Morphological modelling of three‐phase microstructures of anode layers using SEM images

A general method is proposed to model 3D microstructures representative of three‐phases anode layers used in fuel cells. The models are based on SEM images of cells with varying morphologies. The materials are first characterized using three morphological measurements: (cross‐)covariances, granulometry and linear erosion. They are measured on segmented SEM images, for each of the three phases. Second, a generic model for three‐phases materials is proposed. The model is based on two independent underlying random sets which are otherwise arbitrary. The validity of this model is verified using the cross‐covariance functions of the various phases. In a third step, several types of Boolean random sets and plurigaussian models are considered for the unknown underlying random sets. Overall, good agreement is found between the SEM images and three‐phases models based on plurigaussian random sets, for all morphological measurements considered in the present work: covariances, granulometry and linear erosion. The spatial distribution and shapes of the phases produced by the plurigaussian model are visually very close to the real material. Furthermore, the proposed models require no numerical optimization and are straightforward to generate using the covariance functions measured on the SEM images.     

Efficient three‐phase reconstruction of heterogeneous material from 2D cross‐sections via phase‐recovery algorithm

Digital reconstruction of a complex heterogeneous media from the limited statistical information, mostly provided by different imaging techniques, is the key to the successful computational analysis of this important class of materials. In this study, a novel approach is presented for three‐dimensional (3D) reconstruction of a three‐phase microstructure from its statistical information provided by two‐dimensional (2D) cross‐sections. In this three‐step method, first two‐point correlation functions (TPCFs) are extracted from the cross‐section(s) using a spectral method suitable for the three‐phase media. In the next step, 3D TPCFs are approximated for all vectors in a representative volume element (RVE). Finally, the 3D microstructure is realized from the full‐set TPCFs obtained in the previous step, using a modified phase‐recovery algorithm. The method is generally applicable to any complex three‐phase media, here illustrated for an SOFC anode microstructure. The capabilities and shortcomings of the method are then investigated by performing a qualitative comparison between example cross‐sections obtained computationally and their experimental equivalents. Finally, it is shown that the method almost conserves key microstructural properties of the media including tortuosity, percolation and three‐phase boundary length (TPBL).     

Simulation of transmission electron microscope images of biological specimens

We present a new approach to simulate electron cryo‐microscope images of biological specimens. The framework for simulation consists of two parts; the first is a phantom generator that generates a model of a specimen suitable for simulation, the second is a transmission electron microscope simulator. The phantom generator calculates the scattering potential of an atomic structure in aqueous buffer and allows the user to define the distribution of molecules in the simulated image. The simulator includes a well defined electron–specimen interaction model based on the scalar Schrödinger equation, the contrast transfer function for optics, and a noise model that includes shot noise as well as detector noise including detector blurring. To enable optimal performance, the simulation framework also includes a calibration protocol for setting simulation parameters. To test the accuracy of the new framework for simulation, we compare simulated images to experimental images recorded of the Tobacco Mosaic Virus (TMV) in vitreous ice. The simulated and experimental images show good agreement with respect to contrast variations depending on dose and defocus. Furthermore, random fluctuations present in experimental and simulated images exhibit similar statistical properties. The simulator has been designed to provide a platform for development of new instrumentation and image processing procedures in single particle electron microscopy, two‐dimensional crystallography and electron tomography with well documented protocols and an open source code into which new improvements and extensions are easily incorporated.     

