Journal of Mathematical Imaging and Vision

, Volume 60, Issue 5, pp 634–650 | Cite as

Rendering Deformed Speckle Images with a Boolean Model

  • Frédéric Sur
  • Benoît Blaysat
  • Michel Grédiac


Rendering speckle images affected by a given deformation field is of primary importance to assess the metrological performance of displacement measurement methods used in experimental mechanics and based on digital image correlation (DIC). This article describes how to render deformed speckle images with a classic model of stochastic geometry, the Boolean model. The advantage of the proposed approach is that it does not depend on any interpolation scheme likely to bias the assessment process, and that it allows the user to render speckle images deformed with any deformation field given by an analytic formula. The proposed algorithm mimics the imaging chain of a digital camera, and its parameters are carefully discussed. A MATLAB software implementation and synthetic ground-truth datasets for assessing DIC software programs are publicly available.


Boolean model Random speckle rendering Digital image correlation (DIC) 



F.S. is grateful to Antoine Fond (Magrit team, Loria) for his help with the NVidia Titan X GPU.


  1. 1.
    Standard 1288, standard for characterization of image sensors and cameras, release 3.0. Tech. rep., European Machine Vision Association (EMVA) (2010)Google Scholar
  2. 2.
    Amiot, F., Bornert, M., Doumalin, P., Dupré, J.C., Fazzini, M., Orteu, J.J., Poilâne, C., Robert, L., Rotinat, R., Toussaint, E., Wattrisse, B., Wienin, J.: Assessment of digital image correlation measurement accuracy in the ultimate error regime: main results of a collaborative benchmark. Strain 49(6), 483–496 (2013)CrossRefGoogle Scholar
  3. 3.
    Baddeley, A.: Spatial point processes and their applications. In: Weil, W. (ed.) Stochastic Geometry: Lectures Given at the C.I.M.E. Summer School Held in Martina Franca, Italy, September 13–18, 2004, pp. 1–75 (2007)Google Scholar
  4. 4.
    Balcaen, R., Wittevrongel, L., Reu, P.L., Lava, P., Debruyne, D.: Stereo-DIC calibration and speckle image generator based on FE formulations. Exp. Mech. 57(5), 703–718 (2017)Google Scholar
  5. 5.
    Baldi, A.: Digital image correlation and color cameras. Exp. Mech. (2017).
  6. 6.
    Barranger, Y., Doumalin, P., Dupré, J.C., Germaneau, A.: Strain measurement by digital image correlation: influence of two types of speckle patterns made from rigid or deformable marks. Strain 48(5), 357–365 (2012)CrossRefGoogle Scholar
  7. 7.
    Blaysat, B., Grédiac, M., Sur, F.: Effect of interpolation on noise propagation from images to DIC displacement maps. Int. J. Numer. Methods Eng. 108(3), 213–232 (2016)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Blaysat, B., Grédiac, M., Sur, F.: On the propagation of camera sensor noise to displacement maps obtained by DIC—an experimental study. Exp. Mech. 56(6), 919–944 (2016)CrossRefGoogle Scholar
  9. 9.
    Blaysat, B., Grédiac, M., Sur, F.: Assessing the metrological performance of DIC applied on RGB images. In: Proceedings of the 2016 Annual Conference of the International Digital Imaging Correlation Society, Philadelphia (PA) USA (2017)Google Scholar
  10. 10.
    Bomarito, G., Hochhalter, J., Ruggles, T.: Development of optimal multiscale patterns for digital image correlation via local grayscale variation. Exp. Mech. (2017).
  11. 11.
    Bornert, M., Brémand, F., Doumalin, P., Dupré, J.C., Fazzini, M., Grédiac, M., Hild, F., Mistou, S., Molimard, J., Orteu, J.J., Robert, L., Surrel, Y., Vacher, P., Wattrisse, B.: Assessment of digital image correlation measurement errors: methodology and results. Exp. Mech. 49(3), 353–370 (2009)CrossRefGoogle Scholar
  12. 12.
    Bornert, M., Doumalin, P., Dupré, J.C., Poilâne, C., Robert, L., Toussaint, E., Wattrisse, B.: Short remarks about synthetic image generation in the context of sub-pixel accuracy of digital image correlation. In: Proceedings of the 15th International Conference on Experimental Mechanics (ICEM15), Porto, Portugal (2012)Google Scholar
