## 3 Experiments and Results
### Experiments in a Noise-Free Setup  
Figure 4 illustrates eight examples of raw images, and the predicted result of a number of different networks, all training on accurate labels: UNet [1], residual UNet [13], dense UNet [13], MultiResUnet [19], LinkNet [38], FPN [39], UNet++ [2], UNet3+ [18], VNet [10], RARUNet [17], and QAPNet [3]. Our NR-UNet was compared with these for a setting of \(\beta=0\) (hence, also training on accurate labels).  
Batch normalization [40] and Dropout [41] were deployed after CNN layers for all UNet-based baseline methods for a fair comparison. A quantitative comparison of NR-UNet against the other ten baseline methods is given in Table 1. The best results are highlighted in bold.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Network (\(\beta=0\))** & **Dice** & **IoU** & **Acc** & **Pre** & **Rec** & **Spe** & **Par\({}^{\phi}\)** \\ \hline FPN [39] & 0.9373 & 0.8821 & 0.9944 & 0.9191 & 0.9563 & 0.9961 & 17.59 \\ Residual UNet [13] & 0.9416 & 0.8897 & 0.9949 & 0.9481 & 0.9353 & 0.9976 & 9.90 \\ VNet [10] & 0.9446 & 0.8950 & 0.9950 & 0.9202 & **0.9703** & 0.9961 & 14.74 \\ LinkNet [38] & 0.9524 & 0.9091 & 0.9959 & 0.9662 & 0.9390 & 0.9985 & 20.32 \\ UNet [1] & 0.9580 & 0.9193 & 0.9963 & 0.9619 & 0.9541 & 0.9983 & 8.64 \\ Dense UNet [13] & 0.9612 & 0.9252 & 0.9966 & 0.9600 & 0.9624 & 0.9982 & 15.47 \\ MultiRes UNet [19] & 0.9644 & 0.9312 & 0.9969 & 0.9633 & 0.9655 & 0.9983 & 7.76 \\ UNet++ [2] & 0.9659 & 0.9340 & 0.9970 & 0.9676 & 0.9642 & 0.9985 & 8.86 \\ RARUNet [17] & 0.9674 & 0.9369 & 0.9972 & 0.9721 & 0.9629 & 0.9987 & 11.79 \\ QAPNet [3] & 0.9690 & 0.9399 & 0.9973 & 0.9715 & 0.9666 & 0.9987 & 15.14 \\ \hline
**NR-UNet** & **0.9703** & **0.9424** & **0.9974** & **0.9740** & **0.9667** & **0.9988** & 182.90 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Direct comparison against existing algorithms.  
In Figure 5, we present the box plot of the Dice coefficient for each model prediction. The Dice coefficient quantifies the performance of each model by assessing the overlap between the model prediction and the ground truth. The coefficients range between 0 and 1, where 1 signifies a perfect overlap between the prediction and the ground truth, and 0 signifies no overlap. The variation in box heights and positions provides an overview of the performance differences across the models. A higher median and a narrower box suggest that a model has a high overall performance and a consistent prediction quality across different slices. Additionally, pairwise \(t\)-tests were conducted to determine the statistical significance of the differences in Dice coefficients between NR-UNet and UNet, where the \(t\)-statistic is 2.64 and the \(p\)-value is 0.0085. A low \(p\)-value (typically \(<0.05\)) indicates a statistically significant difference in performance between two models. A comparison  
Figure 4: The example images of input CT spine images; prediction of each network against ground truth.  
of the training progress of NR-UNet against UNet is depicted in Figure 6. The line charts illustrate the evolution of loss on the training set (in blue) and the validation set (in red). On the \(y\)-axis, each type of loss is plotted against the number of training epochs on the \(x\)-axis.