Microscopic skin laceration segmentation and classification: A framework of statistical normal distribution and optimal feature selection

Among precision medical techniques, medical image processing is rapidly growing as a successful tool for cancer detection. Skin cancer is one of the crucial cancer types. It is identified through computer vision (CV) techniques using dermoscopic images. The early diagnosis skin cancer from dermoscopic images can be decrease the mortality rate. We propose an automated system for skin lesion detection and classification based on statistical normal distribution and optimal feature selection. Local contrast is controlled using a brighter channel enhancement technique, and segmentation is performed through a statistical normal distribution approach. The multiplication law of probability is implemented for the fusion of segmented images. In the feature extraction phase, optimized histogram, optimized color, and gray level co‐occurrences matrices features are extracted and covariance‐based fusion is performed. Subsequently, optimal features are selected through a binary grasshopper optimization algorithm. The selected optimal features are finally fed to a classifier and evaluated on the ISBI 2016 and ISBI 2017 data sets. Classification accuracy is computed using different Support Vector Machine (SVM) kernel functions, and the best accuracy is obtained for the cubic function. The average accuracies of the proposed segmentation on the PH2 and ISBI 2016 data sets are 93.79 and 96.04%, respectively, for an image size 512 × 512. The accuracies of the proposed classification on the ISBI 2016 and ISBI 2017 data sets are 93.80 and 93.70%, respectively. The proposed system outperforms existing methods on selected data sets.     

A three‐dimensional statistical model for imaged microstructures of porous polymer films

A thresholded Gaussian random field model is developed for the microstructure of porous materials. Defining the random field as a solution to stochastic partial differential equation allows for flexible modelling of nonstationarities in the material and facilitates computationally efficient methods for simulation and model fitting. A Markov Chain Monte Carlo algorithm is developed and used to fit the model to three‐dimensional confocal laser scanning microscopy images. The methods are applied to study a porous ethylcellulose/hydroxypropylcellulose polymer blend that is used as a coating to control drug release from pharmaceutical tablets. The aim is to investigate how mass transport through the material depends on the microstructure. We derive a number of goodness‐of‐fit measures based on numerically calculated diffusion through the material. These are used in combination with measures that characterize the geometry of the pore structure to assess model fit. The model is found to fit stationary parts of the material well.     

A comparative study of the quantitative accuracy of three-dimensional reconstructions of spinal cord from serial histological sections

We evaluated the accuracy of estimating the volume of biological soft tissues from their three‐dimensional (3D) computer wireframe models, reconstructed from histological data sets obtained from guinea‐pig spinal cords. We compared quantification from two methods of three‐dimensional surface reconstruction to standard quantitative techniques, Cavalieri method employing planimetry and point counting and Geometric Best‐Fitting. This involved measuring a group of spinal cord segments and test objects to evaluate the accuracy of our novel quantification approaches. Once a quantitative methodology was standardized there was no statistical difference in volume measurement of spinal segments between quantification methods. We found that our 3D surface reconstructions’ ability to model precisely actual soft tissues provided an accurate volume quantification of complex anatomical structures as standard approaches of Cavalieri estimation and Geometric Best‐Fitting. Additionally, 3D reconstruction quantitatively interrogates and three‐dimensionally images spinal cord segments and obscured internal pathological features with approximately the same effort required for standard quantification alone.     

Identification of the three-dimensional gel microstructure from transmission electron micrographs

Mass transport in gels depends crucially on local properties of the gel network. We propose a method for identifying the three‐dimensional (3D) gel microstructure from statistical information in transmission electron micrographs. The gel strand network is modelled as a random graph with nodes and edges (branches). The distribution of edge length, the number of edges at nodes and the angles between edges at a node are estimated from transmission electron micrographs by image analysis methods. The 3D network is simulated by Markov chain Monte Carlo, with a probability function based on the statistical information found from the micrographs. The micrographs are projections of stained gel strands in slices, and we derive a formula for estimating the thickness of the stained gel slice based on the total projected gel strand length and the number of times that gel strands enter or exit the slice.     

