3D Binary Images Research Articles

Multiple Cubes Growth Algorithms for Simple Representative Elementary Volume Determination on 3D Binary Images

Porosity analysis is fundamental for understanding various material properties and transport phenomena in scientific and engineering disciplines. This study delves into the challenging task of determining the representative elementary volume (REV) in porous media, crucial for accurate analyses. Two novel algorithms, Center-Corner Cubes Growing (3CG) and Random Cubes Growing (RCG), were proposed and tested on synthetic body-centered cubic (BCC) sphere packing and natural porous structures of Berea sandstone and Indiana limestone, obtained using µCT. First algorithm (3CG) operates by analyzing porosity within cubes growing from each of the eight corners and a central region of a 3D binarized stack. In contrast, the Random Cube Growing (RCG) algorithm randomly selects seed points within the 3D stack and grows cubic regions around them. Both algorithms systematically compute porosity for various cube sizes, determining the average porosity and standard deviation for each extent. These visual analytics tools contribute to identifying the specific size ranges where porosity curves converge and stabilize, indicating potential REV within the material. While 3CG simplifies the approach by focusing on a limited number of curves, RCG provides a broader view, capturing diverse porosity patterns. The absence of consistent local minima in certain cases indicates high porosity heterogeneity and the impossibility of achieving REV in certain sample sizes.

A parallel programming application of the A* algorithm in digital rock physics

Pore-scale analysis and characterization of reservoir rocks provide valuable information for the definition and management of underground hydrogen storage and CO2 storage or sequestration.This article presents an optimized implementation of the A* algorithm, the most popular pathfinding method in the presence of obstacles. In this context, the algorithm is applied to recognize the minimum length connected paths through each flow direction of 3D images of a porous medium representative of a reservoir rock. The identification of the main paths allows the characterization of the pore space and the calculation of fundamental petrophysical properties such as tortuosity and effective porosity, which can be used for permeability estimation. Compared to other algorithms available for pore-scale characterization, such as the pore centroid, A* provides a better approximation of the pore space available for the flow and, therefore, a reliable characterization of the petrophysical properties. On the other hand, path identification is significantly consuming in terms of time and memory. In this paper, an efficient and optimized implementation based on C++/OpenMP programming language is presented.The proposed implementation aims to the analysis of large-scale models profiting from parallelization, memory optimization, and enhanced managing of dead paths. Three test cases of increasing sizes are presented, to analyze the advantages and the disadvantages of the algorithm as the number of explored points increases. The 3D binary images analyzed are related to a synthetic domain (1 million voxels) and two actual sandstone samples (about 4 and 64 million voxels respectively). The code is validated against a Matlab serial implementation, showing a significant improvement in efficiency. Remarkable test cases of several millions of voxels were afforded, overcoming the memory and execution slowness issues. Moreover, the proposed implementation is suitable for large pore-scale models run in HPC environments.

Evaluation of Skeletonization Techniques for 2D Binary Images

In the realm of modern image processing, the emphasis often lies on engineering-based approaches rather than scientific solutions to address diverse practical problems. One prevalent task within this domain involves the skeletonization of binary images. Skeletonization is a powerful process for extracting the skeleton of objects located in digital binary images. This process is widely employed for automating many tasks in numerous fields such as pattern recognition, robot vision, animation, and image analysis. The existing skeletonization techniques are mainly based on three approaches: boundary erosion, distance coding, and Voronoi diagram for identifying an approximate skeleton. In this work, we present an empirical evaluation of a set of well-known techniques and report our findings. We specifically deal with computing skeletons in 2d binary images by selecting different approaches and evaluating their effectiveness. Visual evaluation is the primary method used to showcase the performance of selected skeletonization algorithms. Due to the absence of a definitive definition for the "true" skeleton of a digital object, accurately assessing the effectiveness of skeletonization algorithms poses a significant research challenge. Although researchers have attempted quantitative assessments, these measures are typically customized for specific domains and may not be suitable for our current work. The experimental results shown in this work illustrate the performance of the three main approaches in applying skeletonization with respect to different perspectives.

