# Deep Learning-Based Crack Detection on Cultural Heritage Surfaces
## 3 Results
### Pixel-Level Segmentation of Crack Regions  
The SegNet deep learning model was utilized for crack segmentation in cultural heritage images to assess structural integrity. The model was trained on a dataset of 300 images, employing a 70:30 split for training and validation. Before conducting the overall training and validation of SegNet, K-fold cross-validation was also performed. The IoU values from the five validations were 0.798, 0.823, 0.857, 0.815, and 0.866, respectively. The difference between the maximum and minimum values was less than 0.1, indicating that the distribution of different image patterns in the training set was relatively balanced, without excessive concentration.  
Figure 3: Training and validation process of the GoogleNet model for (**a**) accuracy and (**b**) loss coefficient.  
Performance metrics, including training accuracy, validation accuracy, training loss, and validation loss, were recorded across 75,000 iterations. Initially, the training accuracy was measured at 61.48% and increased to 98.11% within 1000 iterations. It stabilized above 98.5% by 2000 iterations and reached 99.29% at 45,000 iterations, demonstrating robust learning capability and stability (Figure 4a). Similarly, validation accuracy improved from 62.35% to 98.06% after 1000 iterations and stabilized at 98.62% beyond 45,000 iterations, indicating strong generalization performance.  
Training loss, initially recorded at 0.763, reflecting a high prediction error, steadily declined to 0.019 at 45,000 iterations (Figure 4b). Validation loss followed a similar trend, decreasing from 0.762 to 0.052, demonstrating consistent error minimization. However, at 75,000 iterations, training accuracy reached 99.99%, while validation accuracy declined slightly to 99.39%. Training loss dropped to 0.001, whereas validation loss increased to 0.083, suggesting potential overfitting.  
The model trained at 45,000 iterations was selected for further analysis, as it demonstrated the optimal trade-off between accuracy and generalization, achieving an Intersection over Union (IoU) of 0.832. To further assess the model's generalization performance, an external dataset [53] comprising 237 images was employed for validation. The resulting IoU of 0.726 suggests that, although the SegNet model exhibited reduced performance on external data compared to internal validation, it nonetheless maintained a reasonable level of predictive capability.  
Figure 4: Training and validation process of the SegNet model for (**a**) accuracy and (**b**) loss coefficient.  
Figure 5 presents the results of semantic segmentation, demonstrating the model's capability to effectively differentiate crack regions (green) from non-crack regions (red). In Figure 5a, certain fine cracks remain undetected, as indicated by the blue box. This limitation is primarily attributed to the loss of detail during image downscaling, which causes narrow cracks to fall below the model's detection threshold. This issue may be mitigated by increasing image resolution, capturing images at a closer distance, or performing segmentation directly on the original high-resolution images. Alternatively, image preprocessing techniques, such as contrast enhancement or the application of sharpening filters, can improve crack visibility and facilitate more accurate segmentation.