Digital Volume Correlation Algorithm Research Articles

Sensitivity Study Using Synthetic 3D Image Datasets to Investigate the Effect of Noise Artefacts on Digital Volume Correlation

BackgroundThe potential effect of image noise artefacts on Digital Volume Correlation (DVC) analysis has not been thoroughly studied and, more particularly quantified, even though DVC is an emerging technique widely used in life and material science over the last decade.ObjectiveThis paper presents the results of a sensitivity study to shed light on the effect of various noise artefacts on the full-field kinematic fields generated by DVC, both in zero and rigid body motion.MethodsVarious noise artefacts were studied, including the Gaussian, Salt & Pepper, Speckle noise and embedded Ring Artefacts. A noise-free synthetic microstructure was generated using Discrete Element Modelling (DEM), representing an idealistic case, and acting as the reference dataset for the DVC analysis. Noise artefacts of various intensities (including selected extreme cases) were added to the reference image datasets using MATLAB (R2022) to form the outline of the parametric study. DVC analyses were subsequently conducted employing AVIZO (Thermo Fisher). A subset-based local approach was adopted. A three-dimensional version of the Structural Similarity Index Measure (SSIM) was used to define the similarity between the compared image datasets on each occasion. Sub-pixel rigid body motion was applied on the DEM-generated microstructure and subsequently “poisoned” with noise artefacts to evaluate mean bias and random error of the DVC analysis.ResultsWhen the local approach is implemented, the sensitivity study on zero motion data revealed the insignificant effect of the Gaussian, Salt & Pepper, and Speckle noise on the DVC-computed kinematic field. Therefore, the presence of such noise artefacts can be neglected when DVC is executed. On the contrary, Ring Artefacts can pose a considerable challenge and therefore, DVC results need to be evaluated cautiously. A linear relationship between SSIM and the correlation index is observed for the same noise artefacts. Gaussian noise has a pronounced effect on the mean bias error for sub-pixel rigid body motion.ConclusionsGenerating synthetic image datasets using DEM enabled the investigation of a variety of noise artefacts that potentially affect a DVC analysis. Given that, any microstructure – resembling the material studied – can be simulated and used for a DVC sensitivity analysis, supporting the user in appropriately evaluating the computed kinematic field. Even though the study is conducted for a two-phase material, the method elaborated in this paper also applies to heterogeneous multi-phase materials also. The conclusions drawn are valid within the environment of the AVIZO DVC extension module. Alternative DVC algorithms, utilising different approaches for the cross-correlation and the sub-pixel interpolation methods, need to be investigated.

Material representativeness of a polymer matrix doped with nanoparticles as the random speckle pattern for digital volume correlation of fibre-reinforced composites

Combining tomographic imaging with digital volume correlation allows in-situ 3D strain mapping, leading to a quantitative assessment of damage mechanisms and associated material properties in structural materials. Being based on pattern recognition, digital volume correlation is well-suited for materials with intrinsic and stable microstructural heterogeneity, such as certain biological tissues. Unfortunately, conventional polymers and fibre-reinforced polymer composites lack the required heterogeneity. Recently, solutions like doping the polymers with particles have been explored to overcome this limitation. The particles embedded in the polymer matrix provide a random, volumetric speckle pattern, acting as displacement trackers for the digital volume correlation algorithm. However, the particles might influence the mechanical and rheological behaviour of the polymer, which is detrimental in investigations of the composite material properties. This paper investigates the mechanical, mechanistic, and rheological representativeness of an epoxy doped with two types of sub-micrometre particles optimised for digital volume correlation. Since particle dispersion is considered a key driver for representativeness, we simultaneously quantitatively assess the dispersion by combining scanning electron microscopy and X-ray computed tomography.