Improving patch-based simulation using Generative Adversial Networks

Multiple-Point Simulation (MPS) is a geostatistical simulation technique commonly used to model complex geological patterns and subsurface heterogeneity. There have been a great variety of implementation methods developed within MPS, of which Patch-Based Simulation is a more recently developed class. While we have witnessed great progress in Patch-Based algorithms lately, they are still faced with two challenges: conditioning to point data and the occurrence of verbatim copy. Both of them are partly due to finite size of Training image, from which a limited size of pattern database is constructed. To address these questions, we propose a novel approach that we call Generative-Patched-Simulation (GPSim), which is based on Generative Adversarial Networks (GAN). With this method, we are able to generate sufficient (in theory an infinite) number of new patches based on the current pattern database. As demonstrated by the results on a simple 2D binary image, this approach shows its potential to address the two issues and thus improve Patch-based Simulation methods.

Prediction of 3D Velocity Field of Reticulated Foams Using Deep Learning for Transport Analysis

Data-driven deep learning models are emerging as a new method to predict the flow and transport through porous media with very little computational power required. Previous deep learning models, however, experience difficulty or require additional computations to predict the 3D velocity field which is essential to characterize porous media at the pore scale. We design a deep learning model and incorporate a physics-informed loss function that enforces the mass conservation for incompressible flows to relate the spatial information of the 3D binary image to the 3D velocity field of porous media. We demonstrate that our model, trained only with synthetic porous media as binary data without additional image processing, can predict the 3D velocity field of real reticulated foams which have microstructures different from porous media that were studied in previous works. Our study provides deep learning framework for predicting the velocity field of porous media and conducting subsequent transport analysis for various engineering applications. As an example, we conduct heat transfer analysis using the predicted velocity fields and demonstrate the accuracy and advantage of our deep learning model.

Efficient Strategies for Computing Euler Number of a 3D Binary Image

As an important topological property for a 3D binary image, the Euler number can be computed by finding specific a voxel block with 2 × 2 × 2 voxels, named the voxel pattern, in the image. In this paper, we introduce three strategies for enhancing the efficiency of a voxel-pattern-based Euler number computing algorithm used for 3D binary images. The first strategy is taking advantage of the voxel information acquired during computation to avoid accessing voxels repeatedly. This can reduce the average number of accessed voxels from 8 to 4 for processing a voxel pattern. Therefore, the efficiency of computation will be improved. The second strategy is scanning every two rows and processing two voxel patterns simultaneously in each scan. In this strategy, only three voxels need to be accessed when a voxel pattern is processed. The last strategy is determining the voxel accessing order in the processing voxel pattern and unifying the processing of the voxel patterns that have identical Euler number increments to one group in the computation. Although this strategy can theoretically reduce the average number of voxels accessed from 8 to 4.25 for processing a voxel pattern, it is more efficient than the above two strategies for moderate- and high-density 3D binary images. Experimental results demonstrated that the three algorithms with each of our proposed three strategies exhibit greater efficiency compared to the conventional Euler number computing algorithm based on finding specific voxel patterns in the image.

Parallel border tracking in binary images for multicore computers

Border tracking in binary images is an important operation in many computer vision applications. The problem consists in finding borders in a 2D binary image (where all of the pixels are either 0 or 1). There are several algorithms available for this problem, but most of them are sequential. In a former paper, a parallel border tracking algorithm was proposed. This algorithm was designed to run in Graphics Processing units, and it was based on the sequential algorithm known as the Suzuki algorithm. In this paper, we adapt the previously proposed GPU algorithm so that it can be executed in multicore computers. The resulting algorithm is evaluated against its GPU counterpart. The results show that the performance of the GPU algorithm worsens (or even fails) for very large images or images with many borders. On the other hand, the proposed multicore algorithm can efficiently cope with large images.

