# Deep Learning-Based Crack Detection on Cultural Heritage Surfaces
## 3 Results  
### Crack Identification Results  
The GoogleNet model was trained on a dataset comprising 66 images, equally distributed between cracked and non-cracked surfaces. Prior to conducting overall training and validation of the GoogleNet model, K-fold cross-validation was employed to assess its generalization capability. The results demonstrate consistently high performance across all five folds, with the model achieving an average accuracy, precision, recall, and F1-score of 98% (Table 1), indicating strong robustness and generalizability. Although minor variations were observed, such as a precision of 91% in fold 1 and a recall of 90% in fold 3, all folds yielded F1-scores of 95% or higher. This reflects a well-balanced performance between identifying true positives and minimizing false predictions. Overall, the findings suggest that GoogleNet is highly effective for binary classification of crack versus non-crack images, even under varying training and validation splits. In this study, a dataset comprising 66 images was divided into 70% for training and 30% for validation. Figure 3 presents the training and validation performance of the GoogleNet model, demonstrating its strong learning efficiency and adaptability. The training accuracy exhibited a rapid increase from 30% to 100%, while the validation accuracy improved from 47.83% to a range of 97.83-100%, indicating high generalization capability. Additionally, the training loss significantly decreased from 1.086 to near zero, while the validation loss declined from 1.184 to below 0.46, signifying a steady enhancement in predictive accuracy. Among all iterations, the 75 th iteration yielded the optimal performance, achieving 100% accuracy on both training and validation datasets. At this stage, the training loss reduced to 7.224 \(\times\) 10\({}^{-5}\), approaching zero, while the validation loss was recorded at 0.004, highlighting the model's efficiency and stability. Consequently, the 75 th iteration was identified as the most effective stage in the training process. The trained model was subsequently tested on an independent set of 34 images, achieving 100% accuracy, recall, and precision (Table 2). These results indicate flawless crack detection, with no false positives or false negatives. The F1-score of 1.0 further confirms a perfect balance between precision and recall, validating the effectiveness of the GoogleNet model in accurately identifying cracks. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**K-Fold**} & **Accuracy** & **Precision** & **Recall** & \multirow{2}{*}{**F1-Score**} \\  & **(\%)** & **(\%)** & **(\%)** & **(\%)** & \\ \hline
1 & 95 & 91 & 100 & 95 \\
2 & 100 & 100 & 100 & 100 \\
3 & 95 & 100 & 90 & 95 \\
4 & 100 & 100 & 100 & 100 \\
5 & 100 & 100 & 100 & 100 \\ Average & 98 & 98 & 98 & 98 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: K-fold cross-validation results using GoogleNet. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Data Set**} & \multirow{2}{*}{**Number of Images**} & **Accuracy** & **Precision** & **Recall** & \multirow{2}{*}{**F1-Score**} \\  & & **(\%)** & **(\%)** & **(\%)** & **(\%)** \\ \hline
66 & 34 & 100 & 100 & 100 & 1.0 \\
66 & 20,000 & 72 & 65 & 100 & 0.79 \\
76 & 20,000 & 97 & 95 & 98 & 0.97 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comprehensive evaluation metrics of the GoogleNet model. When evaluated on an external dataset [52] comprising 10,000 crack images and 10,000 non-crack images, the GoogleNet model trained on the original dataset achieved an accuracy of 72%, a precision of 65%, a recall of 100%, and an F1-score of 0.79 (Table 2), indicating evidence of overfitting. However, after augmenting the training set with only 10 images from the external dataset and retraining the model, performance improved substantially: accuracy increased to 97%, precision to 95%, recall to 98%, and F1-score to 0.97 (Table 2). These findings align with the observations discussed in Section 4.3.1.