Comparison of linear and nonlinear stepwise μFE displacement predictions to digital volume correlation measurements of trabecular bone biopsies

Digital volume correlation (DVC) enables to evaluate the ability of μFE models in predicting experimental results on the mesoscale. In this study predicted displacement fields of three different linear and materially nonlinear μFE simulation methods were compared to DVC measured displacement fields at specific load steps in the elastic regime (StepEl) and after yield (StepUlt). Five human trabecular bone biopsies from a previous study were compressed in several displacement steps until failure. At every compression step, μCT images (resolution: 36 μm) were recorded. A global DVC algorithm was applied to compute the displacement fields at all loading steps. The unloaded 3D images were then used to generate homogeneous, isotropic, linear and materially nonlinear μFE models. Three different μFE simulation methods were used: linear (L), nonlinear (NL), and nonlinear stepwise (NLS). Regarding L and NL, the boundary conditions were derived from the interpolated displacement fields at StepEl and StepUlt, while for the NLS method nonlinear changes of the boundary conditions of the experiments were captured using the DVC displacement field of every available load step until StepEl and StepUlt. The predicted displacement fields of all μFE simulation methods were in good agreement with the DVC measured displacement fields (individual specimens: R2>0.83 at StepEl and R2>0.59 at StepUlt; pooled data: R2>0.97 at StepEl and R2>0.92 at StepUlt). At StepEl, all three simulation methods showed similar intercepts, slopes, and coefficients of determination while the nonlinear μFE models improved the prediction of the displacement fields slightly in all Cartesian directions at StepUlt (individual specimens: L: R2>0.59 and NL, NLS: R2>0.68; pooled data: L: R2>0.92 and NL, NLS: R2>0.94). Damaged/overstrained elements in L, NL, and NLS occurred at similar locations but the number of overstrained elements was overestimated when using the L simulation method. Considering the increased solving time of the nonlinear μFE models as well as the acceptable performance in displacement prediction of the linear μFE models, one can conclude that for similar use cases linear μFE models represent the best compromise between computational effort and accuracy of the displacement field predictions.

Application of phase-field fracture theories and digital volume correlation to synchrotron X-ray monitored fractures in human trabecular bone: A case study

Fracture processes of trabecular bone have been studied using various approaches over the years. However, reliable methods to analyse fracture at the single trabecula level are limited. In this study, a digital volume correlation (DVC) and a phase-field fracture model are applied and contrasted for human trabecular bone to analyse its failure under global compression at high resolution.A human trabecular bone sample was fractured in situ under synchrotron-based X-ray micro computed tomography (CT). Reconstructed CT data was then used in DVC algorithms to obtain high-resolution displacement fields in the bone at different load steps. A high-resolution specimen-specific structural mesh was discretized from the CT data and used for the phase-field simulation of the fracturing bone.The DVC analysis showed opening mode cracks as well as shear mode cracks. Strains in cracked regions were analysed. The load distribution in the trabecular structure resulted in two completely separated fracture regions in the sample body. A phenomenon that was also captured in the phase-field model. The results encourage us to believe improvements in boundary conditions and material models are worthwhile pursuing. Findings in this study support further development of a phase-field method to analyse fracture in samples with complex morphology, such as trabecular bone, and the capacity of DVC to quantify strains and slowly growing stable fractures during step-wise loading of trabecular bone.

An Adaptive and Reliable Guided Digital Volume Correlation Algorithm for Sandstone Based on 3D Scale-Invariant Feature Transform

An Adaptive and Reliable Guided Digital Volume Correlation Algorithm for Sandstone Based on 3D Scale-Invariant Feature Transform

Image analysis on grain kinematics and grain breakage of carbonate sands from South China Sea during confined compression

This paper presents a morphological study on the carbonate sands taken from the South China Sea (SCS), by means of image analysis of in situ confined compression tests carried out in an X-ray scanner. Sands with coarse and fine grading, each with two samples, were investigated. An adaptive watershed segmentation method and a fast iterative digital volume correlation algorithm were employed to identify the individual grains in the scanned image and derive the displacement field during compression, respectively. Then the grain sizes and shapes as well as grain kinematics were analysed. Clear upper and lower boundary limits were noticed in the correlations between sphericity and convexity, elongation and sphericity, as well as sphericity and angularity. Besides, approximately linear relations were observed between the characteristic grain size and a number of characteristic grain size descriptors. These results can hopefully be used when specifying the distribution of grain sizes and shapes in future discrete element modeling, to capture more realistic mechanical behavior of SCS carbonate sands.