An Efficient Connected-Component Labeling Algorithm for 3-D Binary Images

Conventional voxel-based algorithms for labeling connected components in 3D binary images use the same mask to process all object voxels. To reduce the number of times that neighboring voxels are checked when object voxels are processed, we propose an algorithm that uses two different masks for processing two different types of object voxels. One type of mask is used when the voxel preceding the object voxel being processed is an object voxel, and the other type is used otherwise. In either case, an optimal order is used for checking the voxels in the corresponding mask. Experimental results demonstrate that our proposed algorithm checked fewer voxels, and was more efficient than conventional algorithms.

Pore-network extraction using discrete Morse theory: Preserving the topology of the pore space.

Pore-scale modeling based on the 3D structural information of porous materials has enormous potential in assessing physical properties beyond the capabilities of laboratory methods. Such capabilities are pricey in terms of computational expenses, and this limits the applicability of the direct simulations to a small volume and requires high-performance computational resources, especially for multiphase flow simulations. The only pore-scale technique capable of dealing with large representative volumes of porous samples is pore-network (PNM) based modeling. The problem of the PNM approach is that 3D pore geometry first needs to be simplified into a graph of pores and throats that conserve topological and geometrical properties of the original 3D image. While significant progress has been achieved in terms of geometry representation, no methodology provides full conservation of the topological features of the pore structure. In this paper we present a pore-network extraction algorithm for binary 3D images based on discrete Morse theory and persistent homology that by design targets topology preservation. In addition to methodological developments, we also clarify the relationship between topological characteristics of constructed Morse chain complex and pore-network elements. We show that the Euler numbers calculated for PNMs based on our methodology coincide with those obtained using the direct topological analysis. The characteristics of the extracted pore network are calculated for several 3D porous binary images and compared with the results of maximum inscribed balls-based and watershed-based approaches as well as a hybrid approach to support our methodology.

A 3D convolutional neural network accurately predicts the permeability of gas diffusion layer materials directly from image data

Three dimensional convolutional neural networks (3D CNNs) were used to accurately predict the permeability of fuel cell gas diffusion layer (GDL) materials directly from 3D binary image data. A straightforward 3D CNN architecture was trained and evaluated on a dataset of 7500 numerically generated GDL materials using five-fold cross validation. The permeability of the generated GDL materials was calculated using pore network modelling and comported with literature reported values. The 3D CNN converged to acceptable prediction error quickly and with minimal hand tuning of hyperparameters. The trained 3D CNN had low prediction error when compared to contemporary models performing similar tasks, with an average mean absolute error (MAE) of 4.660E-13 m2 and an R2 of 0.9885, when evaluated on test fold materials. Lastly, a learning curve analysis was also performed.

Automatic Lung Cancer Segmentation in [18F]FDG PET/CT Using a Two-Stage Deep Learning Approach.

Since accurate lung cancer segmentation is required to determine the functional volume of a tumor in [18F]FDG PET/CT, we propose a two-stage U-Net architecture to enhance the performance of lung cancer segmentation using [18F]FDG PET/CT. The whole-body [18F]FDG PET/CT scan data of 887 patients with lung cancer were retrospectively used for network training and evaluation. The ground-truth tumor volume of interest was drawn using the LifeX software. The dataset was randomly partitioned into training, validation, and test sets. Among the 887 PET/CT and VOI datasets, 730 were used to train the proposed models, 81 were used as the validation set, and the remaining 76 were used to evaluate the model. In Stage 1, the global U-net receives 3D PET/CT volume as input and extracts the preliminary tumor area, generating a 3D binary volume as output. In Stage 2, the regional U-net receives eight consecutive PET/CT slices around the slice selected by the Global U-net in Stage 1 and generates a 2D binary image as the output. The proposed two-stage U-Net architecture outperformed the conventional one-stage 3D U-Net in primary lung cancer segmentation. The two-stage U-Net model successfully predicted the detailed margin of the tumors, which was determined by manually drawing spherical VOIs and applying an adaptive threshold. Quantitative analysis using the Dice similarity coefficient confirmed the advantages of the two-stage U-Net. The proposed method will be useful for reducing the time and effort required for accurate lung cancer segmentation in [18F]FDG PET/CT.

