Abstract

Digital Image Correlation (DIC) has been established as a flexible and effective technique to measure the displacements on specimen surface by matching the reference subsets in the undeformed image with the target subsets in the deformed image. With the existing DIC techniques, the user must rely on experience and intuition to manually define the size of the reference subset, which is found to be critical to the accuracy of measured displacements. In this paper, the problem of subset size selection in the DIC technique is investigated. Based on the Sum of Squared Differences (SSD) correlation criterion as well as the assumption that the gray intensity gradients of image noise are much lower than that of speckle image, a theoretical model of the displacement measurement accuracy of DIC is derived. The theoretical model indicates that the displacement measurement accuracy of DIC can be accurately predicted based on the variance of image noise and Sum of Square of Subset Intensity Gradients (SSSIG). The model further leads to a simple criterion for choosing a proper subset size for the DIC analysis. Numerical experiments have been performed to validate the proposed concepts, and the calculated results show good agreements with the theoretical predictions.

© 2008 Optical Society of America

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References

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  1. M. A. Sutton, S. R. McNeill, J. D. Helm, and Y. J. Chao, "Advances in two-dimensional and three-dimensional computer vision," in Topics in Applied Physics, 1st ed., P. K. Rastogi, ed., (Springer, Berlin: Springer, 2000) 323-372.
  2. W. Tong, "An evaluation of digital image correlation criteria for strain mapping applications," Strain. 41, 167-175 (2005).
    [CrossRef]
  3. H. W. Schreier and M. A. Sutton, "Systematic errors in digital image correlation due to undermatched subset shape functions," Exp. Mech. 42, 303-310 (2002).
    [CrossRef]
  4. H. W. Schreier, J. R. Braasch, and M. A. Sutton, "Systematic errors in digital image correlation caused by intensity interpolation," Opt. Eng. 39, 2915-2921 (2000).
    [CrossRef]
  5. B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, "Performance of sub-pixel registration algorithms in digital image correlation," Meas. Sci. Technol. 17, 1615-1621 (2006).
    [CrossRef]
  6. D. S. Zhang, M. Luo, and D. D. Arola, "Displacement/strain measurements using an optical microscope and digital image correlation," Opt. Eng. 45, 033605 (2006).
    [CrossRef]
  7. S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, "Lens distortion correction for digital image correlation by measuring rigid body displacement," Opt. Eng. 45, 023602 (2006).
    [CrossRef]
  8. http://www.correlatedsolutions.com.
  9. Z. Y. Wang, H. Q. Li, J. W. Tong, and J. T. Ruan, "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 (2007).
    [CrossRef]
  10. Y. F. Sun and H. J. Pang, "Study of optimal subset size in digital image correlation of speckle pattern images," Opt. Lasers Eng. 45, 967-974 (2007).
    [CrossRef]
  11. B. Pan, H. M. Xie, Z. Q. Guo, and T. Hua, "Full-field strain measurement using a two-dimensional Savitzky-Golay digital differentiator in digital image correlation," Opt. Eng. 46, 033601 (2007).
    [CrossRef]

2007

Z. Y. Wang, H. Q. Li, J. W. Tong, and J. T. Ruan, "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 (2007).
[CrossRef]

Y. F. Sun and H. J. Pang, "Study of optimal subset size in digital image correlation of speckle pattern images," Opt. Lasers Eng. 45, 967-974 (2007).
[CrossRef]

B. Pan, H. M. Xie, Z. Q. Guo, and T. Hua, "Full-field strain measurement using a two-dimensional Savitzky-Golay digital differentiator in digital image correlation," Opt. Eng. 46, 033601 (2007).
[CrossRef]

2006

B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, "Performance of sub-pixel registration algorithms in digital image correlation," Meas. Sci. Technol. 17, 1615-1621 (2006).
[CrossRef]

D. S. Zhang, M. Luo, and D. D. Arola, "Displacement/strain measurements using an optical microscope and digital image correlation," Opt. Eng. 45, 033605 (2006).
[CrossRef]

S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, "Lens distortion correction for digital image correlation by measuring rigid body displacement," Opt. Eng. 45, 023602 (2006).
[CrossRef]

2005

W. Tong, "An evaluation of digital image correlation criteria for strain mapping applications," Strain. 41, 167-175 (2005).
[CrossRef]

2002

H. W. Schreier and M. A. Sutton, "Systematic errors in digital image correlation due to undermatched subset shape functions," Exp. Mech. 42, 303-310 (2002).
[CrossRef]

2000

H. W. Schreier, J. R. Braasch, and M. A. Sutton, "Systematic errors in digital image correlation caused by intensity interpolation," Opt. Eng. 39, 2915-2921 (2000).
[CrossRef]

Arola, D. D.

