Digital volume correlation from tomographic images: Results and challenges

Procedia Engineering

Procedia Engineering 00 (2012) 000–000

www.elsevier.com/locate/procedia

IUTAM Symposium on Advances of Optical Methods

in Experimental Mechanics

Digital Volume Correlation from Tomographic Images:

Results and Challenges

S. Roux,1*

T. Taillandier-Thomas,1-2

A. Bouterf,1

H. Leclerc,1 T.F. Morgeneyer

2 and F. Hild

1

1LMT-Cachan, ENS Cachan / CNRS UMR8535 / UPMC / PRES UniverSud Paris

61 avenue du Président Wilson, 94235 Cachan Cedex, France 2Mines ParisTech, Centre des Matériaux, CNRS UMR 7633

BP 87, 91003 Evry Cedex, France

Abstract

Although theoretically Digital Volume Correlation (DVC) from tomographic images is a straightforward extension of Digital

Image Correlation to 3D situations, new challenges arise from the use of tomographic imaging itself. The first difficulty is that

the actual microstructure of the material can hardly be modified in the bulk in order to enhance the contrast, and hence the

applicability of the technique may appear limited to a narrow class of materials. Artifacts in image acquisition or in

reconstruction have potentially a more dramatic effect than noise on the computed displacement field. The manipulation of a

large volume of data is yet another classical difficulty. To address these difficulties specific developments are to be devised, the

most important of those is a mechanical regularization strategy that constrains the sought displacement field in order to

compensate for the detrimental effect of noise, artifact and/or poor texture. With such a regularization, DVC offers an

unprecedented wealth of information for analyzing the mechanical behavior of a large class of materials.

© 2012 Published by Elsevier Ltd.

Keywords: Digital Volume Correlation; Regularization; Tomography; Artifacts; GPU.

1. Introduction

Digital Volume Correlation (DVC) allows for the measurement of full three-dimensional field of displacement

from 3D images acquired for instance with an X-ray Computed Tomography (X-CT) system. DVC is a

straightforward extension of Digital Image Correlation (DIC) in three dimensions and thus the different strategies

developed in 2D can readily be transposed in 3D with comparable weaknesses or merits [1].

S. Roux et al./ Procedia Engineering 00 (2012) 000–000

In the same way as DIC is progressively being used routinely in solid mechanics, it is a safe bet to predict a

similar development in the forthcoming decade as tomographs will become more and more common instruments.

The invaluable information brought about by tomography in the field of materials science has been essentially

focused on the 3D imaging of various microstructures, and hence, with the help of 3D image analysis techniques,

access to the constitutive phases of a material, their morphology, the statistical characterization of inclusion number,

size, shape has received a lot of attention, and indeed, this effort revealed very rewarding [2,3]. A second very

appealing virtue of tomography in the industrial context is shape metrology [4]. This pushed tomography to become

even more quantitative than what was called for in simple imaging. This being achieved for lab scale tomographs, it

is now very tempting to follow the evolution of a specimen during its mechanical loading, and hence in situ

mechanical testing is an expanding field of investigation [5]. In this domain, DVC is the technique of predilection

to measure three-dimensional displacement fields and couple experiments with numerical modeling [6].

The present paper points toward the novel challenges specifically attached to DVC, and recent developments

implemented to answer these demands.

2. Challenges

2.1. Material microstructure

The first generic difficulty is that the actual microstructure of the material can hardly be modified in the bulk in

order to enhance the contrast. Some attempts were made (i.e., by adding particles [7] or revealing grain boundaries

[8]) but at the expense of changing the behavior of the investigated material. This is a major difference with 2D

DIC, where a homogeneous or transparent material can always be painted with a speckle pattern, where the

experimentalist can fine-tune the homogeneity, pattern correlation length, and contrast more or less at will. In

synchrotron facilities, the use of phase contrast can enhance the differences between material phases, and make them

visible on the radiographs. However, this technique cannot be used on lab scale tomograph with polychromatic

sources. Thus, this difficulty pushes DVC to deal with microstructures that can be very faint, with very few

contrasting phases, possibly with a contrast that is not very salient as compared to reconstruction artifacts (Figure

1a). Robustness when dealing with such sparse contrast textures is a major challenge that limits a priori the

recourse to DVC for well contrasted materials (e.g., biological tissues [9], foams [10] and cellular materials (Figure

1b), or material with a large proportion of inclusions [6,11,12], Figure 1c).

