## 4 Experiments and Discussion
### Discussion  
For registration, since people's heads vary in shape, even though we selected the closest image to the training data as the reference image for each test image, there are still missed situations. This means that after the registration, the patch we created for the test does not include the ground-truth landmark. For the ISBI dataset, there is only one missed patch, and the rate is about 0.0002 (1/(19 \(\times\) 250)), as presented in Figure 9. Overall, it has little impact on the results. For Testset2 of the ISBI Grand Challenge, we can see that Landmark 3, Landmark 6, Landmark 13, and Landmark 16's have relatively low accuracy. However, the process works fine on Testset1. After we visualize the testing result, we find out that the anatomy of those failed cases are very different from the successfully detected ones. Since our training dataset has only 150 images, even though we did data augmentation, we still cannot deny the fact that people's skeletal anatomies are so different that many types are not included in the training dataset. When we use our trained models to make predictions on those with huge anatomy differences, we will achieve unsatisfying results. We think this explains the poor performance on those landmarks in Testset2. We show an example in Figure 10.  
At first, we try to input all the X-ray images to predict all 19 landmarks simultaneously. We performed conventional data augmentation on training data, such as rotation, cropping, and so on. However, the result is not satisfying; although the location of all the landmarks is very similar to the ground truth, the predicted results are very far from the ground-truth result, as presented in Figure 11.  
When we performed skeletal malformation classification based on the detected result, we found out that the result varies a lot when we use the annotation data of a different doctor as the ground truth (There are two annotation data made by two doctors (junior doctor and senior doctor) in ISBI Grand Challenge 2015; because their landmark locations are different, this results in the variability of the skeletal malformation classification. Table 8 presents the proportion that two doctors have the same classification label.). The result we showed previously was based on the annotation data of the \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline  & **ANB** & **SNB** & **SNA** & **ODI** & **APDI** & **FHI** & **FMA** & **MW** \\ \hline Class1 (C1) & 3.2\({}^{\circ}\)–5.7\({}^{\circ}\) & 74.6\({}^{\circ}\)–78.7\({}^{\circ}\) & 79.4\({}^{\circ}\)–83.2\({}^{\circ}\) & 68.4\({}^{\circ}\)–80.5\({}^{\circ}\) & 77.6\({}^{\circ}\)–85.2\({}^{\circ}\) & 0.65–0.75 & 26.8\({}^{\circ}\)–31.4\({}^{\circ}\) & 2–4.5 mm \\ Class2 (C2) & \textgreater{}5.7\({}^{\circ}\) & \textless{}74.6\({}^{\circ}\) & \textgreater{}83.2\({}^{\circ}\) & \textgreater{}80.5\({}^{\circ}\) & \textless{}77.6\({}^{\circ}\) & \textgreater{}0.75 & \textgreater{}31.4\({}^{\circ}\) & =0 mm \\ Class3 (C3) & \textless{}3.2\({}^{\circ}\) & \textgreater{}78.7\({}^{\circ}\) & \textless{}79.4\({}^{\circ}\) & \textless{}68.4\({}^{\circ}\) & \textgreater{}85.2\({}^{\circ}\) & \textless{}0.65 & \textless{}26.8\({}^{\circ}\) & \textless{}0 mm \\ Class4 (C4) & – & – & – & – & – & – & – & – & \textgreater{}4.5 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Classifications for 8 methods, ANB, SNB, SNA, ODI, APDI, FHI, FMA and MW. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline  & \multicolumn{6}{c}{**SCR (\%)**} \\ \hline  & **ANB** & **SNB** & **SNA** & **ODI** & **APDI** & **FHI** & **FMA** & **MW** \\ \hline [PERSON](2015) [8] & 68.0 & 78.7 & 56.7 & 77.3 & 83.3 & 76.0 & 81.3 & 84.0 \\ [PERSON] [7] & 71.3 & **83.3** & 60.0 & 80.0 & 83.3 & 77.3 & 81.3 & 85.3 \\ [PERSON] [9] & 72.9 & 73.7 & 64.1 & 75.9 & 84.8 & 79.7 & **82.0** & 80.2 \\
**Proposed:** & **82.0** & 83.2 & **75.2** & **85.2** & **86.4** & **86.0** & **82.0** & **86.8** \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Classification results for 8 measures, ANB, SNB, SNA, ODI, APDI, FHI, FMA and MW.