Assessing the fidelity of neural network-based segmentation of soil XCT images based on pore-scale modelling of saturated flow properties

Highlights

• We present the initial results of a novel method of using neural networks for soil XCT image segmentation.

• Depending on the sample, the accuracy in terms of permeability hit 5% error.

• To segment soil images, we used hybrid U-net + ResNet-101 architecture.

• It was shown that the low representativity of XCT images could explain low accuracy cases.

• Larger image libraries, better ground-truth data and network architecture were proposed as ways forward.

Abstract

Direct imaging methods, among which X-ray computed tomography (XCT) continues to dominate, enable the study of soil structure at different scales. However, to compute different morphological parameters or assess soil physical properties using pore-scale modelling we need to perform image segmentation to divide the XCT greyscale image representing local absorption of X-ray radiation into major constituents or phases. Here we focused on the simplest type of segmentation procedure – binarization into pores and solid phases. We present the initial results for soil XCT image segmentation using convolutional neural networks (CNN). We assumed that current state-of-the-art local segmentation approaches could provide ground truth data to perform neural network training. We used hybrid U-net + ResNet-101 architecture and segmented seven soil XCT images. The training was performed by excluding the segmented image from training and validation datasets. The segmentations’ accuracy was assessed using standard computer vision metrics (precision, recall, intersection over union or IoU) and pore-scale simulations to compute the permeability of resulting 3D binary soil images. Depending on the soil sample, the error of segmentations in terms of computed hydraulic properties varied from 5% to 130%. The IoU metric was found to be the most sensitive to false positive and false negative porosity predictions by the neural network. To explain observed variations, we performed ground-truth and original XCT greyscale images analysis with the help of correlation and covariance functions. In addition to a comparison between images, we also trained another segmentation neural network that used all samples as a training/verification dataset that helped to explain the inaccuracies caused by insufficient representativeness of some soil sample structures in the training dataset. We discussed possible ways to improve the segmentation results in the future, including the usage of larger soil image libraries, physically modelled ground-truth data, and advanced neural network architectures.

Introduction

Soil scientists have acknowledged for many decades that the structure of soils, i.e., the spatial organization of the constituent phases, influences significantly the processes that take place in soils.. Soil structure reflects and connects all key functions: e.g., microorganism and soil fauna growing and functioning (Vidal et al., 2018), plant vegetation (Zhao et al., 2017; Metzger et al., 2017), organic matter transformation and its sequestration (Wang et al., 2017), soil resistance to erosion (Barthès & Roose, 2002), water fluxes and transport of solutes (Janssen et al., 2010; Gerke et al., 2015a) – this brief list is far from being complete. Here by soil structure we refer to its spatial composition at all scales from meters to nanometers (Martín et al., 2017; Karsanina et al., 2018; Gerke et al., 2021), unlike the historical misnomer terminology that relates structure exclusively to soil aggregates. This latter misconception is especially unattractive considering the possibility that soil aggregates are not structure forming units (Baveye, 2020); however, this idea is currently debated (e.g., Yudina and Kuzyakov, 2019) and actively researched. One of the most important soil structural components is the pore space that provides the roadway for microorganisms and fauna migration, water and solute fluxes to flow and is dynamic by its nature due to the influence of all the aforementioned functions, including plant roots as well as the influence of other environmental factors (such as climate). While macroscopically, some soils may have similar characteristics, the microscopic structure may significantly affect the soil functions due to differences in pore sizes and their interconnectivity (Baveye et al., 2018 and references therein; Koestel et al., 2020). As all soil functions and soil structure constantly affect each other, such metrics for soil structure as pore-size distribution (e.g., Pires et al., 2017) and correlation functions (e.g., Karsanina et al., 2015) can be used to monitor soil functions (Rabot et al., 2018). Moreover, soil structural data may be used to numerically evaluate soil physical properties (Vogel & Roth, 2001; Khan et al., 2012; Gerke et al., 2019; Pot et al., 2020; Gerke et al., 2020).