-a- -b- -c-

Figure 1: 3D rendering of three different textures.

-a-Aluminum alloy with 0.3-0.4 % of secondary particles (1 voxel 0.7µm).

-b-Plaster with a volume fraction of void of 56 % (1 voxel 48 µm).

-c-Spheroidal graphite cast iron with a 13 % volume fraction of graphite nodules (1 voxel 5.1 µm).

Roux et al. / Procedia Engineering 00 (2012) 000–000

2.2. CT imaging and artifacts

New challenges arise from the use of tomographic imaging itself, namely, artifacts in image acquisition or in

reconstruction can affect the computed displacement field. For instance, in a laboratory tomographic scanner, a

minute displacement of the source gives rise to a magnification change of the image, and hence to an apparent

homogeneous dilation that should not be confused with mechanical strains [13]. For this reason, many recent lab

systems have a thermal regulation that limits this bias.

The occurrence of reconstruction artifacts (such as rings) becomes very detrimental when the contrast due to the

natural microstructure of the material is poor. It is therefore very important to address these cases in order to make

DVC useful for a broader class of materials. Apart from progress in the reconstruction technique itself, one way to

address the problem consists in numerically filtering images prior to a DVC analysis (e.g., ring artifacts can be

significantly reduced [14]). This filtering may however also affect the true microstructure. Another difficulty is that

the actual (reliable) microstructure after filtering may consist of a very faint texture (low gray level gradients, or

very dilute support, see Figure 1a). To address this problem while preserving an acceptable spatial resolution

requires a suited regularization strategy [15].

2.3. Volume of data / Duration of acquisition

Yet another limitation comes from the enormous amount of information in 3D images. This challenge is first met

at the acquisition stage where a complete scan may require up to one hour or more in some cases, duration such that

creep may be responsible for a significant motion in between the first and last radiograph. This bias renders difficult

(or even impedes) a proper reconstruction. Second, at the reconstruction stage, the cost of data processing promotes

fast reconstruction techniques (such as the celebrated Filtered Back-Projection algorithm [16]) rather than algebraic

variants, which are more reliable [17], but more demanding in terms of reconstruction.

DVC by itself involves also a large amount of data, and thus efficient data processing becomes essential. When

regularization strategies are considered, this demand becomes even more stringent. Efficient GPU implementations

can constitute a solution [18]. However, other strategies can be considered, which will call for a very significant

reduction in the number of radiographs [19]. The latter option is extremely appealing as it allows for a much faster

data acquisition. However, such an option generally involves more pronounced artifacts and thus the limitations

mentioned in the previous section become even more stringent.

2.4. Detecting features invisible to the eye

Another difficulty is that some interesting features for the mechanical analysis may not be visible because of

insufficient spatial resolution or because parts of the texture (e.g., particles useful for DVC) have the same gray

levels as the sought feature (Figure 2). An example in this category is crack opening that cannot be detected when

its level is not comparable to the voxel size (Figure 2b). The ability of DVC to detect displacements that are much

smaller than the voxel size (of order 10-1

voxel) is a strength that can be used to identify stress intensity factors (see

Section 3.2). Moreover, the development of new techniques designed specifically for analyzing cracks from the

analysis of remote noisy displacement fields is available to meet this challenge and identify the crack front position

in 3D well ahead of what can be seen on a single image [6].


-a- -b-

Figure 2: -a-3D rendering of correlation residuals clearly locating the crack surface.

