# Black Ice Classification with Hyperspectral Imaging and Deep Learning
## 7 Results  
### Results and Discussion  
To understand a material, a good way is to see how light works on the material. For hyperspectral images, every pixel can have a different spectral signature, which may hold important information. Therefore, for a rough idea about black ice, spectral reflectance curves are shown in Figures 7-9 (from distances of 10 m, 20 m, and 30 m away, respectively), graphing wavelength versus digital count. The black color curve is illustrated as the road, and the blue color curve is the black ice spread on the road. Even though black ice on the road is not clear enough to be seen, the graphs show the difference between them. For better visualization of black ice, random bands were taken into consideration, as shown in Figures 10-12. The figures display the feature variations in different bands. As mentioned in the methodology, Principal Component Analysis was used for dimension reduction and to avoid possible over-fitting during the deep learning process. One of the main reasons was to choose the relevant bands in the data cube. After observation of the first PCA trial, 40 bands were taken for further visualization and implementation. After PCA, the model was structured according to the data dimension. For the mentioned three distances, accuracy and loss curves are shown in Figures 13-15. In this paper, Kappa  
Figure 11: Random band visualization of hyperspectral image of black ice at 20 m.  
Figure 12: Random band visualization of hyperspectral image of black ice at 30 m.  
Figure 9: Digital count vs. wavelength curve of black ice image at 30 m.  
Coefficient (KA), Average Accuracy (AA), and Overall Accuracy (OA) are taken into consideration to judge the classification results. KA, OA, and AA are shown based on the classification results. Overall accuracy describes correctly classified samples, while average accuracy is the average number of correctly classified samples. \[\text{Precision }=\frac{\mathit{TP}}{\mathit{TP+FP}} \tag{3}\]  
\[\text{Recall }=\frac{\mathit{TP}}{\mathit{TP+FN}} \tag{4}\]  
\[\text{Accuracy }=\frac{\mathit{TP+TN}}{\mathit{TP+FN+FP+TN}} \tag{5}\]  
\[\text{F1-score }=2\times\frac{1}{\frac{1}{\text{Precision }+\frac{1}{\text{Recall }}}}=2\times\frac{\text{Precision }\times\text{ Recall}}{\text{Precision }+\text{ Recall}} \tag{6}\]  
Figure 14: The accuracy and loss curves after finishing the iterations for the black ice data taken from a distance of 20 m.  
Figure 13: The accuracy and loss curves after finishing the iterations for the black ice data taken from a distance of 10 m.  
Kappa can be defined as a statistical measure of the relationship between the ground truth and the classification map. Tables 2-4 present the accuracy scores and statistical measurements for each distance. As mentioned in Section 6, we tested our model at three different distances to identify the optimal dataset. When trained on black ice data captured from a distance of 10 m, the values for OA, AA, and KA are 0.97, 0.97, and 0.94, respectively. For black ice spread on the road, the precision, recall, and F1-score are 0.98, 0.97, and 0.97, respectively. For black ice on the box, these performance measurements are 0.96, 0.97, and 0.97. The macro average and weighted average for both precision and F1-score stand at 0.97. When training on black ice data collected from a distance of 20 m, the OA, AA, and KA values are 0.95, 0.93, and 0.86, respectively. For black ice on the road, the precision, recall, and F1-score are 0.94, 0.92, and 0.93, respectively. For black ice in a box, these values are 0.93, 0.94, and 0.93. In contrast, for training on black ice data that are collected from a distance of 30 m, the OA and AA are both 0.93, with a KA of 0.86. For black ice on the road, precision, recall, and F1-score are 0.93. Figures 13-15 illustrate the accuracy loss graphically, clearly showing that the model trained with data from a 10 m distance achieves the highest accuracy, corroborating the findings presented in Tables 2-4.