2D Cross-sectional Images Research Articles

Stereo slit-scanning tomography of the anterior segment of the human eye

We demonstrate a new tomographic imaging device for 2D cross-sectional and 3D volumetric images of the anterior eye segment. The optical system combines optical sectioning with a stereoscopic camera setup to determine the true spatial location of the ocular structures. Moreover, we propose a calibration procedure to estimate the triangulation function that links the stereo camera pixel indices with the eye-referenced 3D spatial coordinates. The proposed instrument will image the entire anterior chamber and contiguous structures, including the corneal limbus, sclera and eyelids. Furthermore, the system can obtain corneal topography. Finally, we studied the repeatability of the instrument and its agreement with a commercial Scheimpflug imaging tomographer in a group of healthy subjects.

Transfer learning-based techniques for efficient 3D-reconstruction of functionally graded materials

The various properties and phenomena in materials significantly depend on the high-quality three-dimensional (3D) microstructure. This paper proposes a novel method for 3D reconstruction of functionally graded materials (FGMs) using transfer learning techniques to overcome the limitations of experimental 3D microscopy. The approach begins by interpolating 2D cross-sectional images of FGM microstructures through a hybrid deep learning method combining StyleGAN and Gatys techniques, generating intermediate images based on style and content. In the next step, transfer learning is applied using convolutional occupancy networks to reconstruct the 3D microstructure from the 2D image depth layers, with the model trained on point clouds obtained from 2D images. To validate the method, the reconstructed microstructures are compared to actual material images at the same depth using various metrics, including lineal path, two-point correlation, and quality of connection functions. The results show a high degree of accuracy, indicating that the reconstructed images closely match the target microstructures. Finally, to show the application of model the approach is implemented to the functionally graded lanthanum strontium manganite (LSM) and 3D microstructure of this FGM has been extracted using the approach

Cross-Professional Evaluation of 3D Visualization of Liver Malignancies in the Decade of AI and Automatic Segmentation: A Benefit for Multidisciplinary Teams and Tumor Board Decisions?

Purpose To investigate whether automatic 3D visualization of computed tomography (CT) data sets with singular liver tumor compared to 2D images could foster a broader understanding of tumor localization and resectability in the liver within a multidisciplinary team and might therefore be a useful tool in multidisciplinary decision-making. Material and methods The study was configured as a web-based questionnaire. Physicians of all levels of medical training from surgery, radiology, and gastroenterology departments were recruited. A total of seven cases with singular liver tumor CT images with adequate quality were selected. Automatic 3D segmentation was performed using Universal Atlas (Release 5.0) as part of the Brainlab of Elements software suite (Brainlab AG, Munich, Germany). All cases were randomly presented in a 2D and 3D manner. After every case-presentation, multiple choice (single answer) questions concerning tumor extent and resectability were asked. The questions as well as the answers defined to be correct, were evaluated by two senior consultants from the radiology and surgery department.The primary outcome parameters were the correctness of answers stratified for medical specialty and for the level of medical training. The secondary outcome was the time needed for the evaluation of seven liver cases using 2D versus 3D images. Sixadditional questions were tailored to evaluate the subjective value of the 3D visualization. Results A total of 92 participants participated in the study, 31.5% of them were abdominal surgeons, 34.8% gastroenterologists, and 33.7% radiologists. Based on the level of medical training, 66 were residents (71.7%) and 26 consultants (28.3%). Only radiologists answered more questions correctly using 2D imaging compared to the 3D method (p = 0.006). There was no statistically significant difference between correctly answered questions when using 2D vs. 3D visualization in the gastroenterologist and surgeon groups (p > 0.05). The resident subgroup showed no statistically significant difference when using the 2D vs. 3D images (p > 0.05), the consultant subgroup answered more questions correctly using 2D imaging (p = 0.009). Physicians with elementary experience of liver pathology also showed no difference in 2D vs. 3D (p = 0.332), physicians with proficient experience of liver pathology answered more questions correctly using 2D imaging (p = 0.010). The median time taken for the evaluation of the seven liver cases was only significantly faster for the gastroenterologist group (p = 0.006) using the 3D analysis (median: 9.1 minutes) than the 2D analysis (median: 10.7 minutes). Over 80% of the participants found the 3D presentation to be a helpful additional tool for the clinical routine according to the subjective questionnaire. Conclusion In this study 3D visualization of liver tumors was evaluated as helpful within a multidisciplinary team of radiologists, surgeons, and gastroenterologists. However, significantly superior results in the understanding of liver anatomy could not be demonstrated by means of 3D visualization. It may be that more immersive technologies such as augmented reality or virtual reality will lead to a superior understanding compared to conventional presentation of information in 2D cross-sectional images.

