# Enhancing Density Prediction of Agricultural Land Soil through Void Area Curve Analysis
## 4 Discussion  
### Accuracy of the Density Prediction Using Void Area Curve  
In this study, we aimed to improve the existing density prediction method that depends on the value of the threshold value. Therefore, instead of selecting a single threshold value, \(n^{\prime}\) was calculated for all possible threshold values, which is called the void area curve. The shape of the histogram in Figure 4g is unimodal because the object (soil solid) and background (void) are not clearly distinguishable in the digital image of the soil. This study does not seek a thresholding method that can perfectly distinguish between a void and a soil solid, but rather predicts density using features from the relationship between \(n^{\prime}\) and the threshold value. This is because the main goal is not to obtain an image with flawless void and soil solid separation, but to obtain a good estimation of the dry density. The void area curve method proposed in this study seems to serve this purpose well. The analysis showed that the standard deviation of the void area curve can be used to predict the \(\rho_{d}\) with high accuracy. As shown in Table 3, the accuracy of \(\rho_{d}\) prediction varies depending on the threshold value. A major advantage of the method proposed in this study is that it can perform robust analysis, unlike existing methods whose accuracy may vary depending on the threshold value. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multicolumn{2}{c}{**Soil Condition**} & \multicolumn{6}{c}{**RMSE (t/m\({}^{3}\))**} \\ \hline \multirow{2}{*}{**Texture**} & \multirow{2}{*}{**Water**} & \multirow{2}{*}{\(\sigma_{n^{\prime}}\)} & \multicolumn{3}{c}{**Simple Thresholding**} & **Otsu** & **Triangle** \\  & & & **70** & **80** & **90** & **Method** & **Method** \\ \hline \multirow{5}{*}{SL} & 5 & 0.067 & 0.081 & 0.077 & 0.072 & 0.039 & 0.100 \\  & 10 & 0.016 & 0.023 & 0.022 & 0.024 & 0.087 & 0.034 \\  & 15 & 0.024 & 0.026 & 0.027 & 0.029 & 0.057 & 0.056 \\  & 20 & 0.011 & 0.015 & 0.016 & 0.017 & 0.012 & 0.063 \\  & 25 & 0.024 & 0.028 & 0.031 & 0.034 & 0.057 & 0.059 \\ \hline \multirow{5}{*}{L} & 5 & 0.110 & 0.064 & 0.060 & 0.056 & 0.106 & 0.071 \\  & 10 & 0.041 & 0.045 & 0.042 & 0.039 & 0.072 & 0.064 \\  & 15 & 0.016 & 0.027 & 0.024 & 0.023 & 0.052 & 0.034 \\  & 20 & 0.024 & 0.022 & 0.023 & 0.025 & 0.030 & 0.111 \\  & 25 & 0.014 & 0.015 & 0.015 & 0.015 & 0.027 & 0.062 \\ \hline \multirow{5}{*}{SiL} & 5 & 0.045 & 0.045 & 0.042 & 0.040 & 0.108 & 0.054 \\  & 10 & 0.026 & 0.025 & 0.023 & 0.022 & 0.081 & 0.057 \\  & 15 & 0.025 & 0.029 & 0.030 & 0.035 & 0.107 & 0.035 \\  & 20 & 0.036 & 0.027 & 0.027 & 0.030 & 0.041 & 0.038 \\  & 25 & 0.044 & 0.049 & 0.054 & 0.061 & 0.050 & 0.068 \\ \hline \multirow{5}{*}{SiCL} & 5 & 0.077 & 0.094 & 0.093 & 0.090 & 0.109 & 0.109 \\  & 10 & 0.042 & 0.070 & 0.068 & 0.067 & 0.044 & 0.066 \\ \cline{1-1}  & 15 & 0.061 & 0.089 & 0.086 & 0.083 & 0.067 & 0.078 \\ \cline{1-1}  & 20 & 0.018 & 0.023 & 0.024 & 0.026 & 0.026 & 0.078 \\ \cline{1-1}  & 25 & 0.020 & 0.021 & 0.021 & 0.021 & 0.023 & 0.034 \\ \hline \multicolumn{2}{c}{Average} & 0.037 & 0.041 & 0.040 & 0.040 & 0.060 & 0.064 \\ \hline \end{tabular}
\end{table} 
Table 3: RMSE of the dry density prediction by soil images under various soil conditions. The accuracy of the \(\rho_{d}\) test and prediction results are summarized in Table 4. [PERSON] et al. [6] conducted a precise test using a large soil tank with a diameter of 122 cm and a height of 100 cm in laboratory conditions to verify the accuracy of the field density test. In addition, [PERSON] et al. [28; 29] performed digital image-based density prediction of soil via a convolutional neural network and deep neural network. The RMSE of \(\rho_{d}\) prediction using \(\sigma_{n^{\prime}}\) was 0.037 t/m\({}^{3}\), which was superior to other experimental methods except sand cone. Additionally, the range of water content during the \(\rho_{d}\) tests was 8.3-13.3%; however, in this study, soils with a water content from 5% to 25% were used.