Abstract
Simple analytical error formulas were derived for one-dimensional deformation parameter estimation by an image correlation analysis with linear subpixel interpolation. A two-parameter deformation function was used in the analysis to account for both rigid-body translation and constant displacement gradient in an image subset. Errors in parameter estimation were found to explicitly relate to the image grayscale error consisting of subpixel approximation, image noise (including quantization error), and subset deformation mismatch at each point of the subset. A power-law dependence of the standard deviation of errors in deformation parameter estimation on the subset size was established when random image noise was dominant and it was confirmed by the numerical results of both nonlinear and linear image correlation analyses of synthetic image pairs. The power-law relationship can be used to guide the selection of suitable image quality, subpixel approximation, subset size, and subset deformation function for the desired measurement precision of deformation parameters.
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References
Lucas BD, Kanade T (1981) An iterative image registration technique with an application to stereo vision. Proceedings of Imaging understanding workshop, pp 121 –130
James MR, Morris WL, Cox BN (1990) A high accuracy automated strain-field mapper. Exp Mech 30:60–67
Franke EA, Wenzel DJ, Davison DL (1991) Measurement of microdisplacements by machine vision photogrammetry. Rev Sci Instrum 62(5):1270–1279
Sutton MA, Turner JL, Bruck HA, Chae T (1991) Full-field representation of discretelysampled surface deformation for displacement and strain analysis. Exp Mech 31:168–177
Choi S, Shah SP (1997) Measurement of deformation on concrete subjected to compression using image correlation. Exp Mech 37(3):307–313
Gonzalez J, Knauss WG (1998) Strain inhomogeneity and discontinuous crack growth in a particulate composite. J Mech Phys Solids 46(1):1981–1995
Tong W, Tao H, Jiang X, Zhang N, Marya M, Hector LG, Gayden XQ (2005) Deformation and fracture of miniature tensile bars with resistance spot-weld microstructures. Metall Mater Trans 36A:2651–2669
Meng LB, Jin GC, Yao XF, Yeh HY (2006) Full-field deformation measurement of fiber composite pressure vessel using 3D digital speckle correlation method. Polymer Testing 25:42–48
Smith BW, Li X, Tong W (1998) Error assessment for strain mapping by digital image correlation. Exp Tech 22(4):19–21
Schreier HW, Braasch JR, Sutton MA (2000) Systematic errors in digital image correlation caused by gray-value interpolation. Opt Eng 39(11):2915–2921
Li X, Tong W (1999) Evaluation of two plastic strain mapping methods. Proc. SEM Annual Conf. On Theoretical, Experimental and Computational Mech., p 23 –26 (Cincinnati, Ohio, USA)
Lu H, Cary PD (2000) Deformation measurements by digital image correlation: implementation of a second-order displacement gradient. Exp Mech 40(4):394–400
Shreier HW, Sutton MA (2002) Systematic errors in digital image correlation due to undermatched subset shape functions. Exp Mech 42(3):303–310
Sun YF, Pang HJ (2007) Study of optimal subset size in digital image correlation of speckle pattern images. Optics and Lasers in Eng 45(9):967–974
Wang ZY, Li HQ, Tong JW, Ruan JT (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
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(100):7037–7048
Tong W (2005) An evaluation of digital image correlation criteria for strain mapping applications. Strain 41:167–175
Sutton MA, Cheng M, Peters WH, Chao YJ, McNeill SR (1986) Application of an optimized digital image correlation method to planar deformation analysis. Image Vis Comput 4(3):143–150
Vendroux G, Knuass WG (1998) Submicron deformation field measurements: Part II. Improved digital image correlation. Exp Mech 38:86–91
Li X (2000) Spatial Characterization of Unstable Plastic Flows in Two Aluminum Alloys, Ph.D. Thesis (Department of Mechanical Engineering, Yale University, New Haven, CT)
Yao H (2007) Mechanical Testing of Bone and Bone-Like Materials Using Image Correlation Strain Measurement Technique, MS. Thesis (Department of Mechanical Engineering, SMU, Dallas, TX)
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
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Tong, W., Yao, H. & Xuan, Y. An Improved Error Evaluation in One-Dimensional Deformation Measurements by Linear Digital Image Correlation. Exp Mech 51, 1019–1031 (2011). https://doi.org/10.1007/s11340-010-9423-6
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DOI: https://doi.org/10.1007/s11340-010-9423-6