# A Cascade Model with Prior Knowledge for Bone Age Assessment
## 3 Results
### Evaluation of Bone Age Assessment
**Assessment performance at different ages. ** In order to detect the performance of the model in each age group, the paper divides 0-18 years into 18 age intervals to verify the performance of the model. A new evaluation metric, RMSE, is also introduced, which will provide a higher weight to larger errors than with MAE will, and for larger errors, RMSE is the most useful evaluation metric with the following expression. \[RMSE=\sqrt{\frac{1}{m}\sum_{i=1}^{m}(y_{i}-\hat{y_{i}})^{2}} \tag{16}\]  
From Table 6, we can find that the model assessment results are more stable at (0, 15) years of age, with low MAE and RMSE, while the error in the assessment is larger at (15, 18) years of age, especially between (17, 18) years of age. We speculate is due to the fact \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **MAE** & \(\pm\)**0.5** & \(\pm\)**1** & \(\pm\)**2** \\ \hline KL & 4.69 & 75.32\% & 93.71\% & 98.80\% \\ FL & 4.53 & 78.15\% & 94.04\% & 99.34\% \\ FL + LS & 4.44 & 79.47\% & 94.70\% & 99.34\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Loss function comparison experiment. that from 15 to 18 years of age, the skeletal development of the hand gradually matures, and its morphology no longer changes significantly, making it difficult for the model to accurately assess bone age. **Comparison experiments with advanced models** To verify the performance as well as the applicability of the proposed model, it is validated on the RNSA2017 public dataset, and since this dataset is not evaluated using the RUS-CHN method, only background denoising RoIs are used in the comparative experiments on the public dataset, and the results of the comparative experiments are shown in Table 7.  
Table 7 shows that when the model uses only background denoised RoIs, it achieves good levels of accuracy on both private and public datasets, with model evaluation accuracies of 93.80% and 95.20% for ground truth within \(\pm\)1 year. Compared with other BAA models using background denoising on public datasets, MAE is lower, and the evaluation accuracy is higher. We believe that this is due to the cascade model proposed in this paper being more consistent with the characteristics of skeletal development and makes full use of the bone age labeling information, thus improving the evaluation of the BAA model. Meanwhile, Table 7 shows that the cascade model proposed in this paper also has some applicability for the public dataset. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Age Groups** & **MAE** & **RMSE** \\ \hline \((0,1]\) & 3.30 & 3.92 \\ \((1,2]\) & 4.29 & 4.69 \\ \((2,3]\) & 3.86 & 4.64 \\ \((3,4]\) & 3.57 & 4.26 \\ \((4,5]\) & 4.20 & 4.82 \\ \((5,6]\) & 3.80 & 4.27 \\ \((6,7]\) & 3.67 & 4.40 \\ \((7,8]\) & 4.13 & 4.65 \\ \((8,9]\) & 3.63 & 4.70 \\ \((9,10]\) & 3.10 & 4.63 \\ \((10,11]\) & 2.11 & 2.53 \\ \((11,12]\) & 3.10 & 3.81 \\ \((12,13]\) & 2.69 & 3.83 \\ \((13,14]\) & 3.62 & 4.29 \\ \((14,15]\) & 4.09 & 4.69 \\ \((15,16]\) & 5.20 & 5.94 \\ \((16,17]\) & 6.00 & 7.84 \\ \((17,18]\) & 11.00 & 11.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: MAE and RMSE for different age groups.