Early diagnosis of pulmonary embolism using deep learning and SPECT/CT Exams Fusion

Background: Pulmonary embolism is a serious disease, which can be life-threatening. Its treatment and its detection are sometimes complicated. The two most commonly used imaging techniques are the computed tomography pulmonary angiography and the pulmonary scintigraphy. Currently, hybrid imagery, combining single photon emission computerized tomography and computed tomography (SPECT/CT), play an important role in the diagnosis of pulmonary embolism. Objective: Our aim, in the analytical study, is to detect the pulmonary embolism. A whole new method based on the fusion of SPECT and CT images by the deep Siamese Neural Network is proposed to early detect this fatal disease. Material and methods: This method consists of two main parts: fusion of SPECT and CT images and detection of the pathological lobes. It starts with the segmentation of both SPECT and CT images to obtain 3D binary images. Next, we detect the different pulmonary lobes in the CT images. Then, we merge the two SPECT and CT images by deep Siamese Neural Network. Afterward, they are compared to the image where the different lobes are identified to finally detect the pulmonary embolism and identify the pathological lobes. Results: The validation achieved an accuracy of 90.5%, with a sensitivity of 88.2% and a specificity of 91.5%. Conclusion: The obtained results prove the effectiveness of the proposed method in the detection of pulmonary embolism.

Application of A∗ algorithm for microstructure and transport properties characterization from 3D rock images

Thorough comprehension of flow behavior in underground porous media is fundamental for several applications such as oil and gas production, Underground Gas Storage, CO2 storage, and Enhanced Geothermal Systems. Macroscale petrophysical parameters, as well as hydraulic parameters, are strongly linked to the microstructure of the rock.In this paper, we present a methodology for the geometric analysis and characterization of the pore structure of 3D binary images of rocks. The geometric analysis is based on the A∗ pathfinding algorithm extended to 3D domains and on the measurement of the pore radius along the identified paths. The analysis is carried out for the main flow directions to obtain a tensorial representation of tortuosity, effective porosity, and representative pore radius, to provide permeability estimation and effective characterization of anisotropy. Moreover, the approach provides the analysis of pore size distribution and constriction.The methodology was applied to synthetic but realistic rock samples, generated through the QSGS algorithm. Two case studies, representative of an isotropic and an anisotropic porous media, are presented. Validation was carried out through comparison with FVM hydrodynamic modeling. Analysis of the results shows that the presented geometric approach can provide thorough and reliable characterization of the porous media.

Investigating The Permeability Prediction Using Geometric Properties of Micro Computed Tomography Images by Linear Regression Models

Challenges on rock absolute permeability prediction from tiny sample when laboratory apparatus is not applicable and without pore network modelling is remarkable. This prediction using the characterization of micro-computed tomography images have been studied in this paper. Twenty series of 2D micro computed tomography rock binary images have been collected, each of them was considered as a 3D binary image. Their geometric measures in 2D and 3D for measuring image properties have been considered using Minkowski functionals and available functions, developing a regression model, absolute permeabilities have been evaluated. Some 2D and 3D geometric properties are considered. The area, the perimeter and the 2D Euler number are 2D binary images properties. The volume, the surface area, the mean breadth also known as integral of the mean curvature, and the 3D Euler Number are 3D binary images properties. Porosity and number of objects also have been considered as parameters of a regression model.To perform linear regression, twenty-four parameters were evaluated and some of them were chosen to be used. An equation is proposed based on the extensive study conducted which can predict rock permeability. This equation has two sets of parameter coefficients, one set predicts high permeability rocks (above two Darcy) and the other for low and medium permeability (less than two Darcy) which can be used for carbonated rock. Average absolute relative error for conducted cases is 0.06.