Freeze-casting uniformity and domains

Freeze-casting is a technique for making centimeter long microchannel structures. Freeze-cast samples are often characterized from 2D cross-sectional images, resulting in weak determination of porosity and surface area as function of height of the sample. Here we analyze a freeze-cast 40 mm long sample of ▪ (LCSM) for which we have a full X-ray tomography dataset with a voxel size of 23.34×23.34×23.34μm3, as well as a high resolution cutout with a voxel size of 2.77×2.77×2.77μm3. We analyze the porosity and tortuosity and show that the latter is 1.17 and 1.27 for the solid and pore phase respective in the direction along the microchannels, but 5.12 and 8.83 in the perpendicular direction. We also quantify the domain structure of the freeze-casted pores and show that this is not uniform for the sample, but that the angular orientation and number of domains is preserved throughout the sample.

A MATLAB approach for developing digital rock models of heterogeneous limestones for reactive transport modeling

Porosity is a key parameter controlling the physico-chemical behavior of porous rocks. Digital rock physics offers a unique technique for imaging the inherently heterogeneous rock microstructure at fine spatial resolutions and its computational reconstruction, through which a better understanding and prediction of the rock behavior can be achieved. In this study, we propose a simple but accurate method to build a 3D porosity map of centimeter-scale carbonate rock cores from X-ray Micro Computed Tomography (XMCT) imaging data. The method consists of 3 main steps: i) decomposition of 3D volumetric XMCT data into sub-volumes, ii) processing of equidistributed 2D cross-section images in each sub-volume and iii) 2D slice-by-slice calculation of porosity and its assembly to reconstruct a 3D continuum porosity map over the whole core domain using a MATLAB code. The proposed approach significantly conserves the required memory to manipulate large image datasets. The digitized porosity representations are used to build 3D permeability maps of the cores by applying an explicit permeability-porosity relationship. The permeability maps are used as input for numerical simulation of the rock response to the percolation of reactive fluids through which the general validity of the approach is verified. The developed digital rock model paves the way for an improved understanding of reactive transport in carbonate rocks.

Transmit beam design for tissue harmonic volume imaging of muscular tissues with a row-column array

Row-Column-addressed Arrays (RCAs), which have recently become commercially available, transmit along the rows and receive along columns of a 2D array in order to produce 3D volume images with low channel count. Imaging of the inherently three-dimensional, layered, and fibrous structure of muscular tissues in 3D using an RCA can improve evaluations of muscle function and disease compared to conventional 2D cross-sectional imaging, but volume images obtained using an RCA suffer from low lateral spatial resolution, low contrast, and grating lobe artifacts. Tissue harmonic imaging (THI) employs nonlinear acoustic effects to image at twice the transmit frequency, and can yield increased spatial resolution, increased contrast, and decreased artifacts from grating lobes. Here we investigate transmission considerations for THI in muscular tissues using a commercially available RCA (Vermon RC6gV). The parameter space is explored efficiently with frequency domain simulations of the 3D Westervelt equation. Pulse inversion imaging is applied experimentally using both steered plane wave and focused transmits to evaluate THI with an RCA in tissue phantoms and in muscular tissue. Pulse inversion volume images are compared to conventional images in terms of signal-to-noise, contrast, and ability to identify layers and fibrous structures in muscle in 3D. [Work supported by NIH HEAL Initiative R61AT012282.]