  13. 13.
    Bornert, M., Doumalin, P., Dupré, J.C., Poilâne, C., Robert, L., Toussaint, E., Wattrisse, B.: Assessment of digital image correlation measurement accuracy in the ultimate error regime: improved models of systematic and random errors. Exp. Mech. (2017).
  14. 14.
    Bornert, M., Doumalin, P., Dupré, J.C., Poilâne, C., Robert, L., Toussaint, E., Wattrisse, B.: Shortcut in DIC error assessment induced by image inerpolation used for subpixel shifting. Opt. Lasers Eng. 91, 124–133 (2017)CrossRefGoogle Scholar
  15. 15.
    Briol, F.X., Oates, C., Girolami, M., Osborne, M., Sejdinovic, D.: Probabilistic integration: a role for statisticians in numerical analysis? Tech. Rep. arXiv:1512.00933, v5 (2016)
  16. 16.
    Cofaru, C., Philips, W., Paepegem, W.V.: Evaluation of digital image correlation techniques using realistic ground truth speckle images. Meas. Sci. Technol. 21(5), 055,102/1–17 (2010)Google Scholar
  17. 17.
    Corless, R., Fillion, N.: A Graduate Introduction to Numerical Methods. Springer, Berlin (2014)zbMATHGoogle Scholar
  18. 18.
    Doumalin, P., Bornert, M., Caldemaison, D.: Microextensometry by image correlation applied to micromechanical studies using the scanning electron microscopy. In: Proceedings of the International Conference on Advanced Technology in Experimental Mechanics, vol. I. The Japan Society of Mechanical Engineering, pp. 81–86 (1999)Google Scholar
  19. 19.
    Estrada, J., Franck, C.: Intuitive interface for the quantitative evaluation of speckle patterns for use in digital image and volume correlation techniques. J. Appl. Mech. 82(9), 095,001-1–095,005-5 (2015)CrossRefGoogle Scholar
  20. 20.
    Galerne, B.: Computation of the perimeter of measurable sets via their covariogram. Applications to random sets. Image Anal. Stereol. 30(1), 39–51 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Galerne, B., Gousseau, Y.: The transparent dead leaves model. Adv. Appl. Probab. 44(1), 1–20 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Gallego, M.A., Ibanez, M.V., Simó, A.: Parameter estimation in non-homogeneous Boolean models: an application to plant defense response. Image Anal. Stereol. 34(1), 27–38 (2015)MathSciNetzbMATHGoogle Scholar
  23. 23.
    Goldberg, D.: What every computer scientist should know about floating-point arithmetic. ACM Comput. Surv. 23(1), 5–48 (1991)CrossRefGoogle Scholar
  24. 24.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  25. 25.
    Healey, G., Kondepudy, R.: Radiometric CCD camera calibration and noise estimation. IEEE Trans. Pattern Anal. Mach. Intell. 16(3), 267–276 (1994)CrossRefGoogle Scholar
  26. 26.
    Hua, T., Xie, H., Wang, S., Hu, Z., Chen, P., Zhang, Q.: Evaluation of the quality of a speckle pattern in the digital image correlation method by mean subset fluctuation. Opt. Laser Technol. 43(1), 9–13 (2011)CrossRefGoogle Scholar
  27. 27.
    Koljonen, J., Alander, J.: Deformation image generation for testing a strain measurement algorithm. Opt. Eng. 47(10), 107,202/1–13 (2008)Google Scholar
  28. 28.
    Lava, P., Cooreman, S., Coppieters, S., Strycker, M.D., Debruyne, D.: Assessment of measuring errors in DIC using deformation fields generated by plastic FEA. Opt. Lasers Eng. 47(7–8), 747–753 (2009)CrossRefGoogle Scholar
  29. 29.
    Lecompte, D., Smits, A., Bossuyt, S., Sol, H., Vantomme, J., Hemelrijck, D.V., Habraken, A.: Quality assessment of speckle patterns for digital image correlation. Opt. Lasers Eng. 44(11), 1132–1145 (2006)CrossRefGoogle Scholar
  30. 30.
    Lehoucq, R., Reu, P., Turner, D.: The effect of the ill-posed problem on quantitative error assessment in digital image correlation. Exp. Mech. (2017).
  31. 31.