A Study on Various Mesh Generation Techniques used for Engineering Applications

In this paper our aim is to provide a survey of mesh generation techniques for some Engineering applications. Mesh generation is a very important requirement to solve any problem by very popular numerical method known as Finite element method (FEM). It has several applications in various fields. One such technique is Automated generation of finite element meshes for aircraft conceptual design. It’s an approach for automated generation of fully connected finite element meshes for all internal structural components, given wing body, geometry model, controlled by a few conceptual level structural layout parameters. Another application where it is used is in the study of biomolecules to generate volumetric mesh of a biomolecule of any size and shape based on its atomic structure. These methods are proved to be a faster method due to the usage of computing techniques. Mesh generator is also used for creating finite element surface and volumetric mesh from 3D binary and gray scale medical images. Some of the applications include volumetric images, surface mesh extraction, surface mesh repairing and many more. It is of great importance in understanding the human brain which is a complex subject. Though 3D visualization is a useful tool available, yet it is inadequate due to its challenging computational problem. This paper also includes the survey on latest tools used for these applications which overcomes many problems associated with the conventional approaches.

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

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.

Compressing soil structural information into parameterized correlation functions

AbstractSoil 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.Highlights The 900–13003 voxels soil XCT scans were compressed into sets of 72 parameters The use of fitted parameters alone may result in the inconsistent analysis of the soil structures Each soil structure was uniquely described by a set of directional correlation functions Correlation functions were found to be sensitive to the structural difference of all the studied soils

Image-based effective medium approximation for fast permeability evaluation of porous media core samples

An image-based effective medium approximation (EMA) is developed so as to permit very fast transport properties evaluations of 3D porous media. From an image-based porous network (IBPN) built upon digital image processing of 3D binary images, we focus on throat’s local geometrical properties at the pore scale, for being the most sensible structural units which build up the local pressure. This approach is a 3D image–based extension of the critical point approach proposed in 2D fractures. We show, from analyzing various core rock samples available in the literature, that the asymptotic assumptions associated with the preeminence of critical points in throats are indeed geometrically relevant. We then describe how the image-based EMA evaluated from the conductances computed from the discrete IBPN can be reliably evaluated. The proposed method is evaluated upon the estimation of core sample permeability from binarized image obtained using X-ray tomography. Since it combines digital image treatments with statistical data post-processing without the need of computational fluid dynamics (CFD) computation, it is extremely cost efficient. The results are compared with a micro-scale Stokes flow computation in various rock samples. The sensitivity to the pore discretization also is discussed and illustrated.

Quantitative Evaluation of Dense Skeletons for Image Compression

Skeletons are well-known descriptors used for analysis and processing of 2D binary images. Recently, dense skeletons have been proposed as an extension of classical skeletons as a dual encoding for 2D grayscale and color images. Yet, their encoding power, measured by the quality and size of the encoded image, and how these metrics depend on selected encoding parameters, has not been formally evaluated. In this paper, we fill this gap with two main contributions. First, we improve the encoding power of dense skeletons by effective layer selection heuristics, a refined skeleton pixel-chain encoding, and a postprocessing compression scheme. Secondly, we propose a benchmark to assess the encoding power of dense skeletons for a wide set of natural and synthetic color and grayscale images. We use this benchmark to derive optimal parameters for dense skeletons. Our method, called Compressing Dense Medial Descriptors (CDMD), achieves higher-compression ratios at similar quality to the well-known JPEG technique and, thereby, shows that skeletons can be an interesting option for lossy image encoding.

Pore structure characterization through path-finding and Lattice Boltzmann simulation

Characterization of underground porous media parameters at the micro and macro scales is fundamental in geosciences. A thorough comprehension of flow phenomena requires analyses and observations at the micro scale through adoption of micromodels as representative as possible of real geological formations. In this paper we focus on the analysis of 2D binary images of real rock thin sections to characterize pore network geometry and to estimate effective porosity, pore size distribution and tortuosity with the aim of providing suitable information for designing micromodels. To this end, a geometrical analysis of the pore structure, based on the identification and characterization of the set of the shortest geometrical pathways between inlets and outlets pairs, was implemented. The geometrical analysis is based on a path-finding algorithm derived from graph theory. Results provided by geometrical analysis were validated against hydrodynamic numerical simulation via the Lattice Boltzmann Method (LBM). Results show that the path-finding approach provides reasonable and reliable estimates of tortuosity and can be successfully applied for analyzing the distribution of effective pore radius, as well as for estimating the effective porosity.