# Enhancing Density Prediction of Agricultural Land Soil through Void Area Curve Analysis
## 1 Introduction  
In agricultural land, the soil density is a factor that greatly affects crop growth [1; 2; 3]. Soil density also greatly influences the pore size, water infiltration, and aeration, which greatly affects the crop growth [4; 5]. The soil density is obtained through in situ density tests such as the sand cone method, drive cylinder method, and nuclear method [6]. All of these methods provide reliable data; however, they are difficult to use in agricultural lands where numerous tests are required. The soil density in agricultural land continuously changes with tillage and agricultural management; as a result, it is necessary to develop a method that can quickly identify soil densities at various points [7; 8]. Therefore, a new method for density management in agricultural lands is needed. Soil pores are classified into macropores, mesopores, microopores, ultramicropores, and cryptopores according to their size, with macropores larger than 0.075 mm being highly dependent on soil density [9; 10; 11]. Accordingly, it is possible to predict soil density by observing changes in soil macropores. Digital image processing (DIP) is receiving great attention as a methodology to replace the existing experimental method. DIP is a process of extracting desired data through theappropriate processing of images [12]. DIP enables low cost, rapid, quantitative, versatile, and nondestructive analysis [13; 14; 15; 16; 17; 18]. As an extension of visual observation, DIP is widely used in various fields, such as medicine, aviation, and manufacturing, and is also used to analyze soil characteristics [19; 20; 21]. Examples of soil analysis using DIP include soil constituents [19], soil redoximorphic features [20], particle size distribution [21; 22], void distribution analysis [23], crack analysis [15; 24], and tensile strength [25]. X-ray micro-tomography creates a three-dimensional, precise image of the inside of a sample with a resolution better than 1 micrometer, enabling noninvasive analysis of the composition and pore space of the sample [26; 27]. However, such detailed analysis techniques are still expensive for application in the agricultural field. The performance of digital cameras has significantly developed recently. The soil density prediction using commercial level digital cameras will be of great help to agricultural land soil management. For this purpose, [PERSON] et al. [28; 29] performed an image analysis of soil density using a commercial-level digital camera with a deep neural network and reported an RMSE of 0.044 to 0.107 t/m\({}^{3}\) using a convolutional neural network and an RMSE of 0.080 t/m\({}^{3}\) using a deep neural network. Visible-near-infrared (vis-NIR) spectroscopy stands out as a rapid and nondestructive technique, demonstrating its ability to predict soil properties both in laboratory and field settings, as highlighted by studies conducted by [PERSON] et al. [30] and [PERSON] et al. [31]. Vis-NIR spectroscopy is commonly incorporated with traditional calibration methods such as partial least squares regression (PLSR), support vector machines regression (SVMR), random forests (RF), or, more recently, neural network techniques to improve accuracy [30]. Furthermore, vis-NIR spectroscopy has found utility in predicting soil density. Researchers have achieved this by combining it with gamma-ray attenuation, as demonstrated by [PERSON] and [PERSON] [32], or by employing PLSR algorithms, as evidenced by the investigations of [PERSON] et al. [33] and [PERSON] et al. [34]. In their study, [PERSON] and [PERSON] [32] successfully calibrated measurements from a gamma-ray attenuation sensor alongside vis-NIR data to predict bulk density, achieving a result with a root mean square error of only 0.055 g/cm\({}^{3}\). Similarly, [PERSON] et al. [33] reported a moderate R\({}^{2}\) value of 0.63 for bulk density prediction by employing vis-NIR in conjunction with PLSR. Meanwhile, [PERSON] et al.