# Automatic Asbestos Control Using Deep Learning Based Computer Vision System +
## 2 Description of the Experimental System and Algorithm of Its Work
### Algorithm of the System Work
The U-net model was pre-trained with datasets \(N\!\!\!N1\) and 2 described above. After that, the model was fine-tuned with datasets \(N\!\!\!N3\) and 4 described above. The fine-tuned data was divided into the test and train parts. Then the train part was mixed and divided into train and validation parts with a proportion of 50 to 50%. The test part was taken as dataset \(N\!\!\!N3\) and part of the dataset \(N\!\!\!N4\): Six open pits, 611 images. The test part of dataset \(N\!\!\!N4\) was taken under hard-winter conditions (January and February). The training part includes 442 images taken from 4 open pits; most of them were taken in autumn conditions. Such division of the data is supposed to be the most representative in the generalization ability. During the training, all images were randomly cropped to size \(1024\times 1024\) from the original images. The training curves are shown in Figure 11.

Figure 11 shows that the U-Net model achieves the best results at the 150 th training epoch. We used the weights of the 150 th epoch as the final model. The obtained measure results Dice coefficient and intersection over union (IoU) are shown in Table 2. The std and average values in Table 2 are calculated by the measure values for each instance in the dataset. Table 2 shows some deterioration of validation results compared to the training one. However, the obtained results appear to be sufficient for the system work as shown below. Typical results of U-Net inference for the test data with confidence threshold 50% are shown in Figure 12. \begin{table}
\begin{tabular}{c c c c c} \hline  & \multicolumn{2}{c}{**Dice**} & \multicolumn{2}{c}{**IoU**} \\  & **Train** & **Validation** & **Train** & **Validation** \\ \hline mean & 0.54 & 0.43 & 0.42 & 0.27 \\ std & 0.29 & 0.17 & 0.25 & 0.13 \\ \hline \end{tabular}
\end{table} 
Table 2: U-Net model train and test results (Dice coefficient). Figure 11: Training curves of the U-Net ((**a**) is the loss function, (**b**) is the _Jaccard_ coefficient, (**c**) is the _Dice_ coefficient). ## 5 Asbestos Content Estimation

### Method of Asbestos Productivity (Content) Estimation

The overall productivity of an open pit is determined by the average function of the estimated asbestos productivity for each of the selected rock chunks. The productivity for each rock chunk was evaluated as follows:

\[\hat{y}_{i}=\left(k\frac{A_{v}}{A_{R}}+b\right)100\%, \tag{1}\]

where \(\hat{y}_{i}\) is the asbestos content for one \(i\)-th image \(i=1,...,N\) is the number of images taken from one open pit; \(A_{v},A_{R}\) are the areas of veins (\(A_{v}\)) and rock chunks (\(A_{R}\)) for each image; \(k\) and \(b\) are the graduation multiplicative and additive coefficients. For determining \(A_{v}\), the results of segmentation were rounded to binary mask with the confidence threshold of 0.5. Then the value \(A_{v}\) was taken as the sum of pixels. The estimation of the overall productivity of an open pit was taken as an average value among all estimated \(\hat{y}_{i}\) due to the high variation of asbestos content values between different rock chunks. For a more precise average value, the calculation was made by the approximation of the \(\hat{y}_{i}\) histogram (i.e., distribution). The distribution of estimated \(\hat{y}_{i}\) was approximated using the Parzen-Rosenblatt method with the normal kernel [28]. The graduation coefficients \(k\) and \(b\) in (1) were determined as the linear mean-square approximation of average measured value (average\({}_{i}(\hat{y}_{i})\)) for each open pit to its value estimated by geological specialists. ### Results Discussion

The results of the average asbestos content estimation for each open pit correspond to dataset \(N3\) are shown in Table 3, where the asbestos content means its volume relative to the corresponding rock chunk volume. Table 3 shows the expert estimations, our estimations before the graduation (\(k=1\), \(b=1\)) (column 3), the variance of our estimation, and the number of chunks taken into account.