基于<bold>CT</bold>成像和数字体图像相关法的岩石内部变形场量测方法的研究进展

<p indent="0mm">Rock mechanics plays a critical role in mining engineering, slope engineering, tunnel engineering, water conservancy, hydropower engineering, and some newly developing rock mass engineering, such as deeply buried oil and gas storage, underground nuclear waste repository, geothermal development, etc. The evolution of the internal discontinuous structure of rock under the coupling of multiple physical fields such as stress field, seepage field, and temperature field is an important research topic in the field of rock mechanics. Scholars have investigated the internal structure characteristics and their evolution process at different scales with various equipment. High-resolution microtomography (Micro CT) with micron or even nanoscale resolution has been widely used in internal structure detection, digital core modeling, and numerical modeling of rock. The digital volume correlation (DVC) method can quantitatively analyze and visualize the internal 3D deformation field of rock, and its combination with Micro CT provides a new method for transparent analysis and deduction of discontinuous structures and multi-physical fields in rocks. This paper systematically reviews the research on internal deformation measurement of rocks by using Micro CT and DVC in terms of <italic>in-situ</italic> loading device with Micro CT, the theory of DVC, the influence of micro/meso-structures in rocks, and experimental measurements. To view the internal structures of rocks under different physical fields, various <italic>in-situ</italic> loading devices combined with Micro CT were developed, e.g., uniaxial loading device, triaxial loading coupled with seepage device, gas adsorption device, and heating device. In these devices, factors such as the strength of rock, physical field, material strength of chamber, X-ray energy and penetration, real-time performance of image acquisition, and quality of reconstructed images should be comprehensively considered. By using <italic>in-situ</italic> loading devices and Micro CT, a series of volume images of rocks are obtained before and after deformation, and then DVC is adopted to calculate the three-dimensional deformation field by analyzing the correlation between these volume images. According to the registration algorithms, DVC can be categorized into local DVC (L-DVC) and global DVC (G-DVC). The basic principle and development of DVC are reviewed. Due to the limitation of the heterogeneity of rocks and the accuracy of the image acquisition equipment, natural micro structures in rocks do not have ideal speckle patterns, which affects the accuracy of DVC. It is indicated that the larger the average gray gradient and Shannon entropy and the smaller the structural variation coefficient of a rock image, the higher the accuracy of DVC. The accuracy of G-DVC is slightly better than that of L-DVC, but its calculation efficiency is lower, especially when the mesh size is small. The applications of DVC for investigating strain localization in rocks, measuring carbon dioxide-induced strain in coal, and oil shale pyrolysis are presented. Despite some impressive achievements, DVC is still faced with some core challenges, e.g., the low accuracy of the DVC algorithm and artifact error correction, the influence of the microstructures in rocks, parameter identification and numerical model verification of rocks, and deformation field measurement under the coupling of multiple physical fields. With the popularization of Micro-CT in laboratories, DVC will be further applied to measuring the three-dimensional deformation field in rocks.

Global digital volume correlation of large volumes: a sub-volume adaptive meshing approach

While global Digital Volume Correlation (DVC) yields more accurate results compared to local DVC, its main drawback remains the computational power needed to store and update the entire reference and deformed volumes during the optimisation process. This effectively prevents the use of global DVC for large volumes, with the exact size limit depending on the accessible RAM of the workstation or server running the DVC algorithm. This paper presents a development made at the University of Manchester at Harwell to perform a global DVC on X-ray Computed Tomography (XCT) volumes larger than the capabilities of a given computer hardware. The method relies on dividing the large meshed volume into smaller overlapping volumes, and corresponding meshes, that can be handled successively by the computer hardware to perform global DVC. Then, the nodes in the overlapping regions are assessed and the resulting sub-volumes global DVC results are merged into a single output result file covering the entire XCT volume. Overall, this sub-volume adaptive meshing approach is a solution to overcomes hardware limitations in cases where global DVC is required over large volumes and meshing density can be user-defined to fit the expected damage location within the sample.