Accurate stochastic reconstruction of heterogeneous microstructures by limited x‐ray tomographic projections

An accurate knowledge of the complex microstructure of a heterogeneous material is crucial for its performance prediction, prognosis and optimization. X‐ray tomography has provided a nondestructive means for microstructure characterization in 3D and 4D (i.e. structural evolution over time), in which a material is typically reconstructed from a large number of tomographic projections using filtered‐back‐projection (FBP) method or algebraic reconstruction techniques (ART). Here, we present in detail a stochastic optimization procedure that enables one to accurately reconstruct material microstructure from a small number of absorption contrast x‐ray tomographic projections. This discrete tomography reconstruction procedure is in contrast to the commonly used FBP and ART, which usually requires thousands of projections for accurate microstructure rendition. The utility of our stochastic procedure is first demonstrated by reconstructing a wide class of two‐phase heterogeneous materials including sandstone and hard‐particle packing from simulated limited‐angle projections in both cone‐beam and parallel beam projection geometry. It is then applied to reconstruct tailored Sn‐sphere‐clay‐matrix systems from limited‐angle cone‐beam data obtained via a lab‐scale tomography facility at Arizona State University and parallel‐beam synchrotron data obtained at Advanced Photon Source, Argonne National Laboratory. In addition, we examine the information content of tomography data by successively incorporating larger number of projections and quantifying the accuracy of the reconstructions. We show that only a small number of projections (e.g. 20–40, depending on the complexity of the microstructure of interest and desired resolution) are necessary for accurate material reconstructions via our stochastic procedure, which indicates its high efficiency in using limited structural information. The ramifications of the stochastic reconstruction procedure in 4D materials science are also discussed.     

Combining quantitative 2D and 3D image analysis in the serial block face SEM: application to secretory organelles of pancreatic islet cells

A combination of two‐dimensional (2D) and three‐dimensional (3D) analyses of tissue volume ultrastructure acquired by serial block face scanning electron microscopy can greatly shorten the time required to obtain quantitative information from big data sets that contain many billions of voxels. Thus, to analyse the number of organelles of a specific type, or the total volume enclosed by a population of organelles within a cell, it is possible to estimate the number density or volume fraction of that organelle using a stereological approach to analyse randomly selected 2D block face views through the cells, and to combine such estimates with precise measurement of 3D cell volumes by delineating the plasma membrane in successive block face images. The validity of such an approach can be easily tested since the entire 3D tissue volume is available in the serial block face scanning electron microscopy data set. We have applied this hybrid 3D/2D technique to determine the number of secretory granules in the endocrine α and β cells of mouse pancreatic islets of Langerhans, and have been able to estimate the total insulin content of a β cell.     

Comparison of three‐dimensional analysis and stereological techniques for quantifying lithium‐ion battery electrode microstructures

Lithium‐ion battery performance is intrinsically linked to electrode microstructure. Quantitative measurement of key structural parameters of lithium‐ion battery electrode microstructures will enable optimization as well as motivate systematic numerical studies for the improvement of battery performance. With the rapid development of 3‐D imaging techniques, quantitative assessment of 3‐D microstructures from 2‐D image sections by stereological methods appears outmoded; however, in spite of the proliferation of tomographic imaging techniques, it remains significantly easier to obtain two‐dimensional (2‐D) data sets. In this study, stereological prediction and three‐dimensional (3‐D) analysis techniques for quantitative assessment of key geometric parameters for characterizing battery electrode microstructures are examined and compared. Lithium‐ion battery electrodes were imaged using synchrotron‐based X‐ray tomographic microscopy. For each electrode sample investigated, stereological analysis was performed on reconstructed 2‐D image sections generated from tomographic imaging, whereas direct 3‐D analysis was performed on reconstructed image volumes. The analysis showed that geometric parameter estimation using 2‐D image sections is bound to be associated with ambiguity and that volume‐based 3‐D characterization of nonconvex, irregular and interconnected particles can be used to more accurately quantify spatially‐dependent parameters, such as tortuosity and pore‐phase connectivity.     

