Soil structure is highly interconnected to all of its properties and functions. The structure for most soils is very complex and hierarchical in nature. Considering the fact that a truly multiscale digital 3D soil structure model for a single genetic horizon, even with the resolution not finer than 1 μm, will contain an enormous amount (approx. up to 10¹⁵ voxels or even more) of data, it is an appealing idea to compress this structural information. Effective management and pore‐scale simulations based on such datasets do not seem feasible at the moment. Another approach would be to reduce the complexity to a limited but meaningful set of characteristics/parameters, for example using universal correlation functions (CFs). In this study, we successfully compressed the soil structural information in the form of 3D binary images into a set of correlation functions, each of which is described using only six parameters. We used four different correlation functions (two‐point probability, lineal, cluster and surface‐surface functions) computed in three orthogonal directions for the pores. The methodology was applied to 16 different soil 3D images obtained using X‐ray microtomography (XCT) and segmented into pores and solids. All computed CFs were fitted using a superposition of three basis functions. In other words, we reduced 900–1300³ voxel images into sets of 72 parameters. Fitting of computed correlation functions and reducing them to a number of parameters is a powerful way of compressing soil structural information. However, the analysis based on parameters alone is different from the one where correlation functions are used. This problem can be negated by uncompressing the correlation functions back from these parameters before any application. This way, correlation functions are not only a way to compress the soil structural information with minimal loss, but also may be used to solve a number of additional problems, including the comparison and differentiation of soil samples, location of elementary volumes, effective physical property prediction using machine learning, and fusion of hierarchical soil structures.

中文翻译：

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将土壤结构信息压缩为参数化相关函数

土壤结构与其所有特性和功能高度相关。大多数土壤的结构在本质上是非常复杂和分层的。考虑到一个事实，即即使单个分辨率不超过1μm，一个真正的多尺度数字3D土壤结构模型也将包含大量的数据（大约10 ¹⁵体素甚至更多的数据），压缩此结构信息是一个很吸引人的想法。目前，基于此类数据集的有效管理和孔隙尺度模拟似乎并不可行。另一种方法是例如使用通用相关函数（CF）将复杂度降低到有限的但有意义的特征/参数集合。在这项研究中，我们成功地将3D二进制图像形式的土壤结构信息压缩为一组相关函数，每个函数仅使用六个参数进行描述。我们使用了在三个正交方向上计算的四个不同的相关函数（两点概率，线性，聚类和表面-表面函数）。该方法适用于使用X射线显微断层扫描（XCT）获得的16种不同的土壤3D图像，并细分为孔隙和固体。使用三个基函数的叠加拟合所有计算出的CF。换句话说，我们减少了900–1300^将3个体素图像分为72个参数集。拟合计算的相关函数并将其简化为多个参数是压缩土壤结构信息的一种有效方法。但是，仅基于参数的分析与使用相关函数的分析不同。通过在任何应用程序之前从这些参数解压缩相关函数可以解决此问题。这样，相关函数不仅是一种以最小的损失压缩土壤结构信息的方法，而且还可以用于解决许多其他问题，包括土壤样品的比较和区分，基本体积的位置，有效的物理性质。使用机器学习进行预测，以及分层土壤结构的融合。