Rendering deformed speckle images with a Boolean model. (English) Zbl 1437.94028
Summary: 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.
MSC:
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 62H35 | Image analysis in multivariate analysis |
References:
| [1] | Standard 1288, standard for characterization of image sensors and cameras, release 3.0. Tech. rep., European Machine Vision Association (EMVA) (2010) |
| [2] | Amiot, F; Bornert, M; Doumalin, P; Dupré, JC; Fazzini, M; Orteu, JJ; 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, 483-496, (2013) · doi:10.1111/str.12054 |
| [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) · Zbl 1127.62086 |
| [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) |
| [5] | Baldi, A.: Digital image correlation and color cameras. Exp. Mech. (2017). https://doi.org/10.1007/s11340-017-0347-2 |
| [6] | Barranger, Y; Doumalin, P; Dupré, JC; Germaneau, A, Strain measurement by digital image correlation: influence of two types of Speckle patterns made from rigid or deformable marks, Strain, 48, 357-365, (2012) · doi:10.1111/j.1475-1305.2011.00831.x |
| [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, 213-232, (2016) · Zbl 07870100 · doi:10.1002/nme.5212 |
| [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, 919-944, (2016) · doi:10.1007/s11340-016-0130-9 |
| [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) |
| [10] | Bomarito, G., Hochhalter, J., Ruggles, T.: Development of optimal multiscale patterns for digital image correlation via local grayscale variation. Exp. Mech. (2017). https://doi.org/10.1007/s11340-017-0348-1 |
| [11] | Bornert, M; Brémand, F; Doumalin, P; Dupré, JC; Fazzini, M; Grédiac, M; Hild, F; Mistou, S; Molimard, J; Orteu, JJ; Robert, L; Surrel, Y; Vacher, P; Wattrisse, B, Assessment of digital image correlation measurement errors: methodology and results, Exp. Mech., 49, 353-370, (2009) · doi:10.1007/s11340-008-9204-7 |
| [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) |
| [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). https://doi.org/10.1007/s11340-017-0328-5 |
| [14] | Bornert, M; Doumalin, P; Dupré, JC; 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) · doi:10.1016/j.optlaseng.2016.11.014 |
| [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] | 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) |
| [17] | Corless, R., Fillion, N.: A Graduate Introduction to Numerical Methods. Springer, Berlin (2014) · Zbl 1295.65001 |
| [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) |
| [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, 095,001-1-095,005-5, (2015) · doi:10.1115/1.4030821 |
| [20] | Galerne, B, Computation of the perimeter of measurable sets via their covariogram. applications to random sets, Image Anal. Stereol., 30, 39-51, (2011) · Zbl 1228.60019 · doi:10.5566/ias.v30.p39-51 |
| [21] | Galerne, B; Gousseau, Y, The transparent dead leaves model, Adv. Appl. Probab., 44, 1-20, (2012) · Zbl 1245.60011 · doi:10.1239/aap/1331216642 |
| [22] | Gallego, MA; Ibanez, MV; Simó, A, Parameter estimation in non-homogeneous Boolean models: an application to plant defense response, Image Anal. Stereol., 34, 27-38, (2015) · Zbl 1356.92049 |
| [23] | Goldberg, D, What every computer scientist should know about floating-point arithmetic, ACM Comput. Surv., 23, 5-48, (1991) · doi:10.1145/103162.103163 |
| [24] | Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2000) · Zbl 0956.68149 |
| [25] | Healey, G; Kondepudy, R, Radiometric CCD camera calibration and noise estimation, IEEE Trans. Pattern Anal. Mach. Intell., 16, 267-276, (1994) · doi:10.1109/34.276126 |
| [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, 9-13, (2011) · doi:10.1016/j.optlastec.2010.04.010 |
| [27] | Koljonen, J., Alander, J.: Deformation image generation for testing a strain measurement algorithm. Opt. Eng. 47(10), 107,202/1-13 (2008) |
