Abstract
Digital image correlation (DIC) metrology has gained significant popularity over the past few decades because of its ease of use and reliable displacement measurement. Unlike other optical methods, such as for example interferometric techniques, which produce a fixed resolution depending on the particulars of the optical set-up used, key factors affecting accuracy and resolution of DIC include among others correlation point density (i.e., which pixels are selected as measurements points) and subset size (i.e., the area around the measurement pixel used in the correlation). Intuitively, following reasoning from experience with numerical techniques, a smaller correlation grid spacing and smaller subset size would be expected to produce more accurate results. However, this is not the case in DIC, thus implying that the overall accuracy of DIC metrology would benefit by selecting subset size and correlation point frequency depending on the strain field under observation. Such an adaptive parameter selection would be even more relevant when using DIC in three dimensions (termed Digital Volume Correlation, or DVC), where the computational cost is significantly increased over two-dimensional problems. Here we explore this idea of adaptive refinement by implementing a scheme for subset size selection and then applying it, first to a numerically defined test problem, and then to an actual experimental application. We investigate the relation between subset size and errors in DVC and propose an adaptivity parameter for subset refinement based on the norm of the gradient of the displacement gradient. This gradient parameter, which contains a significant amount of noise since it represents the second derivative of a discrete displacement field, is not used in a metrological sense, but only to determine areas where refinement is needed. In those areas, DVC is then re-computed with appropriately refined parameters and the results are merged with coarser analyses outside these areas. An application of the scheme to a compression experiment with a spherical inclusion in an elastic matrix is performed and shows increased result sensitivity in the region near the inclusion when parameter refinement is adaptively performed there.
Similar content being viewed by others
References
Sutton MA, Orteu JJ, Schreier H (2009) Image correlation for shape, motion and deformation measurements. Springer, New York
Zauel R, Yeni YN, Bay BK, Dong XN, Fyhrie DP (2006) Comparison of the linear finite element prediction of deformation and strain of human cancellous bone to 3D digital volume correlation measurements. J Biomech Eng 128:1–6
Lenoir N, Bornert M, Desrues J, Bésuelle P, Viggiani G (2007) Volumetric digital image correlation applied to X-ray microtomography images from triaxial compression tests on argillaceous rock. Strain 43:193–205
Liu L, Morgan EF (2007) Accuracy and precision of digital volume correlation in quantifying displacements and strains in trabecular bone. J Biomech 40:3516–3520
Limodin N, Réthoré J, Adrien J, Buffière J-Y, Hild F, Roux S (2011) Analysis and artifact correction for volume correlation measurements using tomographic images from a laboratory X-ray source. Exp Mech 51:959–970
Hild F, Roux S, Bernard D, Hauss G, Rebai M (2013) “On the use of 3D images and 3D displacement measurements for the analysis of damage mechanisms in concrete-like materials”, in VIII International Conference on Fracture Mechanics of Concrete and Concrete Structures, pp 1–12
Yang Z, Ren W, Mostafavi M, Mcdonald SA, Marrow TJ (2013) “Characterisation of 3D fracture evolution in concrete using in-situ x- ray computed tomography testing and digital volume correlation”, in VIII International Conference on Fracture Mechanics of Concrete and Concrete Structures, pp 1–7
Bay BK, Smith TS, Fyhrie DP, Saad M (1999) Digital volume correlation: three- dimensional strain mapping using X-ray tomography. Exp Mech 39:217–226
Franck C, Hong S, Maskarinec S, Tirrell D, Ravichandran G (2007) Three-dimensional full-field measurements of large deformations in soft materials using confocal microscopy and digital volume correlation. Exp Mech 47:427–438
Gates M, Lambros J, Heath MT (2011) Towards high performance digital volume correlation. Exp Mech 51(4):491–507
Gates M, Heath MT, Lambros J (2013) “High performance hybrid CPU and GPU parallel algorithm for digital volume correlation”, to appear. Int J High Perform Comput Appl
Yaofeng S, Pang JH (2007) Study of optimal subset size in digital image correlation of speckle pattern images. Opt Lasers Eng 45:967–974
Pan B, Xie H, Wang Z, Qian K, Wang Z (2008) Study on subset size selection in digital image correlation for speckle patterns. Opt Express 16:7037–7048
Wang Z, Li H, Tong J, Ruan J (2007) Statistical analysis of the effect of intensity pattern noise on the displacement measurement precision of digital image correlation using self-correlated images. Exp Mech 47:701–707
Wang YQ, Sutton MA, Bruck HA, Schreier HW (2009) Quantitative error assessment in pattern matching: effects of intensity pattern noise, interpolation, strain and image contrast on motion measurements. Strain 45:160–178
Pan B, Lu Z, Xie H (2010) Mean intensity gradient: an effective global parameter for quality assessment of the speckle patterns used in digital image correlation. Opt Lasers Eng 48:469–477
Schreier HW, Sutton MA (2002) Systematic errors in digital image correlation due to undermatched subset shape functions. Exp Mech 42:303–310
Forsberg F, Siviour CR (2009) 3D deformation and strain analysis in compacted sugar using Xray microtomography and digital volume correlation. Meas Sci Technol 20:1–8
Forsberg F, Sjödahl M, Mooser R, Hack E, Wyss P (2010) Full three-dimensional strain measurements on wood exposed to three-point bending: analysis by use of digital volume correlation applied to synchrotron radiation micro-computed tomography image data. Strain 46:47–60
Padilla HA, Lambros J, Beaudoin A, Robertson IM (2012) Relating inhomogeneous deformation to local texture in zirconium through grain-scale digital image correlation strain mapping experiments. Int J Solids Struct 49:18–31
Schreier HW, Braasch JR, Sutton MA (2000) Systematic errors in digital image correlation caused by intensity interpolation. Opt Eng 39:2915–2921
Gates M (2011) “High performance digital volume correlation”, Ph.D. thesis, University of Illinois at Urbana-Champaign
Reinsch CH (1967) Smoothing by spline functions. Numer Math 10:177–183
Craven P, Wahba G (1979) Smoothing noisy data with spline functions. Numer Math 31:377–403
Golub G, Heath MT, Wahba G (1979) Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21:217–223
Hansen PC, O’Leary DP (1993) The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J Sci Comput 14(6):1487–1503
Goodier JN (1933) Concentration of stress around spherical and cylindrical inclusions and flaws. J Appl Mech 55(7):39–44
Gonzalez J, Lambros J (2014a) “Influence of internal speckle pattern on results of digital volume correlation”, in preparation
Gonzalez J, Lambros J (2014b) “Interfacial debonding of a sphere form a polymeric matrix: three dimensional measurements and analysis”, in preparation
Garcia D (2010) Robust smoothing of gridded data in one and higher dimensions with missing values. Comput Stat Data Anal 54:1167–1178
Acknowledgments
We are grateful to Charles Mark Bee, Leilei Yin, and the Imaging Technology Group at the Beckman Institute for use of the Xradia MicroCT scanner. This work was supported in part by the Center for Simulation of Advanced Rockets under contract by the U.S. Department of Energy [contract number B523819]; the Institute for Advanced Computing Applications and Technologies; the University of Illinois Campus Research Board [award number 09084]; and the University of Illinois In3 program [award number 12027]. Joseph Gonzalez also acknowledges the National Science Foundation for the award of an NSF GSRP fellowship.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gates, M., Gonzalez, J., Lambros, J. et al. Subset Refinement for Digital Volume Correlation: Numerical and Experimental Applications. Exp Mech 55, 245–259 (2015). https://doi.org/10.1007/s11340-014-9881-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11340-014-9881-3