A pixel selection rule based on the number of different-phase neighbours for the simulated annealing reconstruction of sandstone microstructure

Sandstone reservoir is one of the main types of oil and gas reservoirs in China. It has porous microstructure, which directly affects the transport properties of a sandstone. Hence, the study of porous microstructure is important to the exploration and exploitation of oil and gas. Three-dimensional microstructure of a sandstone can be reconstructed using the simulated annealing method based on statistical properties of its two-dimensional micrograph. The aim of reconstruction is to minimize the discrepancy between the statistical properties of the reconstructed microstructure and those of the two-dimensional image. To accelerate the rate of convergence, we proposed a different-phase neighbours (DPNs)-based pixel selection rule to replace the random pixel selection rule of the simulated annealing reconstruction. In this rule, pixels with the largest number of DPNs have the largest selection probability. The selection probabilities of other pixels are proportional to their DPNs. Microstructure reconstructed with the DPNs-based rule is compared with those with the random selection rule and two other biased pixel selection rules. The DPNs-based rule is the most effective in enhancing convergence. Permeability of the microstructure reconstructed with the DPNs-based rule is estimated by the Kozeny–Carman formula and is in good agreement with the one reconstructed with the random pixel selection rule.     

Algorithms for accurate 3D registration of neuronal images acquired by confocal scanning laser microscopy

This paper presents automated and accurate algorithms based on high‐order transformation models for registering three‐dimensional (3D) confocal images of dye‐injected neurons. The algorithms improve upon prior methods in several ways, and meet the more stringent image registration needs of applications such as two‐view attenuation correction recently developed by us. First, they achieve high accuracy (≈ 1.2 voxels, equivalent to 0.4 µm) by using landmarks, rather than intensity correlations, and by using a high‐dimensional affine and quadratic transformation model that accounts for 3D translation, rotation, non‐isotropic scaling, modest curvature of field, distortions and mechanical inconsistencies introduced by the imaging system. Second, they use a hierarchy of models and iterative algorithms to eliminate potential instabilities. Third, they incorporate robust statistical methods to achieve accurate registration in the face of inaccurate and missing landmarks. Fourth, they are fully automated, even estimating the initial registration from the extracted landmarks. Finally, they are computationally efficient, taking less than a minute on a 900‐MHz Pentium III computer for registering two images roughly 70 MB in size. The registration errors represent a combination of modelling, estimation, discretization and neuron tracing errors. Accurate 3D montaging is described; the algorithms have broader applicability to images of vasculature, and other structures with distinctive point, line and surface landmarks.     

A Hybrid Search Algorithm for Porous Air Bearings Optimization

The study deals with the development of a hybrid search algorithm for efficient optimization of porous air bearings. Both the compressible Reynolds equation and Darcy's law are linearized and solved iteratively by a successive-over-relaxation method for modeling parallel-surface porous bearings. Three factors affecting the computational efficiency of the numerical model are highlighted and discussed. The hybrid optimization is performed by adopting genetic algorithm (GA) for initial search and accelerated by simplex method (SM) for refined solution. A simple and useful variable transformation is presented and used to convert the unconstrained SM to a constrained method. In this study, the hybrid search algorithm for a multi-variable design exhibits better efficiency compared with the search efficiency by using the SM. The proposed hybrid method also eliminates the need of several trials with random initial guesses to ensure high probability of global optimization. This study presents a new approach for optimizing the performance of porous air bearings and other tribological components.     

Analysis of spatial cross‐correlations in multi‐constituent volume data

We investigate spatial cross‐correlations between two constituents, both belonging to the same microstructure. These investigations are based on two approaches: one via the measurement of the cross‐correlation function and the other uses the spatial distances between the constituents. The cross‐correlation function can be measured using the fast Fourier transform, whereas the distances are determined via the Euclidean distance transform. The characteristics are derived from volume images obtained by synchrotron microtomography. As an example we consider pore formation in metallic foams, knowledge of which is important to control the foam production process. For this example, we discuss the spatial cross‐correlation between the pore space and the blowing agent particles in detail.     