Three-dimensional body composition parameters using automatic volumetric segmentation allow accurate prediction of colorectal cancer outcomes.

Parameters obtained from two-dimensional (2D) cross-sectional images have been used to determine body composition. However, data from three-dimensional (3D) volumetric body images reflect real body composition more accurately and may be better predictors of patient outcomes in cancer. This study aimed to assess the 3D parameters and determine the best predictive factors for patient prognosis. Patients who underwent surgery for colorectal cancer (CRC) between 2010 and 2016 were included in this study. Preoperative computed tomography images were analysed using an automatic segmentation program. Body composition parameters for muscle, muscle adiposity, subcutaneous fat (SF) and abdominal visceral fat (AVF) were assessed using 2D images at the third lumbar (L3) level and 3D images of the abdominal waist (L1-L5). The cut-off points for each parameter were determined using X-tile software. A Cox proportional hazards regression model was used to identify the association between the parameters and the treatment outcomes, and the relative influence of each parameter was compared using a gradient boosting model. Overall, 499 patients were included in the study. At a median follow-up of 59months, higher 3D parameters of the abdominal muscles and SF from the abdominal waist were found to be associated with longer overall survival (OS) and disease-free survival (all P<0.001). Although the 3D parameters of AVF were not related to survival outcomes, patients with a high AVF volume and mass experienced higher rate of postoperative complications than those with low AVF volume (27.4% vs. 18.7%, P=0.021, for mass; 27.1% vs. 19.0%, P=0.028, for volume). Low muscle mass and volume (hazard ratio [HR] 1.959, P=0.016; HR 2.093, P=0.036, respectively) and low SF mass and volume (HR 1.968, P=0.008; HR 2.561, P=0.003, respectively), both in the abdominal waist, were identified as independent prognostic factors for worse OS. Along with muscle mass and volume, SF mass and volume in the abdominal waist were negatively correlated with mortality (all P<0.001). Both AVF mass and volume in the abdominal waist were positively correlated with postoperative complications (P<0.05); 3D muscle volume and SF at the abdominal waist were the most influential factors for OS. 3D volumetric parameters generated using an automatic segmentation program showed higher correlations with the short- and long-term outcomes of patients with CRC than conventional 2D parameters.

In-air and in-water performance comparison of Passive Gamma Emission Tomography with activated Co-60 rods

A first-of-a-kind geological repository for spent nuclear fuel is being built in Finland and will soon start operations. To make sure all nuclear material stays in peaceful use, the fuel is measured with two complementary non-destructive methods to verify the integrity and the fissile content of the fuel prior to disposal. For pin-wise identification of active fuel material, a Passive Gamma Emission Tomography (PGET) device is used. Gamma radiation emitted by the fuel is assayed from 360 angles around the assembly with highly collimated CdZnTe detectors, and a 2D cross-sectional image is reconstructed from the data. At the encapsulation plant in Finland, there will be the possibility to measure in air. Since the performance of the method has only been studied in water, measurements with mock-up fuel were conducted at the Atominstitut in Vienna, Austria. Four different arrangements of activated Co-60 rods, steel rods and empty positions were investigated both in air and in water to confirm the functionality of the method. The measurement medium was not observed to affect the ability of the method to distinguish modified rod positions from filled rod positions. More extended conclusions about the method performance with real spent nuclear fuel cannot be drawn from the mock-up studies, since the gamma energies, activities, material attenuations and assembly dimensions are different, but full-scale measurements with spent nuclear fuel are planned for 2023.

