# Determining Effective Threshold Range of Image Pixel Values for Municipal Waste-Contaminated Clay
## 3 Results
### Effective Threshold Range of Image Pixel Values Based on Apparent Void Ratio of Contaminated Clay  
After enhancement, segmentation, binarization and denoising of the SEM images, the black and white pixels in the binary images represent pores and soil particles, respectively. Therefore, the apparent void ratio can be calculated according to the ratio of the black area to the white area in each image. With the use of the data collected by IPP, the apparent void ratio and image pixel values of the seeping municipal waste-contaminated clay samples are shown in Figure 5, and the apparent void ratio and image pixel values of the soaking municipal waste-contaminated clay samples are shown in Figure 6.  
Figure 5: Relationship between apparent void ratio and pixel threshold values of samples at different column depths.  
Figure 6: Relationship between apparent void ratio and pixel threshold values of samples at different concentrations.  
Table 1 indicates that the void ratio of all soaking municipal waste-contaminated clay samples was 0.97. Table 3 indicates that the void ratios of the seeping municipal waste-contaminated clay samples collected at column depths of 3.1, 17.3, 36.8, 48.5, 56.3, and 75.8 cm were 0.34, 0.64, 0.73, 0.79, 0.81, and 0.83, respectively. As such, a value of 130 could be used as the threshold value for the contaminated clay collected at a seepage depth of 3.1 cm, since at this depth, the apparent void ratio was approximately 0.31, which is closer to the measured void ratio of 0.34. The reasonable threshold values for the contaminated clay collected at seepage depths of 17.3, 36.8, 48.5, 56.3, and 75.8 cm were 130, 130, 130, 130, 110, and 110, respectively, with the apparent void ratio closely approximating the measured void ratio as the determination basis. The reasonable threshold values for the CaCO\({}_{3}\)-contaminated clay samples with concentrations of 0.2, 0.4 and 0.6 mol/L were 120, 130, and 140, respectively. The reasonable threshold values for the CH\({}_{3}\)COOH-contaminated clay samples with concentrations of 0.2, 0.4, and 0.6 mol/L were 130, 125, and 110, respectively.  
Effective Threshold Range of Image Pixel Values Based on the Fractal Dimension of Contaminated Clay Particles  
The fractal dimension is an important parameter to quantitatively describe the shape contour of particles. Through image analysis, the fractal dimension can quantitatively describe the complexity of particle contours.  
Figures 7 and 8 show the link between the fractal dimension and the image pixel threshold value of the seeping and soaking municipal waste-contaminated clay samples, respectively, using the data obtained by IPP. The fractal dimension of the particles initially increased with increasing pixel value, tended to stabilize, and then sharply declined. The fractal dimension of clay particles should be investigated within a constant interval, according to [PERSON] et al. (2015). The fractal dimension of the contaminated clay particles at a column depth of 3.1 cm exhibited a relatively constant pixel value with a range of 110-170. Similarly, the pixel value intervals for the fractal dimensions of the seeping municipal waste-contaminated clay samples at column depths of 17.3, 36.8, 48.5, 56.3, and 75.8 cm were 110-190, 110-190, 110-210, 110-170, and 90-150, respectively; the pixel value intervals for the fractal dimensions of the CaCO\({}_{3}\)-contaminated clay samples with concentrations of 0.2, 0.4, and 0.6 mol/L were 80-150, 110-140, and 90-180, respectively; and the pixel value intervals for the fractal dimensions of the CH\({}_{3}\)COOH-contaminated clay samples with concentrations of 0.2, 0.4 and 0.6 mol/L were 100-140, 110-150, and 100-180, respectively. In summary, the optimal pixel value interval was 110-140 based on the fractal dimension of the contaminated clay particles, and calculations based on this range should be very reliable.