| [28] | Lava, P; Cooreman, S; Coppieters, S; Strycker, MD; Debruyne, D, Assessment of measuring errors in DIC using deformation fields generated by plastic FEA, Opt. Lasers Eng., 47, 747-753, (2009) · doi:10.1016/j.optlaseng.2009.03.007 |
| [29] | Lecompte, D; Smits, A; Bossuyt, S; Sol, H; Vantomme, J; Hemelrijck, DV; Habraken, A, Quality assessment of Speckle patterns for digital image correlation, Opt. Lasers Eng., 44, 1132-1145, (2006) · doi:10.1016/j.optlaseng.2005.10.004 |
| [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). https://doi.org/10.1007/s11340-017-0360-5 |
| [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) · doi:10.1016/j.optlaseng.2014.08.004 |
| [32] | Morel, JM; Yu, G, ASIFT: a new framework for fully affine invariant image comparison, SIAM J. Imaging Sci., 2, 438-469, (2009) · Zbl 1181.68252 · doi:10.1137/080732730 |
| [33] | Murthagh, F; Starck, J; Bijaoui, A, Image restoration with noise suppression using a multiresolution support, Astron. Astrophys., 112, 179-189, (1995) |
| [34] | Newson, A., Delon, J., Galerne, B.: A stochastic film-grain model for resolution-independent rendering. Comput. Graph. Forum 36(8), 684-699 (2017) |
| [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) |
| [36] | Newson, A; Faraj, N; Galerne, B; Delon, J, Realistic film grain rendering, Image Process. Online (IPOL), 7, 165-183, (2017) · doi:10.5201/ipol.2017.192 |
| [37] | Orteu, J.J., Garcia, D., Robert, L., Bugarin, F.: A speckle texture image generator. Proc. SPIE 6341, 63,410H 1-6 (2006) |
| [38] | Pan, B; Xie, HM; Xu, BQ; Dai, FL, Performance of sub-pixel registration algorithms in digital image correlation, Meas. Sci. Technol, 17, 1615-1621, (2006) · doi:10.1088/0957-0233/17/6/045 |
| [39] | Perlin, K, An image synthesizer, SIGGRAPH Comput. Graph., 19, 287-296, (1985) · doi:10.1145/325165.325247 |
| [40] | Quenouille, M, The evaluation of probabilities in a normal multivariate distribution, with special reference to the correlation ratio, Proc. Edinb. Math. Soc., 8, 95-100, (1949) · Zbl 0037.08104 · doi:10.1017/S0013091500002613 |
| [41] | Reu, PL, Experimental and numerical methods for exact subpixel shifting, Exp. Mech., 51, 443-452, (2011) · doi:10.1007/s11340-010-9417-4 |
| [42] | Schneider, R., Weil, W.: Stochastic and Integral Geometry. Springer, Berlin (2008) · Zbl 1175.60003 · doi:10.1007/978-3-540-78859-1 |
| [43] | Schreier, H; Sutton, M, Systematic errors in digital image correlation due to undermatched subset shape functions, Exp. Mech., 42, 303-310, (2002) · doi:10.1007/BF02410987 |
| [44] | Serra, J, The Boolean model and random sets, Comput. Graph. Image Process., 12, 99-126, (1980) · doi:10.1016/0146-664X(80)90006-4 |
| [45] | Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, London (1982) · Zbl 0565.92001 |
| [46] | Small, C.: Expansions and Asymptotics for Statistics. Monographs on Statistics and Applied Probability, vol. 115. CRC Press, Boca Raton (2010) · Zbl 1196.62002 · doi:10.1201/9781420011029 |
| [47] | Society for Experimental Mechanics: DIC challenge. https://sem.org/dic-challenge/ |
| [48] | Stoyan, D., Kendall, W., Mecke, J., Kendall, D.: Stochastic Geometry and Its Applications. Wiley, New York (1987) · Zbl 0622.60019 |
| [49] | Su, Y; Zhang, Q; Gao, Z, Statistical model for Speckle pattern optimization, Opt. Express, 25, 30259-30275, (2017) · doi:10.1364/OE.25.030259 |
| [50] | Sutton, M., Orteu, J.J., Schreier, H.: Image Correlation for Shape, Motion and Deformation Measurements. Springer, Berlin (2009) |
| [51] | Triconnet, K; Derrien, K; Hild, F; Baptiste, D, Parameter choice for optimized digital image correlation, Opt. Lasers Eng., 47, 728-737, (2009) · doi:10.1016/j.optlaseng.2008.10.015 |
| [52] | Yu, L; Pan, B, The errors in digital image correlation due to overmatched shape functions, Meas. Sci. Technol., 26, 045-202, (2015) · doi:10.1088/0957-0233/26/4/045202 |
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