-b-Thresholded gray levels in the vicinity of the crack surface. It is impossible to locate the crack surface because

the nodules and the crack have similar gray levels (Figure 1c).

3. Recent solutions

3.1. Filtering 3D images

3D images are reconstructed from radiographs acquired at different orientations of the sample with respect to the

beam. However, a dead (or bad) pixel on the detector, a poor “flat field” normalization or more generally any

deviation from the general assumptions (such as the displacement occurring during the scan) typically induces “ring

artifacts” [20]. This is especially true when the reconstruction method is known to be approximate (e.g., away from

the median plane with a fan-beam or cone-beam tomography, or laminography (Figure 3)).

-a- -b-

Figure 3: 3D rendering of an aluminum alloy with 0.3-0.4 % of secondary particles (1 voxel 0.7µm).

-a-Raw reconstructed volume. -b-Filtered reconstruction.

Filtering of the reconstructed image to erase the ring artifacts while preserving the microstructure can be


performed as shown in Figure 3b. As a consequence, it is observed that the histogram of gray levels that was

already rather poor for DVC becomes even narrower. Assuming that this histogram thinning is mostly due to

artifact correction, it becomes clear that relying on the texture of direct reconstructions may lead to spurious

displacement evaluations as the rings do not necessarily follow the material kinematics. For this particular

example, the amount of inclusions in the material was estimated to be about 0.3-0.4 vol%. It is worth noting that

a direct attempt to use DVC on the filtered images does not lead to convergence. Such a poor microstructural

texture makes more limiting the ill-posedness nature of DVC. It will be shown in a forthcoming section (3.4) that

DVC can be used on the non-filtered images, as in this particular case, rings originate from phase contrast and

hence are translated together with the inclusions. Let us note however, that the rings do not rotate with the

material microstructure and hence they are fragile markers for DVC.

-a- -b-

Figure 4: Gray level histograms of an aluminum alloy laminographies (Figure 3).

-a-Raw reconstructed volume. -b-Filtered reconstruction.

3.2. Global DVC

Paralleling the distinction between local and global DIC strategies [1], both propositions can simply be extended

to DVC. In fact, from a theoretical point of view, space dimensionality does not play a key role in image

correlation. Local DVC consists in analyzing interrogation sub-volumes and determining their mean displacements

from the registration of corrected deformed sub-volume with the corresponding reference [9,21]. These corrections

generally involve a linear displacement gradient, albeit only the mean displacement is retained. In contrast, global

DVC consists in solving for the “best” displacement field in a specified vector space of displacement. A common

choice of this space is given by finite element shape functions [10], thereby providing a natural interface with

numerical simulations [6]. The “best” displacement field is the argument that minimizes a functional qualifying

image registration. The price to pay for this formulation is that the unknowns (i.e., nodal displacements) are

coupled, in contrast with the local approach where each sub-volume is treated independently. Thus a parallel

treatment is straightforward for the local approach, but requires skills used in the field of computational mechanics

for global DVC [18]. Among the different variants, a very generic one is based on finite-element type

decompositions for the displacement field, with an image-driven mesh with C8 elements (8-noded cubes with tri-

linear displacement shape functions). However, unstructured meshes based on the imaged microstructure are also

implemented within this framework [22].

The material studied hereafter is lightweight gypsum. Cylinders (17 mm in diameter) are extracted from

industrial plasterboard plates. In situ experiments with a spherical indenter (6 mm in diameter) were performed.

The specimen was imaged when unloaded and loaded at nine different levels. After each step, the crosshead

displacement was kept motionless and a 20-minute dwell time was used to let relaxation take place. Figure 5 shows

the reconstructed volumes of the sample observed by CT for the reference configuration (figure 5a) and at the eighth

load level (figure 5b). The compacted zone is clearly visible on the top part of the 3D rendering. It was masked in

the following DVC analyses since the gray level conservation is not satisfied. First, a C8-DVC analysis is

performed for a zone close to the compacted area. The corresponding longitudinal displacement field is shown in

Figure 7a for a discretization with 6-voxel elements. Displacement fluctuations are clearly visible since the dynamic

range is very small (i.e., less than 2 voxels) as outside the compacted volume plaster remains mostly elastic. Many


of these fluctuations are due to measurement uncertainties associated with very small element sizes. This first

analysis shows that even with very small element sizes, global DVC provides a good first displacement estimate.

