Experimental Mechanics

, Volume 55, Issue 1, pp 261–274 | Cite as

A Fast Iterative Digital Volume Correlation Algorithm for Large Deformations

  • E. Bar-Kochba
  • J. Toyjanova
  • E. Andrews
  • K.-S. Kim
  • C. Franck
Article

Abstract

Digital volume correlation (DVC), the three-dimensional (3D) extension of digital image correlation (DIC), measures internal 3D material displacement fields by correlating intensity patterns within interrogation windows. In recent years DVC algorithms have gained increased attention in experimental mechanics, material science, and biomechanics. In particular, the application of DVC algorithms to quantify cell-induced material deformations has generated a demand for user-friendly, and computationally efficient DVC approaches capable of detecting large, non-linear deformation fields. We address these challenges by presenting a fast iterative digital volume correlation method (FIDVC), which can be run on a personal computer with computation times on the order of 1–2 min. The FIDVC algorithm employs a unique deformation-warping scheme capable of capturing any general non-linear finite deformation. The validation of the FIDVC algorithm shows that our technique provides a unique, fast and effective experimental approach for measuring non-linear 3D deformations with high spatial resolution.

Keywords

Digital volume correlation Large deformations 3D strain measurements GPU Laser scanning confocal microscopy 

Supplementary material

11340_2014_9874_MOESM1_ESM.pdf (429 kb)
(PDF 432 KB)