Estimating Permeability of Porous Media from 2D Digital Images

Digital rock physics (DRP) has been widely used as an effective approach for estimating the permeability of porous media. However, conventional implementation of DRP requires the reconstruction of three-dimensional (3D) pore networks, which suffer from intensive memory and underlying uncertainties. Therefore, it is highly significant to develop an approach only based on two-dimensional (2D) cross-sections of parent samples without 3D reconstruction. In this study, we present a novel approach that combines the Kozeny–Carman equation with fractal theory to derive a bridge function that links 2D cross-sectional images and 3D pore structures of parent samples in flow equivalence. Using this bridge function, we predicted the physical properties of the parent samples, including the permeability, bulk porosity, tortuosity, and pore fractal dimension. To validate our model, we performed Lattice Boltzmann (LB) simulations on nine carbonate samples and compared the LB simulation results with our model’s predictions. We also compared our predicted results with available data on various porous materials, such as sandstone, glass beads, and carbonate, in the literature. Our findings demonstrate that without reconstructing 3D pore networks, our method provides a reliable estimation of sample permeability using 2D cross-sectional images. This approach not only simplifies the determination of sample permeability in heterogeneous porous media but also sheds new light on the inherent correlations between 2D cross-sectional information and 3D pore structures of parent samples. Moreover, the derived model may be conducible to a better understanding of flow in reservoirs during the extraction of unconventional onshore and offshore oil/gas.

Bulk characterization of highly structured tissue paper based on 2D and 3D evaluation methods

The structure of the fibre network in tissue paper can be complex and difficult to analyze, due to the presence of superimposed structures such as creping and patterns that occur, for example, in through-air-dried (TAD) tissue. Properties like high absorbency, a pleasant handfeel, and strength-related characteristics are closely related to the fibre network structure. Therefore, in addition to standard tissue testing methods, techniques that provide insights into the intrinsic properties of the tissue fibre network are essential for a deeper understanding and potential for further optimization. In this study, we utilized 2D cross-sectional images and 3D X-ray microtomography (mu-CT) to evaluate and quantify the intrinsic properties of highly structured TAD tissue. We compared the results obtained from these two methods, focusing on intrinsic thickness, porosity, and the fibre volume to fibre surface area (Fv/Fs) ratio. The open structure of the fibre network, fabric patterns, creping, and protruding fibres make it challenging to define bulk boundaries. Therefore, we examined the effect of different bulk expansion diameters on intrinsic properties. This procedure allows to quantify the effects of under- and overestimation of bulk boundaries, and to determine which regions within the fibre network are affected by bulk expansion. In terms of intrinsic thickness, both 2D and 3D evaluations show similar trends, which facilitates direct comparison of 2D and 3D data. Porosity, on the other hand, does not show any correlation between 2D and 3D-based data. Together with the Fv/Fs parameter, this leads to the conclusion that the depiction of 2D data does not represent the whole fibrous material but predominantly fibres perpendicular or close to perpendicular to the cut plane, whereas 3D data represents all fibres, fibre bonds and network connectivity. This work aims at presenting modern approaches and novel procedures to quantify intrinsic properties of open fibre structures such as tissue, but could also be applied to fibrous networks in general. The introduced methods could provide the basis for future research on the interrelations between intrinsic properties and key tissue properties such as absorbency and handfeel.

SmartOCT: smartphone-integrated optical coherence tomography.

Smartphone devices have seen unprecedented technical innovation in computational power and optical imaging capabilities, making them potentially invaluable tools in scientific imaging applications. The smartphone's compact form-factor and broad accessibility has motivated researchers to develop smartphone-integrated imaging systems for a wide array of applications. Optical coherence tomography (OCT) is one such technique that could benefit from smartphone-integration. Here, we demonstrate smartOCT, a smartphone-integrated OCT system that leverages built-in components of a smartphone for detection, processing and display of OCT data. SmartOCT uses a broadband visible-light source and line-field OCT design that enables snapshot 2D cross-sectional imaging. Furthermore, we describe methods for processing smartphone data acquired in a RAW data format for scientific applications that improves the quality of OCT images. The results presented here demonstrate the potential of smartphone-integrated OCT systems for low-resource environments.