However, it is corrupted by measurement uncertainties and strain evaluation cannot be achieved faithfully at such a

small scale. In the following section, an alternative route will be followed.

-a- -b-

Figure 5: 3D rendering of the observed volume of interest.

-a-Reference configuration. -b-Deformed configuration.

The next analysis deals with nodular graphite cast iron (Figure 1c). A larger sample was first pre-cracked in

fatigue. A smaller sample was cut and subsequently tested in situ for various stages of propagation. After

45 kcycles, a scan was taken at maximum and minimum load. The displacement field was first measured with a C8-

DVC code. By using the correlation residuals (as exemplified in Figure 2a), an enriched kinematics is sought by

using the same kinematic hypotheses as in eXtended Finite Element Methods (X-FEM) [23,24], it is referred to as

eXtended Digital Volume Correlation (or X-DVC [6,25,26]). The crack front is determined by projecting the

measured displacement field onto Williams’ series, in particular, by canceling out the amplitude associated with the

first supersingular field [27]. Another output of this procedure is the stress intensity profiles (Figure 6a).

-a- -b-

Figure 6: -a-Profiles of KI, KII and KIII stress intensity factors determined experimentally by post-processing X-DVC

results, and numerically by resorting to X-FEM analyses.

-b-3D rendering of the longitudinal displacement field calculated by X-FEM in the cracked nodular graphite cast

iron (Figure 1c). The scale bar is expressed in micrometers. The boundary conditions used for the calculation

correspond to the experimental displacements obtained by X-DVC (after [26]).


The latter is compared with the predicted profiles with the same cracked surface, the same front, and the measured

boundary conditions applied to the top and bottom faces of the volume of interest (Figure 6b). A very good

agreement is observed between the experimentally determined and numerically predicted stress intensity profiles.

Such a result shows the benefit of combining advanced experimental and numerical tools to analyze 3D cracks.

3.3. Reduced basis in DVC

The analysis of displacements both for local and global DVC typically results from a compromise between

spatial resolution and displacement uncertainty [18]. To enhance the spatial resolution, smaller interrogation

windows (local DVC) or elements (global DVC) are to be used to allow for local adjustments. However, this leads

to an increase in the number of unknowns, and hence less available information for each one. Consequently, the

measurement uncertainty increases. Similarly, the sensitivity to noise is increased. This may be tolerable for

displacement measurements, but soon becomes harmful to the determination of strain fields.

One possibility to circumvent this problem is to design a reduced basis, i.e., allowing for much less numerous

degrees of freedom, yet being faithful to the actual displacement within the specimen. The advantage of this

approach is that one may easily benefit from prior knowledge on the expected displacement field. However, this

knowledge cannot be expressed as analytical solutions since they are very scarce in 3D situations. Conversely, a

specific basis can be built numerically as soon as the “true” unknowns of the problem are parameterized using any

finite-element code.

To exemplify this concept, let us revert to the example of plaster indentation of the previous section. Here the

specimen is expected to behave elastically away from the indentation. The “true” unknowns describe the loading

along the boundary of the elastic domain. If a spherical harmonics decomposition of the unknown displacement on

the surface of the crushed region is performed, a truncation to low order terms constitutes a suited reduced basis

with less than 10 degrees of freedom. This displacement basis is obtained from a finite element simulation of the

whole sample assumed to behave elastically (Poisson’s ratio: 0.15). The DVC results with this reduced kinematic

basis are shown in Figure 7b. Many of the fluctuations are filtered out when compared to a standard C8-DVC result

(Figure 7a), yet the long wave features are still captured. Because the correlation residuals in both analyses are

virtually identical, the DVC results with a reduced basis are deemed trustworthy.

