# Cascaded Regression-Based Segmentation of Cardiac CT under Probabilistic Correspondences
## 3 Results
### System Evaluation
We tested the proposed method by varying the vertex number of 3D model \(n_{M}\) in Table 3. Experiments only show that a small \(n_{M}\) of 3000 or 4500 can degrade the segmentation accuracy. As \(n_{k}\) statistics is 9219 \(\pm\) 1696, a selection of 3000 and 4500 can make shape loss. Since there is not much difference between 6000 and 7500, we selected 6000 as \(n_{M}\) in experiments of Tables 1 and 2. \begin{table}
\begin{tabular}{l l l l l l l} \hline  & **SSD(LV)** & **SSD(LA)** & **SSD(LH)** & **HD(LV)** & **HD(LA)** & **DC(LH)** \\  & **(mm)** & **(mm)** & **(mm)** & **(mm)** & **(mm)** & **(\%)** \\ \hline PairICP & 2.59 \(\pm\) 0.96 & 3.61 \(\pm\) 1.15 & 3.10 \(\pm\) 1.01 & 17.33 \(\pm\) 5.60 & 24.73 \(\pm\) 5.48 & 70.51 \(\pm\) 9.33 \\  & *** & *** & *** & *** & *** & *** \\ GroupICP & 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 \\  & * & * & ** & * & *** & *** \\ \hline \end{tabular}  
* All \(p\) values derive from paired \(t\)-tests comparing ICP registration with cascaded regression method.
* \(p<0.05\), *
* \(p<0.01\), **
* \(p<\)0.001. PairICP: evaluation result of ICP registration with pairwise correspondence construction method, GroupICP : segmentation result of ICP registration with group-wise correspondence construction method of the proposed method.  
\end{table} 
Table 2: ICP registration result comparison according to correspondence construction methods. This result is calculated with 35 cases under six-fold cross-validation. Figure 4: Training curves of the proposed method in six-folds. \begin{table}
\begin{tabular}{l l l l l l l} \hline  & **SSD(LV)** & **SSD(LA)** & **SSD(LH)** & **HD(LV)** & **HD(LA)** & **DC(LH)** \\  & **(mm)** & **(mm)** & **(mm)** & **(mm)** & **(mm)** & **(\%)** \\ \hline
3000 & 2.25 \(\pm\) 0.35 & 2.40 \(\pm\) 0.51 & 2.33 \(\pm\) 0.34 & 13.76 \(\pm\) 2.41 & 19.26 \(\pm\) 5.50 & 79.29 \(\pm\) 4.09 \\  & *** & *** & *** & *** & *** \\
4500 & 2.05 \(\pm\) 0.36 & 2.35 \(\pm\) 0.62 & 2.20 \(\pm\) 0.38 & 15.17 \(\pm\) 2.53 & 19.76 \(\pm\) 5.65 & 79.90 \(\pm\) 4.83 \\  & *** & *** & *** & *** & *** \\
6000 & 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 \\  & 1.88 \(\pm\) 0.37 & 2.25 \(\pm\) 0.51 & 2.06 \(\pm\) 0.34 & 14.71 \(\pm\) 2.59 & 19.10 \(\pm\) 5.17 & 80.45 \(\pm\) 4.27 \\  & * & * & * & & & \\ \hline \end{tabular}  
* All \(p\) values derive from paired \(t\)-tests comparing the proposed method of \(n_{M}\) of 6000 with other methods.
* \(p<0.05\), *
* \(p<0.01\), **  
\end{table} 
Table 3: Segmentation results of group-wise separate according to vertex number of 3D model \(n_{M}\). This result is calculated with 35 cases under six-fold cross-validation. As the additional experiment, we checked which model is better between a combined model of two objects and a separate shape model. We can duplicate the shape eigenvector and set the other part of this eigenvector to zero. Under this condition, a combined model with 26 shape eigenvectors extended to a separate model with 46 eigenvectors. The number 6 here is the number of shape eigenvectors. The evaluation result of the separate model in \(n_{M}\) of 6000 was (1.91 \(\pm\) 0.37 mm, 2.24 \(\pm\) 0.52 mm *, 2.07 \(\pm\) 0.32 mm **, 14.38 \(\pm\) 2.82 mm, 19.21 \(\pm\) 5.18 mm, 81.45% \(\pm\) 3.84%***), where * \(p<\) 0.05, ** \(p<\) 0.01, and *** \(p<\)0.001. All p values derive from paired \(t\)-tests comparing the separate model with the proposed method. The separate model with 46 eigenvectors was slightly better than the proposed method, although conflict between LA and LV could occur in a separate model.