Surrogate modeling of the fan plot of a rotor system considering composite blades using convolutional neural networks with image composition

Abstract This study proposes an image composition technique based on convolutional neural networks (CNNs) to construct a surrogate model for predicting fan plots of three-dimensional (3D) composite blades, which represent natural frequency lists at different rotational speeds. The proposed method composes critical 2D cross-section images to improve the accuracy of the model. Numerical examples with various compositions of cross-section images are presented to demonstrate the efficacy of the CNN model. Additionally, gradient-weighted class activation mapping analysis is used to reveal the relationship between the internal structure of the blade and the fan plots. The study shows that using multiple images in the image composition technique improves the accuracy of the model compared to using single or fewer images. Overall, the proposed method provides a promising approach for predicting fan plots of 3D composite blades using CNN models.

Artificial intelligence method based on multi-feature fusion for automatic macular edema (ME) classification on spectral-domain optical coherence tomography (SD-OCT) images.

A common ocular manifestation, macular edema (ME) is the primary cause of visual deterioration. In this study, an artificial intelligence method based on multi-feature fusion was introduced to enable automatic ME classification on spectral-domain optical coherence tomography (SD-OCT) images, to provide a convenient method of clinical diagnosis. First, 1,213 two-dimensional (2D) cross-sectional OCT images of ME were collected from the Jiangxi Provincial People's Hospital between 2016 and 2021. According to OCT reports of senior ophthalmologists, there were 300 images with diabetic (DME), 303 images with age-related macular degeneration (AMD), 304 images with retinal-vein occlusion (RVO), and 306 images with central serous chorioretinopathy (CSC). Then, traditional omics features of the images were extracted based on the first-order statistics, shape, size, and texture. After extraction by the alexnet, inception_v3, resnet34, and vgg13 models and selected by dimensionality reduction using principal components analysis (PCA), the deep-learning features were fused. Next, the gradient-weighted class-activation map (Grad-CAM) was used to visualize the-deep-learning process. Finally, the fusion features set, which was fused from the traditional omics features and the deep-fusion features, was used to establish the final classification models. The performance of the final models was evaluated by accuracy, confusion matrix, and the receiver operating characteristic (ROC) curve. Compared with other classification models, the performance of the support vector machine (SVM) model was best, with an accuracy of 93.8%. The area under curves AUC of micro- and macro-averages were 99%, and the AUC of the AMD, DME, RVO, and CSC groups were 100, 99, 98, and 100%, respectively. The artificial intelligence model in this study could be used to classify DME, AME, RVO, and CSC accurately from SD-OCT images.

Diagnostic accuracy of fused CBCT images in the evaluation of temporomandibular joint condylar bone resorption.

To evaluate the diagnostic accuracy of fused CBCT images for patients with condylar bone resorption of temporomandibular joint (TMJ) osteoarthrosis. Forty-two TMJs from twenty-one patients were included. Bone resorption of condyles evaluated by three experts was used as the reference standard. Three oral and maxillofacial radiology residents evaluated the resorption of condyles with a five-point scale for the four sets of images (two consecutive CBCT images without fusion, fused 2D cross-sectional images, fused 3D images, andcombining fused 2D cross-sectional images and fused 3D images) randomly and independently. Each set of images was evaluated at least 1week apart, and a second evaluation was performed 4weeks later. Intraclass correlation coefficients were calculated to assess the intra- and inter-observer agreement. The areas under the ROC curves (AUCs) were compared among the four image sets using the Z test. Twenty-four TMJs were determined as condylar bone resorption, and eighteen were determined as no obvious change. The average AUC values from the three observers for the three fused image sets (0.94, 0.93, 0.93) were significantly higher than the image set without fusion (p < 0.01). The intra- and inter-observer agreement on the three fused image sets (0.70-0.89, 0.91-0.92) was higher than the image set without fusion (0.37-0.63, 0.75). Fused CBCT images of TMJ osteoarthrosis patients can intuitively display the condylar bone resorption and significantly improve the diagnostic accuracy. Fused CBCT images can help clinicians intuitively observe bone changes of the condyle in TMJ osteoarthrosis patients.