-a- -b-

Figure 7: 3D rendering of the longitudinal displacement field measured during an indentation test on plaster

(Figure 1b). The zone where the material is compacted has been removed.

-a-Standard DVC approach. -b-DVC approach with reduced basis.

The scale bar is expressed in voxels (1 voxel 48 µm).


3.4. Regularized DVC

The previous strategy calls for a rather strong prior knowledge (an elastic behavior was assumed over most of the

domain). It is also possible to introduce such information in a more tunable manner allowing for a more flexible

tool as introduced in [28] and presented for DIC in this volume [29]. The spirit of mechanical regularization

consists in adding to the traditional DVC objective functional (based on the quadratic distance between the

deformed image corrected by a displacement field and the reference image) a second functional based on the

equilibrium gap that penalizes deviations of the displacement field from being the solution of an elastic problem

with known (or null) body forces. The latter functional is the quadratic norm of a linear second-order differential

operator acting on the displacement field, and hence the relative weights given to both functional introduce a length

scale . Below , the regularization functional dominates, whereas at large length scales (above), the DVC

functional is the largest. This combination acts as a low-pass filter for DVC, where the high frequency component

is brought by elasticity. In some sense, the previous approach corresponds to the limit of a very large weight being

given to the regularization as the library of proposed displacement fields all obey exactly elasticity over the entire

domain. When a smaller value of the cut-off wavelength is used, the effect of regularization can be compared to

that of a coarse mesh of size , with however much better smoothness properties. The same method can be extended

to more complex mechanical behavior than linear elasticity or heterogeneous elastic properties if desired. However,

even if homogeneous linear elasticity is used, the latter can simply be considered as a smoothening operator to make

the problem well-posed rather than an accurate description of the mechanical behavior of the studied specimen.

-a- -b-

Figure 8: 3D rendering of von Mises’ equivalent strain measured during an opening test of a notched

aluminum alloy sample (Figure 1a). -a-Standard DVC approach. -b-Regularized DVC approach.

The following analysis deals with an in-situ tearing test on an aluminum alloy sheet monitored via synchrotron

laminography [30]. The details of the experimental conditions can be found in [31,32]. The present case is deemed

difficult, if not impossible, since the volume fraction of secondary particles is of the order of 0.3-0.4 % (Figures 3a

and 4a). It becomes even more difficult after filtering (Figures 3b and 4b). In the unfiltered case, a standard global

C8-DVC (with 16-voxel elements) is performed on a zone far from the notch where the crack initiates and

subsequently propagates. The crack has not yet propagated even though localized bands can be observed (Figure

8a). In Figure 8b, a regularized correlation approach with a regularization length of 50 voxels is used with the same

mesh as previously. However, the considered volumes are filtered. Without the present regularization, the

correlations are not possible. Although the texture is extremely poor, very consistent results are observed between

the equivalent strain maps obtained by both approaches (Figure 8). The filtering of the strain field is clearly


apparent, illustrating its denoising effect for DVC. The question of the possible detrimental effect of this “filter” has

to be evaluated on the quality of the registration, namely on the correlation residual or the difference between the

reference and deformed image after correction by the measured displacement field. In that case, the quality of

registration is excellent so that the filtering is not considered as detrimental to the measured displacement field.

The regularization strategy allows the DVC problem to be made well-posed even when discretized onto a very

fine mesh. It was shown [15] that the ultimate limit of a regular cubic mesh with elements reduced to a single voxel

could be handled with such a strategy. However, in that case, the number of unknown becomes very large, and the

regularization kernel involves a more complex problem to solve, and hence regularized DVC becomes much more

demanding in terms of computation time and memory management. To overcome this difficulty, a dedicated GPU

implementation has been set up that can handle several million degrees of freedom problems within an acceptable

time (less than 10 minutes) [18].

