# Automatic Bridge Crack Detection Using a Convolutional Neural Network
## 3 Experimental Results and Discussion
### Evaluation and Discussion  
#### 3.2.1 Evaluation Factors  
To quantitatively evaluate the performance of our model, several evaluation factors commonly used for classification tasks are used.  
Several basic concepts are shown below:  
1. TP (True Positives): The number of positive classes predicted to be positive classes. In our model, TP refers to the number of cracks that are correctly classified as cracks.
2. TN (True Negatives): The number of negative classes predicted to be negative classes. In our model, TN refers to the number of backgrounds that are correctly classified as backgrounds.
3. FP (False Positives): The number of negative classes predicted to be positive classes. In our model, FP refers to the number of backgrounds that are incorrectly identified as cracks.
4. FN (False Negatives): The number of positive classes predicted to be negative classes. In our model, FN refers to the number of cracks that are incorrectly identified as the background.  
Correspondingly, several evaluation factors commonly used in the binary classification task are listed below [41]:  
Accuracy: Ratio of the number of instances classified correctly to the total number of instances, representing the overall effectiveness of the classifier. Accuracy in our model refers to the ratio of cracks and backgrounds that are correctly classified. Its calculation formula is shown in Equation (9):  
\[\text{Accuracy }=\frac{\text{TP}+\text{TN}}{\text{TP}+\text{TN}+\text{FP}+ \text{FN}} \tag{9}\]  
Precision: Out of all the predicted positive instances, what percentage represents true positive instances. In our model, the precision refers to the proportion of true cracks in all instances classified as cracks. Its calculation formula is shown in Equation (10):  
\[\text{Precision }=\frac{\text{TP}}{\text{TP}+\text{FP}} \tag{10}\]  
Sensitivity (also called Recall): Out of all the positive instances, what percentage is identified correctly, representing the effectiveness of a classifier to identify positive instances. Sensitivity in our model refers to the proportion of true cracks that are classified as cracks. Its calculation formula is shown in Equation (11):  
\[\text{Sensitive }=\frac{\text{TP}}{\text{TP}+\text{FN}} \tag{11}\]  
Specificity: Out of all the negative instances, what percentage is identified correctly, representing the effectiveness of a classifier to identify negative instances. Specificity in our model refers to the proportion of true backgrounds that are classified as backgrounds. Its calculation formula is shown in Equation (12):  
\[\text{Specificity }=\frac{\text{TN}}{\text{TN}+\text{FP}} \tag{12}\]Measure (also known as F-Score): F-Measure is the comprehensive consideration of Precision and Sensitivity, measuring the relationship between the positive label of the data and the label given by the classifier. Its calculation formula is shown in Equation (13):  
\[F=\frac{\left(\alpha^{2}+1\right)\mathrm{P}\cdot\mathrm{R}}{\alpha^{2}(\mathrm{P }+\mathrm{R})} \tag{13}\]  
In the formula, P and R refer to Precision and Sensitivity, respectively.  
When the parameter \(\alpha\) is 1, the F-Measure is the most common \(F_{1}\) score, and its expression is shown in Equation (14):  
\[F_{1}=\frac{2\cdot\mathrm{P}\cdot\mathrm{R}}{\mathrm{P}+\mathrm{R}} \tag{14}\]  
The \(F_{1}\) score comprehensively considers the Precision and Sensitivity, and the experimental model is proven to be more effective when the \(F_{1}\) score is higher.