In vitro and in silico approaches to engineering three-dimensional biological tissues and organoids

<i>In vitro</i> and <i>in silico</i> approaches to engineering three-dimensional biological tissues and organoids

An order statistic approach for inference of the size distribution of 3D particle clusters in metal matrix nanocomposites

Metal matrix nanocomposites (MMNCs) become popular in recent decades due to their superior properties over traditional materials, like high strength and light weight. They are fabricated by dispersing nanoparticles into molten metal matrix. If nanoparticles are not well dispersed and form clusters in the metal matrix, the mechanical properties of the MMNC would be greatly affected. It is crucially important and useful if the size of three-dimensional (3D) clusters in the metal matrix can be extracted for process characterization. This paper proposes a novel approach based on order statistic theory to infer the size distribution of 3D particle clusters based on their two-dimensional (2D) cross-sectional microscopic images. The novelty of this idea is that it utilizes information from only the few largest 2D clusters, hence eliminating the practical difficulties in correctly identifying and accurately measuring the radii of small clusters. The joint probability distribution of the l largest 2D cluster radii is linked to the distribution of the 3D cluster size, based on which then maximum likelihood estimation (MLE) method is used to infer the 3D cluster size distribution. Extensive simulation studies and real cases have demonstrated the effectiveness, efficiency and robustness of the proposed approach compared to the existing methods.

Stochastic reconstruction of 3D microstructures from 2D cross-sectional images using machine learning-based characterization

The availability of high-quality three-dimensional (3D) microstructures is an essential prerequisite to understanding the macroscopic behaviours of heterogeneous media. Considering the high cost of 3D microscopy imaging, it is an economical way to derive large numbers of virtual 3D microstructures from limited morphological information of 2D cross-sectional images. This paper presents an efficient method that incorporates machine learning-based characterization of 2D images to statistically reconstruct 3D microstructures. The latent stochasticity of 2D images is mastered by fitting supervised machine learning models, which essentially characterize the local morphological statistics. A morphology integration scheme is developed to project the 2D morphological statistics into the 3D space, and new equivalent 3D microstructures can then be synthesized by sequentially generating voxel values from probability sampling. The new method is tested on a series of heterogeneous media with distinct morphologies, and it is also compared with two classical methods (i.e. stochastic optimization-based reconstruction and Gaussian random field transformation) in terms of reconstruction accuracy and efficiency. Besides, various microstructural descriptors are used to quantify the discrepancies between the reconstructed and target microstructures. The results confirm that the proposed method provides a highly cost-effective and widely applicable way to reproduce 3D realizations that precisely preserve the statistical characteristics, geometrical irregularities, long-distance connectivity and anisotropy that exist in 2D cross-sectional images.

Integration of 3D Volumetric Computed Tomography Scan Image Data with Conventional Well Logs for Detection of Petrophysical Rock Classes

