# Enhancing Density Prediction of Agricultural Land Soil through Void Area Curve Analysis
## 3 Results  
### Dry Density Prediction by Thresholding of Soil Images  
Figure 3 shows how the soil surface image and histogram change as the \(\rho_{d}\) increases. The soil texture is SiL and the water content is 25%. Soil solids are visible in Figure 3a, and voids, which are dark spaces between soil solids, are also present. Under the condition of low \(\rho_{d}\), numerous voids are distributed, and as the \(\rho_{d}\) increases, the distribution of the voids decreases. Figure 3b shows the histogram after converting the color image of Figure 3a to grayscale. The histogram is bell shaped, skewed to the right with one peak. For the intensity of the digital images and its histogram, 0 means black and 255 means white. As the \(\rho_{d}\) increases, the frequency of the low intensity decreases and the frequency of the high intensity increases in the histogram. The average intensities of the histogram were 81.4, 85.5, 89.7, and 91.3, respectively. Comparing Figure 3a,b, the voids were distributed at a low intensity and the soil solid was distributed at a high intensity. Figure 4 shows the result of th  
Figure 3: Soil images and histogram under various dry densities: (**a**) original color images and (**b**) histogram of grayscale images. Figure 4a is an image with a \(\rho_{d}\) of 1.1 t/m\({}^{3}\) in Figure 3a converted to grayscale. Figure 4b-f are threshold binary images, which are easier to distinguish between soil solids and voids than in the original grayscale image. Figure 4b,c show thresholding results using the Otsu method and Triangle method, respectively. Because both methods are automatic thresholding, the threshold value was automatically determined by the algorithm. In the case of the Otsu method, the soil solid and voids were well distinguished; however, it was difficult to distinguish them from the results of the Triangle method because the threshold value selected by the Triangle method was 149, which is far from the median value of the histogram. As a result, most of the pixels were classified as a void. Figure 4d-f show the results of simple thresholding with threshold values of 70, 80, and 90, respectively. Increasing the threshold value from 70 to 90 appears to noticeably increase the area of the voids displayed in black pixels on the image. Specifically, as the threshold value increases, \(N_{void}\) and \(n^{\prime}\) increase. Therefore, the accuracy of the density prediction will vary according to the threshold value. Figure 5 shows the calculation results of \(n^{\prime}\) according to the threshold value. As the threshold value increased, \(n^{\prime}\) increased from 0 to 1. This is the same as the possible range of \(n\) values as shown in Figure 1. \(n^{\prime}\) is almost close to 1 for threshold values of 170 and above. This is because the pixel intensity of a grayscale image is mostly below 170, as shown in Figure 4g. If the threshold value is the same, the result of the thresholding is the same. The threshold values determined by the Otsu method and the Triangle method were 78 and 149, respectively. So, the \(n^{\prime}\) calculated from the binary images obtained by the Otsu method and the Triangle method showed the same value as the result of performing simple thresholding at the threshold values 78 and 149. Therefore, the thresholding results in Figure 4 all exist on the curve in Figure 5. Because the value of \(n^{\prime}\) is determined by the  
Figure 4: The thresholding of the sample image: (**a**) grayscale image, (**b**) result of the Otsu method, (**c**) result of the Triangle method, and (**d–f**) results of simple thresholding. (**g**) Histogram of (**a**) and threshold values. threshold value, it is necessary to verify whether \(n^{\prime}\) has a correlation with \(\rho_{d}\) under various threshold values. According to the thresholding method, the result of the \(n^{\prime}\) extracted from the same soil image was different, indicating that it is essential to determine an appropriate thresholding method for evaluating soil voids.