# Automated Bone Age Assessment with Image Registration Using Hand X-ray Images
## 6 Results and Discussion  
The regressor is trained for 150 epochs using an additional augmented dataset, which was produced using Keras generator. The synthetic data are generated by varying the zoom ranges, rotation angles, and translational positions, as well as flipping and shearing process. Table 1 shows the hyper-parameter setup of the regressor. Two performance metrics are used to validate the experimental test on 1281 images, which are mean absolute error (\(MAE\)) and mean squared error (\(MSE\)). \[MAE =\frac{\sum_{i=1}^{T_{test}}|lb_{regress}^{gt}-lb_{regress}^{predict }|}{T_{test}} \tag{18}\] \[MSE =\frac{\sum_{i=1}^{T_{test}}(lb_{regress}^{gt}-lb_{regress}^{predict })^{2}}{T_{test}} \tag{19}\]  
where \(T_{test}\) is the total number of test images, while \(lb_{regress}^{gt}\) is the annotated ground truth bone age by the pediatricians and \(lb_{regress}^{predict}\) is the predicted bone age by the regressor network. For performance comparison, 10 other state-of-the-art deep learning networks have been tested while using the same image registration technique that includes MobileNet V1 [17], MobileNet V2 [43], MobileNet V3 [44], ShuffleNet V1 [45] and ShuffleNet V2 [46], VGG-19 [47], Inception V3 [48], ResNet [49], and DenseNet [42]. Basically, six of these models can be regarded as a lightweight model because of the total parameters used are less than 10 million. All of the networks have been trained until convergence, as shown in the training graph of Figure 9. Note that the training graphs have been capped at 40 \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\(\delta_{LR}\)} & \multirow{2}{*}{**Batch Size**} & **Rotation Range of** & **Zoom Range of** & **Shearing Range of** & **Translational Shift** \\  & & **Synthetic Data** & **Synthetic Data** & **Synthetic Data** & **Factor** \\ \hline
0.00001 & 16 & 20\({}^{\circ}\) & 0.15 & 0.15 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Hyper-parameters setting of the regressor network. Figure 8: The architecture of a three-layer residual separable convolution network. epochs for better visualization. The proposed method has obtained the lowest mean squared error at the end of the 40 epochs, as shown by the red line graph. Table 2 shows the experimental results of the bone age prediction of the proposed method and its benchmarked networks. Basically, our method which is based on the Xception regressor has produced the lowest \(MAE\) of 8.200 months and \(MSE\) of 121.902 using a total number of 20,863,529 parameters. The main advantage of the Xception network is its three-layer residual separable convolution unit with 728 filters. Besides, when a down-pooling operator is applied, the skip connection layer will also be down-pooled using a convolution operator and, thus, reducing the probability of diminishing gradient problem. Moreover, this network also applied a unique composite function of the rectified linear unit, convolution layer, and batch normalization operator, while the standard flow for the other networks is convolution layer, rectified linear unit, and batch normalization operator. The second best \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Mean Absolute Error** & **Mean Squared Error** & **Total No. of Parameters** \\ \hline ShuffleNet V1 & 15.728 & 372.575 & 936,457 \\ SqueezeNet & 14.164 & 311.783 & 735,939 \\ VGG-19 & 14.028 & 307.416 & 38,911,041 \\ MobileNet V3 & 13.541 & 282.157 & 1,662,939 \\ ShuffleNet V2 & 12.010 & 226.951 & 5,380,761 \\ MobileNet V2 & 11.394 & 213.454 & 2,260,417 \\ MobileNet V1 & 10.886 & 190.349 & 3,229,889 \\ DenseNet & 10.557 & 190.105 & 31,049,921 \\ ResNet & 10.283 & 264.660 & 23,563,201 \\ Inception V3 & 9.774 & 191.696 & 18,783,649 \\ Proposed method & 8.200 & 121.902 & 20,863,529 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental results of the proposed method and the benchmarked networks. Figure 9: Training graphs of mean squared error for all tested methods.