A combined experimental and numerical method to estimate the elastic modulus of single trabeculae

The elastic modulus at the single trabecular level is an important parameter for the understanding of the mechanical behavior of trabecular bone. Current methods are commonly limited by the irregular trabecular shape and the accuracy of displacement measurement. The aim of this study was to propose a method to estimate the trabecular modulus overcoming some of these limitations. For high-precision displacement measurements, in-situ compression within a synchrotron radiation based X-ray tomograph was used. Trabecular displacements were subsequently estimated by a global digital volume correlation algorithm, followed by high-resolution finite element analyses to account for the irregular geometry. The trabecular elastic moduli were then estimated by comparing the loads from the finite element analyses with those of the experiments. With this strategy, the average elastic modulus was estimated to 3.83 ± 0.54 GPa for three human trabeculae samples. Though limited by the sample size, the demonstrated method shows a potential to estimate the mechanical properties at the single trabecular level.

GPU accelerated parallel reliability-guided digital volume correlation with automatic seed selection based on 3D SIFT

Digital volume correlation (DVC) is a powerful and widely used technique for measuring the internal 3D deformation field of a wide range of materials. One of the most popular DVC algorithms is the reliability-guided DVC (RG-DVC) which is good at dealing with large continuous deformation. However, RG-DVC requires a manually specified seed from which computation starts, and suffers from the efficiency due to a huge amount of computation and data dependency. This paper proposes a GPU accelerated parallel reliability-guided DVC algorithm (CuSIFT-RGDVC) on CUDA, which leverages 3D scale-invariant feature transform (3D SIFT) to assist seed selection to realize fully automation and improves performance utilizing GPU computing. In CuSIFT-RGDVC, reliability-guided displacement tracking (RGDT) is rewritten using sorted array-based batch processing mechanism which is a globally sequential locally parallel model, and multi-granularity parallelism is adopted to maximize GPU utilization. The empirical result shows that the proposed CuSIFT-RGDVC provides up to 29.1x speedup compared with our multi-threaded implementation and achieves the same level of computation speed as the state-of-the-art path-independent DVC without sacrificing accuracy.

High-temperature deformation followed in situ by X-ray microtomography: a methodology to track features under large strain.

Metallic materials processing such as rolling, extrusion or forging often involves high-temperature deformation. Usually under such conditions the samples are characterized post mortem, under pseudo in situ conditions with interrupted tests, or in situ with a limited strain rate. A full in situ 3D characterization, directly during high-temperature deformation with a prescribed strain-rate scheme, requires a dedicated sample environment and a dedicated image-analysis workflow. A specific sample environment has been developed to enable highly controlled (temperature and strain rate) high-temperature deformation mechanical testing to be conducted while performing in situ tomography on a synchrotron beamline. A dedicated digital volume correlation algorithm is used to estimate the strain field and track pores while the material endures large deformations. The algorithm is particularly suitable for materials with few internal features when the deformation steps between two images are large. An example of an application is provided: a high-temperature compression test on a porous aluminium alloy with individual pore tracking with a specific strain-rate scheme representative of rolling conditions.