References

  1. 1.
    Maskarinec SA, Franck C, Tirrell DA, Ravichandran G (2009) Quantifying cellular traction forces in three dimensions. Proc Natl Acad Sci U S A 106(52):22108–22113. doi:10.1073/pnas.0904565106 CrossRefGoogle Scholar
  2. 2.
    Bay BK, Smith TS, Fyhrie DP, Saad M (1999) Digital volume correlation: three-dimensional strain mapping using X-ray tomography. Exp Mech 39(3):217–226. doi:10.1007/BF02323555 CrossRefGoogle Scholar
  3. 3.
    Smith TS, Bay BK, Rashid MM (2002) Digital volume correlation including rotational degrees of freedom during minimization. Exp Mech 42(3):272–278. doi:10.1007/BF02410982 CrossRefGoogle Scholar
  4. 4.
    Franck C, Hong S, Maskarinec SA, Tirrell DA, Ravichandran G (2007) Three-dimensional full-field measurements of large deformations in soft materials using confocal microscopy and digital volume correlation. Exp Mech 47(3):427–438. doi:10.1007/s11340-007-9037-9 CrossRefGoogle Scholar
  5. 5.
    Gates M, Lambros J, Heath MT (2011) Towards high performance digital volume correlation. Exp Mech 51(4):491–507. doi:10.1007/s11340-010-9445-0 CrossRefGoogle Scholar
  6. 6.
    Sutton MA, Wolters WJ, Peters WH, Ranson WF, McNeill SR (1983) Determination of displacements using an improved digital correlation method. Image Vis Comput 1(3):133–139. doi:10.1016/0262-8856(83)90064-1 CrossRefGoogle Scholar
  7. 7.
    Sutton MA, Mingqi C, Peters WH, Chao YJ, McNeill SR (1986) Application of an optimized digital correlation method to planar deformation analysis. Image Vis Comput 4(3):143–150. doi:10.1016/0262-8856(86)90057-0 CrossRefGoogle Scholar
  8. 8.
    Bruck HA, McNeill SR, Sutton MA, Peters WH (1989) Digital image correlation using Newton-Raphson method of partial differential correction. Exp Mech 29(3):261–267. doi:10.1007/BF02321405 CrossRefGoogle Scholar
  9. 9.
    Leclerc H, Périé J-N, Roux S, Hild F (2010) Voxel-scale digital volume correlation. Exp Mech 51(4):479–490. doi:10.1007/s11340-010-9407-6 CrossRefGoogle Scholar
  10. 10.
    Pan B, Wu D, Wang Z (2012) Internal displacement and strain measurement using digital volume correlation: a least-squares framework. Meas Sci Technol 23(4):045002. doi:10.1088/0957-0233/23/4/045002 CrossRefMathSciNetGoogle Scholar
  11. 11.
    Dembo M, Wang YL (1999) Stresses at the cell-to-substrate interface during locomotion of fibroblasts. Biophys J 76(4):2307–2316. doi:10.1016/S0006-3495(99)77386-8 CrossRefGoogle Scholar
  12. 12.
    Lo CM, Wang HB, Dembo M, Wang YL (2000) Cell movement is guided by the rigidity of the substrate. Biophys J 79(1):144–152. doi:10.1016/S0006-3495(00)76279-5 CrossRefGoogle Scholar
  13. 13.
    Sabass B, Gardel ML, Waterman CM, Schwarz US (2008) High resolution traction force microscopy based on experimental and computational advances. Biophys J 94(1):207–220. doi:10.1529/biophysj.107.113670 CrossRefGoogle Scholar
  14. 14.
    Franck C, Maskarinec SA, Tirrell DA, Ravichandran G (2011) Three-dimensional traction force microscopy: a new tool for quantifying cell-matrix interactions. PLoS One 6(3):e17833. doi:10.1371/journal.pone.0017833 CrossRefGoogle Scholar
  15. 15.
    Notbohm J, Kim J-H, Asthagiri AR, Ravichandran G (2012) Three-dimensional analysis of the effect of epidermal growth factor on cell-cell adhesion in epithelial cell clusters. Biophys J 102(6):1323–1330. doi:10.1016/j.bpj.2012.02.016 CrossRefGoogle Scholar
  16. 16.
    Soria J (1996) An investigation of the near wake of a circular cylinder using a video-based digital cross-correlation particle image velocimetry technique. Exp Thermal Fluid Sci 12(2):221–233. doi:10.1016/0894-1777(95)00086-0 CrossRefGoogle Scholar
  17. 17.
    Scarano F, Riethmuller ML (2000) Advances in iterative multigrid PIV image processing. Exp Fluids 29(7):S051–S060. doi:10.1007/s003480070007 CrossRefGoogle Scholar
  18. 18.
    Schrijer FFJ, Scarano F (2006) On the stabilization and spatial resolution of iterative PIV interrogation. In: 13th International Symposium Applied Laser Techniques to Fluid Mechanics Lisbon, PortuguesaGoogle Scholar
  19. 19.
    Benoit A, Guérard S, Gillet B, Guillot G, Hild F, Mitton D, Périé J, Roux S (2009) 3D analysis from micro-MRI during in situ compression on cancellous bone. J Biomech 42(14):2381–2386. doi:10.1016/j.jbiomech.2009.06.034 CrossRefGoogle Scholar
  20. 20.
    Sutton MA, Orteu JJ, Schreier H (2009) Image correlation for shape, motion and deformation measurements. Springer, New YorkGoogle Scholar
  21. 21.
    Verhulp E, van Rietbergen B, Huiskes R (2003) A three-dimensional digital image correlation technique for strain measurements in microstructures. J Biomech 37(9):1313–1320. doi:10.1016/j.jbiomech.2003.12.036 CrossRefGoogle Scholar
  22. 22.
    Hu Z, Xie H, Lu J, Hua T, Zhu J (2010) Study of the performance of different subpixel image correlation methods in 3D digital image correlation. Appl Opt 49(21):4044–4051. doi:10.1364/AO.49.004044 CrossRefGoogle Scholar
  23. 23.
    Huang J, Pan X, Li S, Peng X, Xiong C, Fang J (2011) A digital volume correlation technique for 3-D deformation measurements of soft gels. Int J Appl. Mech 3(2):335–354. doi:10.1142/S1758825111001019 CrossRefGoogle Scholar