Summary Core measurements are used for rock classification and improved formation evaluation in both cored and noncored wells. However, the acquisition of such measurements is time-consuming, delaying rock classification efforts for weeks or months after core retrieval. On the other hand, well-log-based rock classification fails to account for rapid spatial variation of rock fabric encountered in heterogeneous and anisotropic formations due to the vertical resolution of conventional well logs. Interpretation of computed tomography (CT) scan data has been identified as an attractive and high-resolution alternative for enhancing rock texture detection, classification, and formation evaluation. Acquisition of CT scan data is accomplished shortly after core retrieval, providing high-resolution data for use in petrophysical workflows in relatively short periods of time. Typically, CT scan data are used as two-dimensional (2D) cross-sectional images, which is not suitable for quantification of three-dimensional (3D) rock fabric variation, which can increase the uncertainty in rock classification using image-based rock-fabric-related features. The methods documented in this paper aim to quantify rock-fabric-related features from whole-core 3D CT scan image stacks and slabbed whole-core photos using image analysis techniques. These quantitative features are integrated with conventional well logs and routine core analysis (RCA) data for fast and accurate detection of petrophysical rock classes. The detected rock classes are then used for improved formation evaluation. To achieve the objectives, we conducted a conventional formation evaluation. Then, we developed a workflow for preprocessing of whole-core 3D CT-scan image stacks and slabbed whole-core photos. Subsequently, we used image analysis techniques and tailor-made algorithms for the extraction of image-based rock-fabric-related features. Then, we used the image-based rock-fabric-related features for image-based rock classification. We used the detected rock classes for the development of class-based rock physics models to improve permeability estimates. Finally, we compared the detected image-based rock classes against other rock classification techniques and against image-based rock classes derived using 2D CT scan images. We applied the proposed workflow to a data set from a siliciclastic sequence with rapid spatial variations in rock fabric and pore structure. We compared the results against expert-derived lithofacies, conventional rock classification techniques, and rock classes derived using 2D CT scan images. The use of whole-core 3D CT scan image-stacks-based rock-fabric-related features accurately captured changes in the rock properties within the evaluated depth interval. Image-based rock classes derived by integration of whole-core 3D CT scan image-stacks-based and slabbed whole-core photos-based rock-fabric-related features agreed with expert-derived lithofacies. Furthermore, the use of the image-based rock classes in the formation evaluation of the evaluated depth intervals improved estimates of petrophysical properties such as permeability compared to conventional formation-based permeability estimates. A unique contribution of the proposed workflow compared to the previously documented rock classification methods is the derivation of quantitative features from whole-core 3D CT scan image stacks, which are conventionally used qualitatively. Furthermore, image-based rock-fabric-related features extracted from whole-core 3D CT scan image stacks can be used as a tool for quick assessment of recovered whole core for tasks such as locating best zones for extraction of core plugs for core analysis and flagging depth intervals showing abnormal well-log responses.

Predicting the permeability of consolidated silty clay via digital soil reconstruction

Numerical modelling of the pore structure of porous media is still one of the most powerful tools for predicting the soil’s permeability and transport properties for geoengineers. However, that approach relies heavily on both the availability and accuracy of microstructural information, which is often challenging to acquire. In this study, statistically equivalent 3D micropore structures of soil samples were reconstructed using a digital soil model, which generated the 3D microstructures using a probabilistic map derived from 2D cross-section images and parameter sets calibrated via a deep learning neural network. The reconstructed images of the 15 micropore structures generated for each of two soil samples with different consolidation pressures (no disturbance and 3200 kPa) indicated that the pores become homogeneous with the consolidation process. The tortuosity factor was found to have a linear correlation with voxel size for simulation. The permeability of each soil sample was computed using the ABAQUS CFD module, and the results of the simulation were comparable to those for the constant head permeability test.

Estimating Size and Number Density of Three-Dimensional Particles Using Truncated Cross-Sectional Data

Abstract The need for estimating three-dimensional (3D) information based on two-dimensional (2D) images has been increasing in numerous fields. It is essential in quality assessment, quality control, and process optimization. However, all the existing methods have not considered the data truncation issue, which is commonly faced in metrology. This paper proposes a new statistical approach to infer size distribution and volume number density (VND) of 3D particles based on 2D cross-sectional images with data truncation considered. In order to estimate the size distribution, a linkage is established between 3D particles and 2D observations with the existence of data truncation. Subsequently, this paper derives the likelihood function of 2D observations and an efficient Monte Carlo expectation-maximization algorithm is developed to estimate the parameters of size distribution. In addition, an explicit relationship between the 3D and 2D particle number densities is established and leveraged to estimate the VND and volume fraction. The effectiveness of the proposed method is demonstrated through both simulation study and real case studies in metal additive manufacturing and metal-matrix nanocomposites manufacturing.