Error analysis of surface-distribution and non-deformation of fluorescent beads for the IC-GN2 DVC algorithm

Digital volume correlation (DVC) method is extensively used for the internal displacement measurement. In biomechanical experiments, fluorescent beads are used, instead of traditional speckles (or microstructure of materials), as the information feature of the volume image for DVC algorithm. The traditional experimental method and DVC algorithm, together, provide an effective measurement method for the cell deformation. Nevertheless, the aforesaid method has three limitations, viz., (1) low accuracy for complex displacement and poor efficiency for traditional second-order forward additive Gauss-Newton (FA-GN2) algorithm, (2) shape function mismatch induced by the non-deformation of fluorescent beads, and (3) the extreme phototoxicity caused by the long scanning time. To tackle these issues, we introduce the inverse compositional Gauss-Newton DVC algorithm with the second-order shape function (IC-GN2 DVC algorithm) to achieve higher accuracy and establish the four speckle volume image models to analyze the influence of the distribution and non-deformation of fluorescent beads on the results of calculation of DVC method. Henceforth, we propose an experimental method, considering that fluorescent beads are only distributed on the surface of the gel substrate (cells are also placed on the surface of gel substrate) enabling short scanning time (termed speckle-surface-distributed experimental method). The results from the analysis by numerical simulations show that the proposed IC-GN2 DVC algorithm has a very high accuracy (local error < 0.1 voxel). The error analysis of the four models shows that the non-deformation of fluorescent beads will induce significant error into the calculation results, whereas the surface-distribution of fluorescent beads induces little error, which prove the reliability of the speckle-surface-distributed experimental method. The noise robustness of the IC-GN2 DVC algorithm with the speckle-surface-distributed experimental method is also studied. Finally, the migration and deformation of the living cell is analyzed using the IC-GN2 DVC algorithm and the speckle-surface-distributed experimental method.

Digital volume correlation using a spherical shell template and cubic element for large rotation measurement.

The displacement hypothesis of eight-node cubic elements is selected as the shape function of digital volume correlation (DVC), and the Newton-Raphson iterative method is selected to solve the partial differential equation to measure the displacement field. In order to ensure that the DVC algorithm is usable under the large rotation condition, the spherical shell template matching technique is presented to perform the integer-voxel displacement searching for nodes, which can provide the optimal initial values for the Newton-Raphson iterative method due to the rotation and translation invariance of the spherical shell template. Simulated volume images are used to verify the reliability of the proposed method, and the results show that the proposed DVC method can be used to measure the deformation with an arbitrary rigid body rotation angle. This work is expected to be useful to measure deformation with large rotation of the internal structure of materials.

Linking shape and rotation of grains during triaxial compression of sand

Particle shape has a strong effect on the mechanical response of coarse soils. This has been usually observed examining specimen-scale or engineering-scale responses, which are the sum of many microscale interactions. In this work we observe the effects of particle shape directly at the microscale level. X-ray tomography (μ-CT) of two sand specimens is exploited to measure three-dimensional particle shape descriptors but also to track individual particle motions during triaxial compression. A discrete digital volume correlation algorithm is employed to track the motion of individual grains (around 50,000 for each sand specimen) during the test and measure, with good precision, their cumulated displacements and rotations. The specimens examined failed in a clearly localised shear mode. Advantage is taken of this to obtain data relevant for very different kinematical regimes: one uniform and more constrained and the other close to critical state. A direct comparison between the shape and kinematic databases shows to what degree particle shape descriptors are related to observed kinematics. It appears that true sphericity is a good predictor of upper bound rotational restraint.

Augmented Lagrangian Digital Volume Correlation (ALDVC)

Digital volume correlation (DVC), the volumetric extension of the popular digital image correlation (DIC) technique, is a powerful experimental tool for measuring 3D volumetric full-field displacements and strains. Most current DVC algorithms can be categorized into either local or finite-element-based global methods. As with most experimental approaches, there are drawbacks with each of these methods. In the local method the subvolume deformations are estimated independently and the computed displacement field may not necessarily be kinematically compatible. Thus, the deformation gradients can be noisy, especially when using small volumetric subsets. Although the global method often enforces kinematic compatibility, it generally incurs substantially greater computational costs than its local counterpart, which is especially significant for large volumetric data sets. To address these shortcomings, we present a new hybrid DVC algorithm, called augmented Lagrangian digital volume correlation (ALDVC), which combines the advantages of both the local (fast computation time) and global (compatible displacement field) methods. This new algorithm builds on our recent work on the augmented Lagrangian digital image correlation (2D-ALDIC) technique and solves the general motion optimization problem by using the alternating direction method of multipliers (ADMM). We demonstrate that our ALDVC algorithm has high accuracy and precision while maintaining low computational cost, and is a significant improvement compared to current local and global DVC methods. ALDVC is a computationally efficient algorithm to measure 3D volumetric displacements and strains. An open-source Matlab implementation is freely available.