  24. 24.
    Huang J, Pan X, Peng X, Yuan Y, Xiong C, Fang J, Yuan F (2012) Digital image correlation with self-adaptive gaussian windows. Exp Mech 53:505–512. doi:10.1007/s11340-012-9639-8 CrossRefGoogle Scholar
  25. 25.
    Nogueira J, Lecuona A, Rodríguez PA (2001) Local field correction PIV, implemented by means of simple algorithms, and multigrid versions. Meas Sci Technol 12(11):1911–1921. doi:10.1088/0957-0233/12/11/321 CrossRefGoogle Scholar
  26. 26.
    Nogueira J, Lecuona A, Rodríguez PA (1999) Local field correction PIV: on the increase of accuracy of digital PIV systems. Exp Fluids 27:107–116. doi:10.1007/s003480050335 CrossRefGoogle Scholar
  27. 27.
    Nogueira J, Lecuona A, Rodríguez PA, Alfaro JA, Acosta A (2005) Limits on the resolution of correlation PIV iterative methods. Practical implementation and design of weighting functions. Exp Fluids 39(2):314–321. doi:10.1007/s00348-005-1017-1 CrossRefGoogle Scholar
  28. 28.
    Huang HT, Fiedler HE, Wang JJ (1993) Limitation and improvement of PIV. Exp Fluids 15-15(4–5):263–273. doi:10.1007/BF00223404 Google Scholar
  29. 29.
    Jambunathan K, Ju XY, Dobbins DN, Ashforth-Frost S (1995) An improved cross correlation technique for particle image velocimetry. Meas Sci Technol 6:507–514CrossRefGoogle Scholar
  30. 30.
    Wereley ST, Meinhart CD (2001) Second-order accurate particle image velocimetry. Exp Fluids 31:258–268CrossRefGoogle Scholar
  31. 31.
    Scarano F (2002) Iterative image deformation methods in PIV. Meas Sci Technol 13:R1–R19. doi:10.1088/0957-0233/13/1/201 CrossRefGoogle Scholar
  32. 32.
    Astarita T (2006) Analysis of interpolation schemes for image deformation methods in PIV: effect of noise on the accuracy and spatial resolution. Exp Fluids 40(6):977–987. doi:10.1007/s00348-006-0139-4 CrossRefGoogle Scholar
  33. 33.
    Ruijters D, ter Haar Romeny BM, Suetens P (2008) Efficient GPU-based texture interpolation using uniform B-splines. J Graph Tools 13(4):61–69CrossRefGoogle Scholar
  34. 34.
    Schrijer FFJ, Scarano F (2008) Effect of predictorcorrector filtering on the stability and spatial resolution of iterative PIV interrogation. Exp Fluids 45(5):927–941. doi:10.1007/s00348-008-0511-7 CrossRefGoogle Scholar
  35. 35.
    Westerweel J, Scarano F (2005) Universal outlier detection for PIV data. Exp Fluids 39(6):1096–1100. doi:10.1007/s00348-005-0016-6 CrossRefGoogle Scholar
  36. 36.
    Hur SS, Zhao Y, Li Y-S, Botvinick E, Chien S (2009) Live cells exert 3-dimensional traction forces on their substrata. Cell Mol Bioeng 2(3):425–436. doi:10.1007/s12195-009-0082-6 CrossRefGoogle Scholar
  37. 37.
    Liu L, Morgan EF (2007) Accuracy and precision of digital volume correlation in quantifying displacements and strains in trabecular bone. J Biomech 40(15):3516–3520. doi:10.1016/j.jbiomech.2007.04.019 CrossRefGoogle Scholar
  38. 38.
    Rannou J, et al (2010) Three dimensional experimental and numerical multiscale analysis of a fatigue crack. Comput Methods Appl Mech Eng 199(21–22):1307–1325. doi:10.1016/j.cma.2009.09.013 CrossRefMATHGoogle Scholar
  39. 39.
    Carroll JD, Abuzaid W, Lambros J, Sehitoglu H (2013) High resolution digital image correlation measurements of strain accumulation in fatigue crack growth. Int J Fatigue 57:140–150. doi:10.1016/j.ijfatigue.2012.06.010 CrossRefGoogle Scholar
  40. 40.
    Roeder BA (2005) Local, three-dimensional strain measurements within largely deformed extracellular matrix constructs. J Biomech Eng 126(6):699. doi:10.1115/1.1824127 CrossRefGoogle Scholar
  41. 41.
    Farid H, Simoncelli EP (2004) Differentiation of discrete multidimensional signals. IEEE Trans Image Process 13(4):496–508. doi:10.1109/TIP.2004.823819 CrossRefMathSciNetGoogle Scholar
  42. 42.
    Thornley D (2006) Anisotropic multidimensional Savitzky-Golay kernels for smoothing, differentiation and reconstruction. Department of Computing Technical Report, vol 8Google Scholar
  43. 43.
    Zhang B, Zerubia J, Olivo-Marin J (2007) Gaussian approximations of fluorescence microscope point-spread function models. Appl Opt 46(10):1819. doi:10.1364/AO.46.001819 CrossRefGoogle Scholar
  44. 44.
    Richardson WH (1972) Bayesian-based iterative method of image restoration. J Opt Soc Am 62(1):55. doi:10.1364/JOSA.62.000055 CrossRefGoogle Scholar
  45. 45.
    Scarano F (2003) Theory of non-isotropic spatial resolution in PIV. Exp Fluids 35(3):268–277. doi:10.1007/s00348-003-0655-4 CrossRefGoogle Scholar
  46. 46.
    Prewitt JMS (1970) Object enhancement and extraction. In: Lipkin BS, Rosenfeld A (eds) Pict. process. psychopictorics. Academic Press Inc., New YorkGoogle Scholar
  47. 47.
    Gonzalez RC, Woods RE (2008) Digital image processing, 3rd edn. Prentice Hall, Upper Saddle RiverGoogle Scholar
  48. 48.
    Bower AF (2010) Applied mechanics of solids. CRC Press, Boca RatonGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2014

Authors and Affiliations

  • E. Bar-Kochba
    • 1
  • J. Toyjanova
    • 1
  • E. Andrews
    • 1
  • K.-S. Kim
    • 1
  • C. Franck
    • 1
  1. 1.School of EngineeringBrown UniversityProvidenceUSA

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