# Assessment of Bone Aging--A Comparison of Different Methods for Evaluating Bone Tissue
## 3 Results
### Age Estimation on the Statistically Suggested Features  
We selected ten textural features with the highest correlation values for the optimal ROIs identified through statistical analysis (L/R03 and L/R05). Table 2 presents the uncorrelated representations for each ROI. Given that the resolution of the ROIs varies by patient, a maximum common resolution was established (L03: 75 \(\times\) 121, L05: 64 \(\times\) 108, R03: 71 \(\times\) 123, R05: 62 \(\times\) 107). All masks were then adjusted to a uniform size, assuming that the centers of the original and smaller masks overlapped. This adjustment facilitated \begin{table}
\begin{tabular}{c c c c c} \hline
**ROI** & **Anatomical Structure** & **PearsonCoefficient\(\dagger\)** & **SpearmanCoefficient\(\dagger\)** & **KendallCoefficient\(\dagger\)** \\ \hline L01 & Left wing of ilium & 0.22 & 0.25 & 0.17 \\ L02 & Left neck of femur & 0.28 & 0.26 & 0.18 \\ L03 & Left greater trochanter & **0.38** & **0.35** & **0.24** \\ L04 & Left ischium & 0.27 & 0.26 & 0.18 \\
**L05** & Left shaft of femur & **0.46** & **0.40** & **0.32** \\ L06 & Left hip bone above the acetabulum & 0.20 & 0.19 & 0.12 \\ L07 & Left femur head (center) & 0.16 & 0.20 & 0.13 \\ R01 & Right wing of ilium & 0.18 & 0.19 & 0.14 \\ R02 & Right neck of femur & 0.27 & 0.24 & 0.18 \\ R03 & Right greater trochanter & **0.38** & **0.37** & **0.25** \\ R04 & Right ischium & 0.20 & 0.24 & 0.17 \\
**R05** & Right shaft of femur & **0.49** & **0.47** & **0.34** \\ R06 & Right hip bone above the acetabulum & 0.19 & 0.20 & 0.15 \\ R07 & Right femur head (center) & 0.18 & 0.26 & 0.14 \\ \hline \end{tabular}
\end{table} 
Table 1: The statistical evaluation of correlation between the features in the ROI and patient age. the preparation of input data by extracting ROIs from the selected textural feature images (Table 2). Using the imagery data of each ROI (original image and texture feature maps), we trained multiple neural network architectures with different activation functions (refer to Table 3) to address the regression task. In most instances, the training sessions converged without any overfitting of the networks. Table 3 displays the best _MAE_ score selected from three runs of each fold and then across all folds. This straightforward approach demonstrates that estimating a patient's age with an error margin of less than 10 years is feasible. Figure 4 illustrates the top-performing network architecture along with the learning curves from the experiment that achieved the best results. We performed similar experiments for the selected textural features and R/L03 and R/L05 ROIs. We evaluated 10 features from all models accessible in the Matlab framework. In this approach we neglected data preprocessing. Table 4 gathers the best results achieved for the linear SVM. In this case, the age error is around 5 years, with a very high coefficient of determination at around 0.5. These results were obtained for \(\pm\)3 \(\sigma\) ROI normalization and 8-bit gray level range. \begin{table}
\begin{tabular}{c c c c} \hline
**ROI** & **MAE\(\downarrow\)** & **MAPE\(\downarrow\)** & R2\(\uparrow\) \\ \hline L03 & **5.22** & **0.11** & **0.55** \\
**L05** & **5.53** & **0.11** & **0.42** \\ R03 & **5.20** & **0.11** & **0.55** \\
**R05** & **5.66** & **0.11** & **0.43** \\ \hline \end{tabular}
\end{table} 
Table 4: Evaluation of machine learning for uncorrelated features (03—greater trochanter, 05—shaft of femur). \begin{table}
\begin{tabular}{c c c c} \hline
**L03** & **L05** & **R03** & **R05** \\ \hline Yc5 LbpC8 sn5 & Ys10M7 ArmTeta2 & Yc5 LbpC8 sn13 & Yc5 LbpC8 sn5 \\ Yc5 LbpC8 sn11 & Ys10M8 ArmTeta1 & Yc5 LbpC8 sn11 & Yc5 LbpC8 sn13 \\ Yc5 LbpC8 sn4 & Yc5 LbpC8 sn9 & Yc5 LbpC8 sn9 \\ Yc5 LbpC4 tn9 & Yc5M7 GclcmV2 InvDfMom & Yc5 LbpOc4n15 \\  & Yc5M7 GclcmN11 nvDfMom & Yc5M6 GclmV5 hrtREmp & \\ \hline \end{tabular}
\end{table} 
Table 2: The best uncorrelated textural features for the selected ROIs (03—greater trochanter, 05—shaft of femur).