    Mazzoleni, P., Matta, F., Zappa, E., Sutton, M., Cigada, A.: Gaussian pre-filtering for uncertainty minimization in digital image correlation using numerically-designed speckle patterns. Opt. Lasers Eng. 66, 19–33 (2015)CrossRefGoogle Scholar
  32. 32.
    Morel, J.M., Yu, G.: ASIFT: a new framework for fully affine invariant image comparison. SIAM J. Imaging Sci. 2(2), 438–469 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Murthagh, F., Starck, J., Bijaoui, A.: Image restoration with noise suppression using a multiresolution support. Astron. Astrophys. 112, 179–189 (1995)Google Scholar
  34. 34.
    Newson, A., Delon, J., Galerne, B.: A stochastic film-grain model for resolution-independent rendering. Comput. Graph. Forum 36(8), 684–699 (2017)Google Scholar
  35. 35.
    Newson, A., Faraj, N., Delon, J., Galerne, B.: Analysis of a physically realistic film grain model, and a Gaussian film grain synthesis algorithm. In: Proceedings of the 6th Conference on Scale Space and Variational Methods in Computer Vision (SSVM), Kolding, Denmark (2017)Google Scholar
  36. 36.
    Newson, A., Faraj, N., Galerne, B., Delon, J.: Realistic film grain rendering. Image Process. Online (IPOL) 7, 165–183 (2017)CrossRefGoogle Scholar
  37. 37.
    Orteu, J.J., Garcia, D., Robert, L., Bugarin, F.: A speckle texture image generator. Proc. SPIE 6341, 63,410H 1–6 (2006)Google Scholar
  38. 38.
    Pan, B., Xie, H.M., Xu, B.Q., Dai, F.L.: Performance of sub-pixel registration algorithms in digital image correlation. Meas. Sci. Technol 17(6), 1615–1621 (2006)CrossRefGoogle Scholar
  39. 39.
    Perlin, K.: An image synthesizer. SIGGRAPH Comput. Graph. 19(3), 287–296 (1985)CrossRefGoogle Scholar
  40. 40.
    Quenouille, M.: The evaluation of probabilities in a normal multivariate distribution, with special reference to the correlation ratio. Proc. Edinb. Math. Soc. 8(3), 95–100 (1949)MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Reu, P.L.: Experimental and numerical methods for exact subpixel shifting. Exp. Mech. 51(4), 443–452 (2011)CrossRefGoogle Scholar
  42. 42.
    Schneider, R., Weil, W.: Stochastic and Integral Geometry. Springer, Berlin (2008)CrossRefzbMATHGoogle Scholar
  43. 43.
    Schreier, H., Sutton, M.: Systematic errors in digital image correlation due to undermatched subset shape functions. Exp. Mech. 42(3), 303–310 (2002)CrossRefGoogle Scholar
  44. 44.
    Serra, J.: The Boolean model and random sets. Comput. Graph. Image Process. 12(2), 99–126 (1980)CrossRefGoogle Scholar
  45. 45.
    Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, London (1982)zbMATHGoogle Scholar
  46. 46.
    Small, C.: Expansions and Asymptotics for Statistics. Monographs on Statistics and Applied Probability, vol. 115. CRC Press, Boca Raton (2010)CrossRefGoogle Scholar
  47. 47.
    Society for Experimental Mechanics: DIC challenge.
  48. 48.
    Stoyan, D., Kendall, W., Mecke, J., Kendall, D.: Stochastic Geometry and Its Applications. Wiley, New York (1987)zbMATHGoogle Scholar
  49. 49.
    Su, Y., Zhang, Q., Gao, Z.: Statistical model for speckle pattern optimization. Opt. Express 25(24), 30259–30275 (2017)CrossRefGoogle Scholar
  50. 50.
    Sutton, M., Orteu, J.J., Schreier, H.: Image Correlation for Shape, Motion and Deformation Measurements. Springer, Berlin (2009)Google Scholar
  51. 51.
    Triconnet, K., Derrien, K., Hild, F., Baptiste, D.: Parameter choice for optimized digital image correlation. Opt. Lasers Eng. 47(6), 728–737 (2009)CrossRefGoogle Scholar
  52. 52.
    Yu, L., Pan, B.: The errors in digital image correlation due to overmatched shape functions. Meas. Sci. Technol. 26(4), 045–202 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  • Frédéric Sur
    • 1
  • Benoît Blaysat
    • 2
  • Michel Grédiac
    • 2
  1. 1.Université de Lorraine. LORIA UMR CNRS 7503, INRIA projet MagritVandœuvre-lés-Nancy CedexFrance
  2. 2.Institut Pascal-SIGMACampus Universitaire des CézeauxAubière CedexFrance

Personalised recommendations