## 4 Experimental Results and Discussion
### Evaluation of the Proposed Method with Other Existing Methods  
In order to evaluate the performance of the proposed method, we compared it with several methods including the height-based method [8], the curvature-based method [7], the modified curvature-based method [18], and the SVM trained on appearance, cross-section, and local extrema-based features [24]. The parameters used in the proposed method and existing methods are given in Table 5.  
Figure 12(a) shows eight mesh partitions of the test data and Figure 12(b) illustrates the corresponding ground truth labels of the mesh partitions with three classes. The degraded region label is utilized in the SVM-based method and the proposed method, while the label is treated as background in the other methods. As shown in Figure 12(c), the height-based method produces unsatisfactory classification results because of the inconsistencies with the distribution of the heights, largely from the degraded region. Figure 12(d) shows the relief regions extracted using the curvature-based method. The method yields an unreliable extraction of reliefs due to noisy curvatures without the consideration of the rough surface of the stele. Furthermore, the boundaries of the extracted relief regions are not smooth, and it is obvious that the reliefs are not accurately extracted. There is significant improvement in the modified curvature-based method when compared with results from the curvature-based method. However, the modified curvature-based method cannot distinguish degraded region from reliefs, and thus results in many false detections, as shown in Figure 12(e). The machine learning-based methods using SVM and RF are both promising and they outperformed all other methods by eliminating degraded regions (see Figure 12(f),g). However, the SVM-based method misclassifies many thin and small degraded regions as reliefs, which hinders recognition of the characters. The proposed method yielded more pleasant results by suppressing those thin degraded regions and producing reliefs with smooth boundaries. \begin{table}
\begin{tabular}{c|c c} \hline \hline
**Metrics** & **Two-Class** & **Three-Class** \\ \hline Accuracy & 0.9606 & 0.9625 \\ Precision & 0.9120 & 0.8985 \\ Recall & 0.8557 & 0.8832 \\ F1 score & 0.8810 & 0.8889 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the two-class and three-class RF(CSI). \(N_{t}\) and \(N_{d}\) are 1000 and 32 in both models. \begin{table}
\begin{tabular}{c c|c c|c c} \hline \hline  & **Proposed** & & & **Curvature-Based**[7; 18] \\ \hline CSI & & RF & \(\alpha\) & 0.7 \\ \hline \(\Delta\rho\) & 0.6 & \(N_{t}\) & 1000 & \(\beta\) & 0.1 \\ \(\Delta T_{t}\) & 0.5 & \(N_{d}\) & 32 & & \\ \(N_{\rho}\) & 10 & & & & \\ \(N_{\gamma}\) & 10 & & & & \\ \(\sigma\) & 1.6 & & & & \\ \(d_{CSFigure 14 illustrates the results of the comparative methods with respect to the entire ancient stele. The stone rubbing image in Figure 14a indicates not only the reliefs but also cracks and scratches, which makes it difficult for the epigraphists to recognize the characters correctly. The results obtained using the height-based method and the curvature-based method are presented in Figure 14b,c. The classification results are inconsistent as the methods are affected by the degraded regions. There is a significant improvement in the modified curvature-based method, but the extracted reliefs are not accurate and precise (see Figure 14d). For the proposed method, we cross-validated the CSI information by separating the 70 mesh partitions into five folds. Four folds were used to train the RF model in the proposed method and the last fold was selected as test data. This process was repeated until we were able to extract the reliefs for all 70 mesh partitions. One of the RF models trained from the fold was applied to the remaining 113 mesh partitions that were not included in the train. The initial classification result of the 169 mesh partitions were refined with the \(k\)-NN, and the result is presented in Figure 14f.