4. Conclusions

In spite of the difficulties listed above, DVC can be made operational and reliable for a wider class of materials

than usually considered. As demonstrated herein, those extensions require a critical consideration of the

reconstructed images and possibly filtering to — at least partially — erase imaging artifacts, regularization strategies

to allow for noise reduction on strain evaluation and compensate for poor microstructural textures, and efficient

numerical GPU implementation of the resulting algorithms. Such developments are essential for taking the full

benefit of lab scale tomograph equipment and analyze in-situ mechanical testing to get more qualitative and

quantitative insight into the mechanical behaviour of materials.

Acknowledgments

We acknowledge the support of CETIM Foundation (PROPAVANFIS project), ANR (ANR-09-BLAN-0009-01-

RUPXCUBE project), Saint-Gobain Recherche, and Fédération Francilienne de Mécanique. The different examples

cited in this paper were developed with the help of J. Adrien, M.-C. Baïetto, J.-Y. Buffière, A. Combescure, A.

Gravouil, L. Helfen, N. Limodin, W. Ludwig, E. Maire, J. Rannou, and J. Réthoré who are gratefully

acknowledged.

References

[1] Hild F, Roux S. Digital Image Correlation. In: Optical Methods for Solid Mechanics. A Full-Field

Approach. Wiley-VCH; 2012, p. 183-228.

[2] Baruchel J, Buffière J-Y, Maire E, Merle P, Peix G. X-Ray Tomography in Material Sciences. Hermes

Science; 2000.

[3] Weitkamp T, Tafforeau P, Boller E, Cloetens P, Valade J-P, Bernard P, Peyrin F, Ludwig W, Helfen L,

Baruchel J. Status and evolution of the ESRF beamline ID19. In ICXOM 2009, AIP Conf. Proc.; 2010.

[4] Industrial_CT_scanning. en.wikipedia.org/wiki/Industrial_CT_scanning; february 2012.

[5] Buffière J-Y, Maire E, Adrien J, Masse J-P, Boller E. In Situ Experiments with X ray Tomography: an

Attractive Tool for Experimental Mechanics. Exp. Mech. 2010;50:289-305.

[6] Rannou J, Limodin N, Réthoré J, Gravouil A, Ludwig W, Baïetto M-C, Buffière J-Y, Combescure A, Hild

F, Roux S. Three dimensional experimental and numerical multiscale analysis of a fatigue crack. Comp.

Meth. Appl. Mech. Eng. 2010;199:1307-1325.

[7] Bornert M, Chaix J-M, Doumalin P, Dupré J-C, Fournel T, Jeulin D, Maire E, Moreaud M, Moulinec H.

Mesure tridimensionnelle de champs cinématiques par imagerie volumique pour l'analyse des matériaux et

des structures. Inst. Mes. Métrol. 2004;4:43-88.

[8] Ludwig W, Buffière J-Y, Savelli S, Cloetens P. Study of the interaction of a short fatigue crack with grain

boundaries in a cast Al alloy using X-ray microtomography. Acta Mater. 2003;51:585-598.

[9] Bay BK, Smith TS, Fyhrie DP, Saad M. Digital volume correlation: three-dimensional strain mapping

using X-ray tomography. Exp. Mech. 1999;39:217-226.


[10] Roux S, Hild F, Viot P, Bernard D. Three dimensional image correlation from X-Ray computed

tomography of solid foam. Comp. Part A 2008;39:1253-1265.

[11] Hall S, Bornert M, Desrues J, Pannier Y, Lenoir N, Viggiani C, Bésuelle P. Discrete and continuum

analysis of localised deformation in sand using X-ray micro CT and volumetric digital image correlation.

Géotechnique 2010;60:315-322.

[12] Hild F, Fanget A, Adrien J, Maire E, Roux S. Three dimensional analysis of a tensile test on a propellant

with digital volume correlation. Arch. Mech. 2011;63:1-20.

