures illustrate that our model predicted the landmarks very closely to the ground truth. Figure 5: MRE curves according to different epochs. (**a**) Digital Hand Atlas dataset (Hybrid with U-Net). (**b**) ISBI 2015 test1 dataset (Edge Detection with U-Net). Figure 6: Visualization of landmarks of a sample test image in the Digital Hand Atlas and ISBI 2015 datasets. Red dots are the ground-truth of image, and green dots are the prediction result of U-Net with the hybrid perturbation model. (**a**) Digital Hand Atlas. (**b**) ISBI 2015.