Centred contact density functions for the statistical analysis of random sets A stereological study on benign and malignant glandular tissue using image analysis

Real structures investigated in the material and biological sciences, such as minerals or tissues, can often be reduced to two phases. In a stochastic approach, the components of such binary structures may be considered as the union of grains — random sets implanted with their centres at random points — and their complementary space, which is called the pore space. The simplest stochastic germ-grain model is the Boolean model of random sets, which we use here instrumentally as a null model (reference model) for comparison with our biological material. After a brief review of basic properties of the Boolean model and related statistical methods, we introduce centred contact density functions as a new approach. Empirical contact density functions are estimated from the empirical contact distribution functions with an image analyser by dilation of the grain phase. Theoretical contact density functions are then predicted from a set of image parameters, under the assumption that the Boolean model holds. A centred contact density function is the difference between the estimated and the predicted contact density function. Apart from a random error term, centred contact density functions amount to zero irrespective of the area fraction of the grain phase, when the germ-grain model is Boolean. As a section of a spatial Boolean model is a planar Boolean model, the method is also applicable in stereological studies where digitized images are obtained from sections of a three-dimensional structure. Centred contact density functions were determined for mastopathic tissue as compared to mammary cancer, and for tumour-free prostatic tissue as compared to prostatic cancer. For each category of specimens, twenty cases with 10 images each were analysed. Benign and malignant glandular tissue of the aforementioned types deviates significantly from the Boolean model. Centred contact density functions show that malignant transformation is connected with profound geometric remodelling of the pore space.     

Improvement in cytoarchitectonic mapping by combining electrodynamic modeling with local orientation in high‐resolution images of the cerebral cortex

To detect changes of cortical cytoarchitectonics, digital images of cortical laminations are analyzed. Cortical regions are transformed into a rectangular grid for subsequent evaluations. Transformations are realized by stepwise scanning using perpendicular testlines. 3D cytoarchitectonic data of the human brain at a histological resolution are not available and 2D sections deliver partial information only. The problem is to find an optimal scanning‐technique that introduces a minimum of distortions and noise by the transformation of the curvilinear cortex to a rectangular presentation. In the past this was solved by constructing testlines dependent on the outlined cortical contours only. An advanced approach was to model the contours as electrically charged surfaces and to use the resulting field lines as testlines. However, local information of cell distributions were not considered. Hence a novel hybrid approach was developed which is able to construct significantly better testlines in cortical images with mixtures of columnar rich (local orientation rich) and orientation poor parts of strongly curved and large regions of the cerebral cortex. The novel hybrid approach is based on the computer vision methods such as the structure tensor and constrained anisotropic diffusion. In addition, the introduction of projective transformations yields a significant improvement of cortical fingerprints, thereby offering the possibility for detecting weakly pronounced regions of cytoarchitectonic transitions. The statistical evaluation of the novel hybrid approach confirms robustness. This technique can be generalized and applied to different types of cerebral cortex with any kind and amount of local orientation information. Microsc. Res. Tech. 2010. © 2010 Wiley‐Liss, Inc.     

3D reconstruction of elastin fibres in coronary adventitia

A 3D reconstruction of individual fibres in vascular tissue is necessary to understand the microstructure properties of the vessel wall.  The objective of this study is to determine the 3D microstructure of elastin fibres in the adventitia of coronary arteries.  Quantification of fibre geometry is challenging due to the complex interwoven structure of the fibres.  In particular, accurate linking of gaps remains a significant challenge, and complex features such as long gaps and interwoven fibres have not been adequately addressed by current fibre reconstruction algorithms.  We use a novel line Laplacian deformation method, which better deals with fibre shape uncertainty to reconstruct elastin fibres in the coronary adventitia of five swine. A cost function, based on entropy and Euler Spiral, was used in the shortest path search. We find that mean diameter of elastin fibres is 1.67 ± 1.42 m and fibre orientation is clustered around two major angles of 8.9? and 81.8?.  Comparing with CT‐FIRE, we find that our method gives more accurate estimation of fibre width.  To our knowledge, the measurements obtained using our algorithm represent the first investigation focused on the reconstruction of full elastin fibre length.  Our data provide a foundation for a 3D microstructural model of the coronary adventitia to elucidate the structure–function relationship of elastin fibres.