In-situ X-ray Differential Micro-tomography for Investigation of Water-weakening in Quasi-brittle Materials Subjected to Four-point Bending.

Several methods, including X-ray radiography, have been developed for the investigation of the characteristics of water-saturated quasi-brittle materials. Here, the water content is one of the most important factors influencing their strength and fracture properties, in particular, as regards to porous building materials. However, the research concentrated on the three-dimensional fracture propagation characteristics is still significantly limited due to the problems encountered with the instrumentation requirements and the size effect. In this paper, we study the influence of the water content in a natural quasi-brittle material on its mechanical characteristics and fracture development during in-situ four-point bending by employing high-resolution X-ray differential micro-tomography. The cylindrical samples with a chevron notch were loaded using an in-house designed four-point bending loading device with the vertical orientation of the sample. The in-house designed modular micro-CT scanner was used for the visualisation of the specimen’s behaviour during the loading experiments. Several tomographic scans were performed throughout the force-displacement diagrams of the samples. The reconstructed 3D images were processed using an in-house developed differential tomography and digital volume correlation algorithms. The apparent reduction in the ultimate strength was observed due to the moisture content. The crack growth process in the water-saturated specimens was identified to be different in comparison with the dry specimens.

Anisotropic self-adaptive digital volume correlation with optimal cuboid subvolumes

Conventional digital volume correlation (DVC) approaches all use cubic subvolumes for full-field internal displacement mapping. In practical applications, however, real test samples would undergo heterogeneous deformations in three directions due to anisotropic material properties, complex microstructures and/or nonuniform boundary conditions. Based on the self-adaptive DVC (SA-DVC) algorithm we developed recently, here we propose a novel anisotropic self-adaptive DVC (ASA-DVC) approach using cuboid subvolumes and the first-order shape function to realize accuracy-enhanced 3D internal deformation measurement. We first briefly introduce the V-shaped theoretical error model as a function of subvolume size to facilitate optimal subvolume size identification in x, y and z directions. Then, the basic framework of the presented ASA-DVC method capable of automatically specifying optimal subvolume size in three directions at each calculation point is described. Finally, both numerically simulated and real-world experiments are employed to demonstrate the accuracy advantages of the ASA-DVC over routine DVC.

Digital tomosynthesis based digital volume correlation: A clinically viable noninvasive method for direct measurement of intravertebral displacements using images of the human spine under physiological load.

