## 5 Experimental Results
### Results
#### 5.4.1 Components of LMVSegRNN Gradually Improve Its Performance  
Quantitative results of the ablation study are summarized in Table 1. The results regarding the input format reveal a couple of key insights. * Input format: First, depth information is crucial for robustly representing intricate tooth shapes, while normal maps alone represent the teeth less informatively. Second, stacking normal maps with depth maps enables learning a promising inductive bias for improving the results at the tooth-gingiva boundary. Curvature information in normal maps enables the network to generate smoother and more consistent segmentation results, particularly in complex and irregular boundary regions. * Tooth type input signal: Incorporating additional input signals that convey tooth type information from the decoder delivers better results, speeds up training convergence, and enhances training stability. These findings support the hypothesis that adopting a detect-and-segment approach is beneficial. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\(\mathbf{Ds}\)} & \multirow{2}{*}{\(\mathbf{Ns}\)} & \multirow{2}{*}{\(\mathbf{i_{tt}}\)} & \multirow{2}{*}{_Deep s._} & \multirow{2}{*}{_LSTMs_} & \multirow{2}{*}{_CCA_} & \multirow{2}{*}{_Voting_} & \multicolumn{2}{c}{**Basic Cases**} & \multicolumn{2}{c}{**Complex Cases**} \\  & & & & & & & **\(\mathbf{W\text{-}IoU\uparrow}\)** & \multicolumn{2}{c}{**\(\mathbf{W\text{-}IoU\uparrow}\)**} \\ \hline ✓ & & & & & & & \(0.91759\pm 0.087\) & \(0.91857\pm 0.067\) \\  & ✓ & & & & & & \(0.90898\pm 0.093\) & \(0.88943\pm 0.101\) \\ ✓ & ✓ & & & & & & \(0.92045\pm 0.125\) & \(0.92670\pm 0.011\) \\ ✓ & ✓ & ✓ & & & & & \(0.92811\pm 0.103\) & \(0.92564\pm 0.065\) \\ ✓ & ✓ & ✓ & ✓ & & & & \(0.92826\pm 0.090\) & \(0.92980\pm 0.098\) \\ ✓ & ✓ & ✓ & ✓ & ✓ & & & \(0.94796\pm 0.105\) & \(0.94438\pm 0.051\) \\ ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & & \(0.95145\pm 0.105\) & \(0.95132\pm 0.047\) \\ ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & \(\mathbf{0.97676\pm 0.084}\) & \(\mathbf{0.97122\pm 0.038}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Ablation studies on various method components. Ds: depth information at the input in the form of depth maps. Ns: curvature information at the input in the form of normal maps. \(i_{tt}\): tooth type input signal. Deep s.: deep supervision. LSTMs: bi-directional ConvLSTM units for inter-viewpoint content. Voting: region voting for correcting unprojected segmentation masks. CCA: connected component analysis for removing isolated region cells. Results in bold are for the best-performing method. * Deep supervision: Auxiliary segmentation heads in the intermediate layers of the decoder, optimized with the same loss, increase training stability and speed up convergence. These aspects are essential in overfitting prevention when learning from medical data. * Recurrent units: Without imposing an inter-view context, the generated segmentation masks exhibit inconsistent region boundaries, appearing unnatural in some cases, featuring spiky and jagged artifacts. The addition of recurrent units improves the smoothness of region boundaries, which is particularly important for practical applications, as it reduces the need for minor and potentially unnecessary adjustments that do not affect the method's usability. The performance gain (approximately 2% in overlap metric for both simple and complex cases) also suggests that including LSTM layers enhances the understanding of the 3D nature of the data. * Region voting: Introducing the region voting procedure results in substantial improvement (2% on complex test set). Each tooth region is assessed independently and is successively back-projected to the mesh surface sequentially. Any inaccurate segmentation (typically predicted from one viewpoint) is corrected thanks to the computed multi-view certainty. The substantial impact of this module can be seen in Figure 4. It is evident that it suppresses significant errors on surfaces close to areas of contact with neighboring teeth.