# Enhancing Density Prediction of Agricultural Land Soil through Void Area Curve Analysis
## 3 Results
### New Approach for the Dry Density Prediction Using Soil Image Properties  
The \(n^{\prime}\) calculated with every threshold value through simple thresholding is shown in Figure 7. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multicolumn{2}{c}{**Soil Condition**} & \multicolumn{6}{c}{**Correlation Coefficients of \(\rho_{d}\) and \(n^{\prime}\)**} \\ \hline \multirow{3}{*}{**Texture**} & **Water** & \multicolumn{3}{c}{**Simple Thresholding**} & **Otsu** & **Triangle** \\  & **Content (\%)** & **70** & **80** & **90** & **Method** & **Method** \\ \hline \multirow{5}{*}{SL} & 5 & \(-0.69\) & \(-0.73\) & \(-0.77\) & \(0.94\) & \(-0.45\) \\  & 10 & \(-0.98\) & \(-0.98\) & \(-0.98\) & \(0.63\) & \(-0.95\) \\  & 15 & \(-0.97\) & \(-0.97\) & \(-0.97\) & \(-0.86\) & \(-0.86\) \\  & 20 & \(-0.99\) & \(-0.99\) & \(-0.99\) & \(-0.99\) & \(-0.83\) \\  & 25 & \(-0.97\) & \(-0.96\) & \(-0.95\) & \(-0.86\) & \(-0.85\) \\ \hline \multirow{5}{*}{L} & 5 & \(-0.82\) & \(-0.84\) & \(-0.87\) & \(0.33\) & \(-0.77\) \\  & 10 & \(-0.91\) & \(-0.93\) & \(-0.94\) & \(0.76\) & \(-0.82\) \\  & 15 & \(-0.97\) & \(-0.98\) & \(-0.98\) & \(-0.89\) & \(-0.95\) \\  & 20 & \(-0.98\) & \(-0.98\) & \(-0.97\) & \(-0.96\) & \(-0.15\) \\  & 25 & \(-0.99\) & \(-0.99\) & \(-0.99\) & \(-0.97\) & \(-0.83\) \\ \hline \multirow{5}{*}{SiL} & 5 & \(-0.91\) & \(-0.93\) & \(-0.94\) & \(0.24\) & \(-0.87\) \\  & 10 & \(-0.97\) & \(-0.98\) & \(-0.98\) & \(-0.69\) & \(-0.86\) \\  & 15 & \(-0.97\) & \(-0.96\) & \(-0.95\) & \(0.30\) & \(-0.95\) \\  & 20 & \(-0.97\) & \(-0.97\) & \(-0.96\) & \(-0.93\) & \(-0.94\) \\  & 25 & \(-0.90\) & \(-0.88\) & \(-0.84\) & \(-0.90\) & \(-0.80\) \\ \hline \multirow{5}{*}{SiCL} & 5 & \(-0.55\) & \(-0.56\) & \(-0.59\) & \(0.21\) & \(-0.22\) \\  & 10 & \(-0.78\) & \(-0.79\) & \(-0.80\) & \(0.92\) & \(-0.81\) \\ \cline{1-1}  & 15 & \(-0.61\) & \(-0.64\) & \(-0.67\) & \(0.80\) & \(-0.72\) \\ \cline{1-1}  & 20 & \(-0.98\) & \(-0.98\) & \(-0.97\) & \(-0.97\) & \(-0.71\) \\ \cline{1-1}  & 25 & \(-0.98\) & \(-0.98\) & \(-0.98\) & \(-0.98\) & \(-0.95\) \\ \hline \multicolumn{2}{c}{Average} & -0.89 & \(-0.90\) & \(-0.90\) & \(-0.24\) & \(-0.77\) \\ \hline \end{tabular}
\end{table} 
Table 2: Correlation coefficient of the dry density and \(n^{\prime}\) under various soil conditions. Depending on the threshold value, \(n^{\prime}\) shows an increasing curve in the form of a cumulative distribution function (CDF). As the \(\rho_{d}\) increases, the graph moves downward. At the same threshold value, the higher the \(\rho_{d}\), the lower \(n^{\prime}\). Because \(n^{\prime}\) represents the void area in the soil image, the graph of the relationship between the threshold value and \(n^{\prime}\) was named as the void area curve (VAC). A parameter representing the shape of the VAC was extracted based on the shape determinant factor of CDF. Standard deviation (\(\sigma\)) is the most representative parameter that determines the shape of the CDF. The standard deviation of VAC can be calculated by Equation (8). \[\sigma_{n^{\prime}}=\sqrt{\frac{\sum_{i=1}^{N}(n^{\prime}_{i}-\overline{n^{ \prime}})^{2}}{N}} \tag{8}\]  
where \(\sigma_{n^{\prime}}\) is the standard deviation of VAC, \(n^{\prime}_{i}\) is \(n^{\prime}\) at the threshold value = \(i\), \(n^{\prime}\) is the mean value of \(n^{\prime}\), and \(N\) is the sample size. The relationship between the standard deviation of VAC and the \(\rho_{d}\) for soil SiL under various water content conditions is shown in Figure 8.  
Figure 8: The relationship between the dry density and standard deviation of VAC. Figure 7: \(n^{\prime}\) of soil images with various dry densities. \(\sigma_{n^{\prime}}\) has a strong correlation with \(\rho_{d}\). Compared with the results of simple thresholding, it is at a similar level of correlation; however, it is highly practical in that it does not require the determination of the threshold value. As a result of the analysis, the standard deviation represents the shape of the VAC well.