We have developed a clinically viable method for measurement of direct, patient-specific intravertebral displacements using a novel digital tomosynthesis based digital volume correlation technique. These displacements may be used to calculate vertebral stiffness under loads induced by a patient's body weight; this is particularly significant because, among biomechanical variables, stiffness is the strongest correlate of bone strength. In this proof of concept study, we assessed the feasibility of the method through a preliminary evaluation of the accuracy and precision of the method, identification of a range of physiological load levels for which displacements are measurable, assessment of the relationship of measured displacements with microcomputed tomography based standards, and demonstration of the in vivo application of the technique. Five cadaveric T11 vertebrae were allocated to three groups in order to study (a) the optimization of digital volume correlation algorithm input parameters, (b) accuracy and precision of the method and the ability to measure displacements at a range of physiological load levels, and (c) the correlation between displacements measured using tomosynthesis based digital volume correlation vs. high resolution microcomputed tomography based digital volume correlation and large scale finite element models. Tomosynthesis images of one patient (Female, 60yr old) were used to calculate displacement maps, and in turn stiffness, using images acquired in both standing and standing-with-weight (8kg) configurations. We found that displacements were accurate (2.28µm total error) and measurable at physiological load levels (above 267N) with a linear response to applied load. Calculated stiffness among three tested vertebral bodies was within an acceptable range relative to reported values for vertebral stiffness (5651-13260N/mm). Displacements were in good qualitative and quantitative agreement with both microcomputed tomography based finite element (r2 =0.762, P<0.001) and digital volume correlation (r2 =0.799, P<0.001) solutions. For one patient tested twice, once standing and once holding weights, results demonstrated excellent qualitative reproducibility of displacement distributions with superior endplate displacements increasing by 22% with added weight. The results of this work collectively suggest the feasibility of the method for in vivo measurement of intravertebral displacements and stiffness in humans. These findings suggest that digital volume correlation using digital tomosynthesis imaging may be useful in understanding the mechanical response of bone to disease and may further enhance our ability to assess fracture risk and treatment efficacy for the spine.

Three-dimensional static optical coherence elastography based on inverse compositional Gauss-Newton digital volume correlation.

The three-dimensional (3D) mechanical properties characterization of tissue is essential for physiological and pathological studies, as biological tissue is mostly heterogeneous and anisotropic. A digital volume correlation (DVC)-based 3D optical coherence elastography (OCE) method is developed to measure the 3D displacement and strain tensors. The DVC algorithm includes a zero-mean normalized cross-correlation criterion-based coarse search regime, an inverse compositional Gauss-Newton fine search algorithm and a local ternary quadratic polynomial fitting strain calculation method. A 3D optical coherence tomography (OCT) scanning protocol is proposed through theoretical analysis and experimental verification. Measurement errors of the DVC-based 3D OCE method are evaluated to be less than 2.0 μm for displacements and 0.30% for strains by rigid body motion experiments. The 3D displacements and strains of a phantom and a specimen of chicken breast tissue under compression are measured. Results of the phantom show a good agreement with theoretical analysis and tensile testing. The strains of the chicken breast tissue indicate anisotropic biomechanical properties. This study provides an effective method for 3D biomechanical property studies of soft tissue and improves the development of 3D OCE techniques.

A global digital volume correlation algorithm based on higher-order finite elements: Implementation and evaluation

We propose a DVC technique that is based on higher-order finite-element discretization of the displacement field and a global optimization procedure. We use curvature penalization to suppress non-physical fluctuations of the displacement field and resulting erroneous strain concentrations. The performance of the proposed method is compared to the commercial code Avizo using trabecular bone images and found to perform slightly better in most cases.In addition, we stress that the performance of a DVC method needs to be evaluated using double scans (zero strain), virtual deformation (imposed deformation) and real deformation. Double scans give insight into the presence of noise and artifacts whereas virtual deformation benchmarks allows evaluation of the performance without noise and artifacts. Investigation of the performance for actual deformed heterogeneous materials is needed for evaluation with noise, artifacts and non-zero strains.We show that both decreasing the resolution of the displacement field (increasing subvolume size) as well as (increasing) curvature penalization (regularization) have a similar effect on the performance of evaluated DVC methods: Decreasing the detrimental effect of noise, artifacts and interpolation errors, but also decreasing the sensitivity of a DVC method to displacement peaks, discontinuities and strain concentrations. The needed amount of regularization is a trade-off between accuracy and precision of the estimated strain fields and their resolution.The obtainable accuracy and precision of the estimated displacement fields are influenced by interpolation errors in the DVC procedure and the relative amount of detail, noise and artifacts in the images. Errors in the displacement field are typically magnified during the strain calculation. Based on the tests and subvolume sizes (16–50 voxels) in this study, the expected order of magnitude of the accuracy and precision is 0.1 micro-voxels and 1 milli-voxels for the displacements and 0.1 and 1 milli-strains of the strain fields.