There are plenty of methods to assess soil structures, which can be roughly divided into two classes: indirect semi-integral and direct imaging approaches. The first class includes water-retention curve inversion, nuclear magnetic resonance and mercury/gas porosimetry (Hajnos et al., 2006). The second class is predominated by classical thin-sectioning (Skvortsova & Kalinina, 2004; Bryk, 2018), X-ray computed tomography (XCT) imaging (Wildenschild et al., 2002; Gerke et al., 2012; Cnudde et al., 2006), SEM (Schaefer et al., 2004) and FIB-SEM (Gerke et al., 2021) imaging. Direct imaging provides information in the form of a 2/3D digital image that is much more robust, as indirect methods tend to provide approximate or simply unreliable results (e.g., Diamond, 2000). On the other hand, all direct approaches usually suffer from resolution versus field-of-view trade-off (Gerke et al., 2015b) and are more time-consuming/laborious. The former issue can be circumvented with multi-scale image fusion (Karsanina et al., 2018), potentially building a multi-scale 3D digital soil model of any complexity (Karsanina and Gerke, 2018; Karsanina et al., 2020). Among the direct imaging methods, XCT is currently the most prominent approach to the study of soil structure at the micro-scale due to its 3D non-destructive nature. However, XCT imaging results represent stacks of images with local X-ray attenuation at each pixel/voxel and require image processing to extract more useful information needed for soil structure analysis.

The key step in analyzing soil structure based on XCT images is segmentation, or, in case we are considering only pores and solids – binarization. This procedure classifies each pixel/voxel on the XCT greyscale image into the major material or phase. It is important to note that XCT information alone is not enough to segment different chemical/mineral components, as X-ray attenuation is affected by both Z_eff- (effective atomic number) and density. Although the problem can be tackled in some cases using multi-energy scanning and inverse problem solving (Yang et al., 2013; Victor et al., 2017), it is hardly useful for soils due to their vast number of constituents. The multi-energy scanning can be performed with mono and polychromatic X-ray sources, but synchrotron radiation is usually preferable because the polychromatic case humpers inverse problem’s solution and introduces more noise into the resulting distribution. In this context, XCT image segmentation is an approximation, more so due to the inherent problem of partial volume effects – while real materials and interfaces between them have an infinite resolution (well, up to a molecular scale), XCT images have some resolution limitation and, thus, each pixel/voxel may contain a mixture of phases. Nonetheless, in most cases, we do need to perform image processing before analysis and modelling.

The current state-of-the-art segmentation techniques are mainly consisting of local segmentation techniques such as indicator kriging (Oh & Lindquist, 1999; Houston et al., 2013), region growth (Hashemi et al., 2014; Gerke & Karsanina, 2020) or converging active contours (Sheppard et al., 2004). In these methods, unlike in inferior global segmentation approaches (Iassonov et al., 2009), each of the two phases has two thresholds. For example, in the case of binarization, there are the two following thresholds – one at the bottom in which we are sure all pixels/voxels are pores, and the other on top, which is solid. Now, all the pixels/voxels between these two thresholds are processed using different statistical techniques to add them to either the pore or the solid bin. Such thresholds can be chosen either manually or automatically (Schlüter et al., 2010). Unfortunately, as was quite elegantly shown by Baveye et al. (2010), no automatic technique is better than a skilled operator at the time of that study, yet all the operators are prone to severe errors and the results disagree significantly between operators. Another class of segmentation approaches is based on unsupervised learning with clustering (Chauhan et al., 2016). While this may look like a solution to the segmentation problem, in reality, these approaches are far from being perfect. The clustering procedure itself requires the number of clusters as an input parameter dependent on an operator. Markov random field (MRF) methods can perform multi-phase segmentation with an automatic decision on the number of clusters but depend on an additional input parameter (Kulkarni et al., 2012). Furthermore, these segmentations' quality is far from adequate (especially for multi-phase segmentation with “sandwiched” intermediate phase effects) – this is not surprising due to the simplicity of the clustering technique.

To eliminate errors due to the operators or the inaccuracies of automatic/clustering techniques, supervised machine learning with neural networks can be used (Karimpouli & Tahmasebi, 2019; Varfolomeev et al., 2019). The major problem with unsupervised methods lies in the absence of ground-truth data (GT) for training. This paper aims to check the accuracy of neural networks-based segmentations for soil XCT images based on computing saturated flow properties using binarized pore geometries. While the methodology to create GTs for XCT images is under active development, in this contribution we hypothesize that images processed with current state-of-the-art local segmentation methods can serve as proxies for GT datasets. This way, after building a robust technology to create GT, we shall have readily available and robust supervised segmentation tools at our disposal.