[13] Limodin N, Réthoré J, Adrien J, Buffière J-Y, Hild F, Roux S. Analysis and artifact correction for volume

correlation measurements using tomographic images from a laboratory X-ray source. Exp. Mech.

2011;51:959-970.

[14] Prell D, Kyriakou Y, Kalender WA. Comparison of ring artifact correction methods for flat-detector CT.

Phys. Med. Biol. 2009;54:3881-3895.

[15] Leclerc H, Périé J-N, Roux S, Hild F. Voxel-scale digital volume correlation. Exp. Mech. 2011;51:479-490.

[16] Feldkamp LA, Davis LC, Kress JW. Practical cone beam algorithm. J. Opt. Soc. Am. 1984;A1:612-619.

[17] Gabor GT. Fundamentals of Computerized Tomography: Image Reconstruction from Projections. Springer;

2009.

[18] Leclerc H, Périé J-N, Hild F, Roux S. Digital Volume Correlation: What are the limits to the spatial

resolution? Méc. & Ind. 2012:submitted for publication.

[19] Herman GT, Davidi R. Image reconstruction from a small number of projections. Inverse Problems

2008;24.

[20] Vidal FP, Letang JM, Peix G, Cloetens P. Investigation of artefact sources in synchrotron

microtomography via virtual X-ray imaging. Nucl. Inst. Meth. Phys. Res. B 2005;234:333-348.

[21] Smith TS, Bay BK, Rashid MM. Digital volume correlation including rotational degrees of freedom during

minimization. Exp. Mech. 2002;42:272-278.

[22] Besnard G, Hild F, Leclerc H, Périé JN, Roux S, Réthoré J. La corrélation d'images : un outil de mécanique

expérimentale. In: Buffière J-Y, Maire E, editors. Congrès national MECAMAT; 2010.

[23] Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. Int. J.

Num. Meth. Eng. 1999;46:133-150.

[24] Black T, Belytschko T. Elastic crack growth in finite elements with minimal remeshing. Int. J. Num. Meth.

Eng. 1999;45:601-620.

[25] Réthoré J, Tinnes J-P, Roux S, Buffière J-Y, Hild F. Extended three-dimensional digital image correlation

(X3D-DIC). C. R. Mecanique 2008;336:643-649.

[26] Réthoré J, Limodin N, Buffière J-Y, Hild F, Ludwig W, Roux S. Digital volume correlation analyses of

synchrotron tomographic images. J. Strain Analysis 2011;46:683-695.

[27] Roux S, Réthoré J, Hild F. Digital Image Correlation and Fracture: An Advanced Technique for Estimating

Stress Intensity Factors of 2D and 3D Cracks. J. Phys. D: Appl. Phys. 2009;42:214004.

[28] Réthoré J, Roux S, Hild F. An extended and integrated digital image correlation technique applied to the

analysis fractured samples. Eur. J. Comput. Mech. 2009;18:285-306.

[29] Hild F, Leclerc H, Roux S, Swiergiel N, Tomičević Z. Circumventing the curse of resolution versus spatial

resolution in digital image correlation: From Local to Global and Regularized Approaches. In this volume;

2012.

[30] Helfen L, Baumbach T, Mikulík P, Kiel D, Pernot P, Cloetens P, Baruchel J. High-resolution three-

dimensional imaging of flat objects by synchrotron-radiation computed laminography. Appl. Phys. Lett.

2005;86:071915.

[31] Morgeneyer TF, Helfen L, Sinclair I, Proudhon H, Xu F, Baumbach T. Ductile crack initiation and

propagation assessed via in situ synchrotron radiation-computed laminography. Scripta Mater. 2011;

65:1010-1013.

[32] Morgeneyer TF, Helfen L, Mubarak H, Hild F, 3D Digital Volume Correlation of Synchrotron Radiation

Laminography images of ductile crack initiation: an initial feasibility study. Exp. Mech. 2012: in press,

DOI: 10.1007/s11340-012-9660-y

Digital volume correlation from tomographic images: Results and challenges

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