# Cascaded Regression-Based Segmentation of Cardiac CT under Probabilistic Correspondences
## 3 Results
### System Evaluation  
The evaluation metrics between two gold-standard masks of two operators were calculated for the comparison of difference. (1.06 \(\pm\) 0.14 mm, 0.97 \(\pm\) 0.12 mm, 1.02 \(\pm\) 0.12 mm, 9.98 \(\pm\) 2.83 mm, 10.60 \(\pm\) 11.21 mm, 89.33% \(\pm\) 1.87%) were the results of the evaluation, which are denoted as (LV SSD, LA SSD, LV HD, LA HD, LH DC). Since the extent of the structure in four major pulmonary vessels of LA might be different between two gold-standard masks, DC could be lowered to some degree. The repeatability of gold-standard generation can be estimated as 0.51 mm since the repeatability is calculated as the standard deviation of test sets. According to Table 1, the proposed method produced a significantly better result in LH SSD and DC metric than every three methods. The group-wise method showed the performance improvement of LA SSD compared with the pairwise method from 2.88 \(\pm\) 0.70 mm to 2.31 \(\pm\) 0.53 mm. When the atlas of the LA was constructed in the pairwise correspondence method, the structure of four major pulmonary vessels was smoothed. This problem was removed in the proposed method. Group-wise 1 method performs correspondence construction without separate object control. In LV, the inner and outer surface can have a dependence on the soft correspondence construction of GMM. The proposed method showed significantly better LV SSD of 1.94 \(\pm\) 0.34 mm than 2.34 \(\pm\) 0.44 mm of Group-wise 1 method. Because of dependence in two surfaces of LV, Group-wise 1 method's LV SSD is worse than the pairwise method's. In six-folds, training curves of the proposed method are shown in Figure 4.  
The iterative closest point (ICP) method minimizes the difference between two clouds of point [37]. We performed the ICP method with a trained shape model under six-fold cross-validation. Since point cloud extracted from gold-standard mask directly is used for registration of shape model, the appearance of LH is not considered in this registration. In Table 2, PairICP produced the significantly worse result in every metric than the cascaded segmentation of the pairwise method. However, GroupICP showed a registration result reaching the proposed method with a slight difference significance. If the ICP method is improved from simple ICP, then the registration result will be improved. DC was calculated under the appearance correspondence of cascaded regression. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline  & **SSD(LV)** & **SSD(LA)** & **SSD(LH)** & **HD(LV)** & **HD(LA)** & **DC(LH)** \\  & **(mm)** & **(mm)** & **(mm)** & **(mm)** & **(mm)** & **(\%)** \\ \hline Initial & 3.90 \(\pm\) 1.15 & 4.77 \(\pm\) 1.25 & 4.34 \(\pm\) 1.02 & 21.81 \(\pm\) 4.21 & 29.62 \(\pm\) 6.79 & 51.99 \(\pm\) 8.14 \\  & *** & *** & *** & *** & *** & *** \\ Pairwise & 2.00 \(\pm\) 0.47 & 2.88 \(\pm\) 0.70 & 2.44 \(\pm\) 0.48 & 13.50 \(\pm\) 2.74 & 22.86 \(\pm\) 5.68 & 78.05 \(\pm\) 4.20 \\  & *** & *** & *** & *** & *** & *** \\ Group-wise 1 & 2.34 \(\pm\) 0.44 & 2.29 \(\pm\) 0.61 & 2.32 \(\pm\) 0.40 & 15.49 \(\pm\) 2.49 & 19.52 \(\pm\) 5.29 & 73.65 \(\pm\) 5.84 \\  & *** & *** & *** & *** & *** & *** \\ Proposed & 1.94 \(\pm\) 0.34 & 2.31 \(\pm\) 0.53 & 2.12 \(\pm\) 0.33 & 14.61 \(\pm\) 2.33 & 19.21 \(\pm\) 5.38 & 80.27 \(\pm\) 3.74 \\ \hline \hline \end{tabular}  
* All \(p\) values derive from paired \(t\)-tests comparing the proposed method with each of the three methods.
* \(p<\) 0.05, ** \(p<\) 0.01, *** \(p<\)0.001. Initial: segmentation result of two landmarks, Pairwise : segmentation result of pairwise correspondence construction method, Group-wise 1 : segmentation result of group-wise correspondence construction method without separate object control, Proposed : segmentation result of the proposed method.  
\end{table} 
Table 1: Segmentation result comparison according to correspondence construction methods. This result is calculated with 35 cases under six-fold cross-validation.