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A Fast Iterative Digital Volume Correlation Algorithm for Large Deformations

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.

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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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  MathSciNet  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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, Portuguesa

  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

    Article  Google Scholar 

  20. 20.

    Sutton MA, Orteu JJ, Schreier H (2009) Image correlation for shape, motion and deformation measurements. Springer, New York

    Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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 6:507–514

    Article  Google Scholar 

  30. 30.

    Wereley ST, Meinhart CD (2001) Second-order accurate particle image velocimetry. Exp Fluids 31:258–268

    Article  Google 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

    Article  Google 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

    Article  Google 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):61–69

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  Google 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

    Article  MATH  Google 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

    Article  Google 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

    Article  Google 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

    Article  MathSciNet  Google Scholar 

  42. 42.

    Thornley D (2006) Anisotropic multidimensional Savitzky-Golay kernels for smoothing, differentiation and reconstruction. Department of Computing Technical Report, vol 8

  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

    Article  Google 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

    Article  Google 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

    Article  Google Scholar 

  46. 46.

    Prewitt JMS (1970) Object enhancement and extraction. In: Lipkin BS, Rosenfeld A (eds) Pict. process. psychopictorics. Academic Press Inc., New York

    Google Scholar 

  47. 47.

    Gonzalez RC, Woods RE (2008) Digital image processing, 3rd edn. Prentice Hall, Upper Saddle River

    Google Scholar 

  48. 48.

    Bower AF (2010) Applied mechanics of solids. CRC Press, Boca Raton

    Google Scholar 

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Acknowledgments

This work is in part supported by NIH R21 Al101469-01 and an NSF Graduate Research Fellowship to E.B.K. The authors wish to thank Dr. Allan Bower for his helpful discussions regarding the algorithm’s convergence, Dr. Gabriel Taubin for his valuable input on numerical gradient techniques, and Ronnie Bar-Kochba for help with the GPU implementation of the code.

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Correspondence to C. Franck.

Additional information

Eyal Bar-Kochba and Jennet Toyjanova contributed equally to this work.

Erik Andrews is a posthumous author.

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Bar-Kochba, E., Toyjanova, J., Andrews, E. et al. A Fast Iterative Digital Volume Correlation Algorithm for Large Deformations. Exp Mech 55, 261–274 (2015). https://doi.org/10.1007/s11340-014-9874-2

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Keywords

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