D. S. Zhang, M. Luo, and D. D. Arola, "Displacement/strain measurements using an optical microscope and digital image correlation," Opt. Eng. 45, 033605 (2006).
[CrossRef]

Braasch, J. R.

H. W. Schreier, J. R. Braasch, and M. A. Sutton, "Systematic errors in digital image correlation caused by intensity interpolation," Opt. Eng. 39, 2915-2921 (2000).
[CrossRef]

Dai, F. L.

B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, "Performance of sub-pixel registration algorithms in digital image correlation," Meas. Sci. Technol. 17, 1615-1621 (2006).
[CrossRef]

Guo, Z. Q.

B. Pan, H. M. Xie, Z. Q. Guo, and T. Hua, "Full-field strain measurement using a two-dimensional Savitzky-Golay digital differentiator in digital image correlation," Opt. Eng. 46, 033601 (2007).
[CrossRef]

Hua, T.

B. Pan, H. M. Xie, Z. Q. Guo, and T. Hua, "Full-field strain measurement using a two-dimensional Savitzky-Golay digital differentiator in digital image correlation," Opt. Eng. 46, 033601 (2007).
[CrossRef]

Kikuta, H.

S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, "Lens distortion correction for digital image correlation by measuring rigid body displacement," Opt. Eng. 45, 023602 (2006).
[CrossRef]

Kitagawa, A.

S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, "Lens distortion correction for digital image correlation by measuring rigid body displacement," Opt. Eng. 45, 023602 (2006).
[CrossRef]

Kitamura, K.

S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, "Lens distortion correction for digital image correlation by measuring rigid body displacement," Opt. Eng. 45, 023602 (2006).
[CrossRef]

Li, H. Q.

Z. Y. Wang, H. Q. Li, J. W. Tong, and J. T. Ruan, "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 (2007).
[CrossRef]

Luo, M.

D. S. Zhang, M. Luo, and D. D. Arola, "Displacement/strain measurements using an optical microscope and digital image correlation," Opt. Eng. 45, 033605 (2006).
[CrossRef]

Pan, B.

B. Pan, H. M. Xie, Z. Q. Guo, and T. Hua, "Full-field strain measurement using a two-dimensional Savitzky-Golay digital differentiator in digital image correlation," Opt. Eng. 46, 033601 (2007).
[CrossRef]

B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, "Performance of sub-pixel registration algorithms in digital image correlation," Meas. Sci. Technol. 17, 1615-1621 (2006).
[CrossRef]

Pang, H. J.

Y. F. Sun and H. J. Pang, "Study of optimal subset size in digital image correlation of speckle pattern images," Opt. Lasers Eng. 45, 967-974 (2007).
[CrossRef]

Ruan, J. T.

Z. Y. Wang, H. Q. Li, J. W. Tong, and J. T. Ruan, "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 (2007).
[CrossRef]

Schreier, H. W.

H. W. Schreier and M. A. Sutton, "Systematic errors in digital image correlation due to undermatched subset shape functions," Exp. Mech. 42, 303-310 (2002).
[CrossRef]

H. W. Schreier, J. R. Braasch, and M. A. Sutton, "Systematic errors in digital image correlation caused by intensity interpolation," Opt. Eng. 39, 2915-2921 (2000).
[CrossRef]

Sun, Y. F.

Y. F. Sun and H. J. Pang, "Study of optimal subset size in digital image correlation of speckle pattern images," Opt. Lasers Eng. 45, 967-974 (2007).
[CrossRef]

Sutton, M. A.

H. W. Schreier and M. A. Sutton, "Systematic errors in digital image correlation due to undermatched subset shape functions," Exp. Mech. 42, 303-310 (2002).
[CrossRef]

H. W. Schreier, J. R. Braasch, and M. A. Sutton, "Systematic errors in digital image correlation caused by intensity interpolation," Opt. Eng. 39, 2915-2921 (2000).
[CrossRef]

Tong, J. W.

Z. Y. Wang, H. Q. Li, J. W. Tong, and J. T. Ruan, "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 (2007).
[CrossRef]

Tong, W.

W. Tong, "An evaluation of digital image correlation criteria for strain mapping applications," Strain. 41, 167-175 (2005).
[CrossRef]

Wang, Z. Y.

Z. Y. Wang, H. Q. Li, J. W. Tong, and J. T. Ruan, "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 (2007).
[CrossRef]

Xie, H. M.

B. Pan, H. M. Xie, Z. Q. Guo, and T. Hua, "Full-field strain measurement using a two-dimensional Savitzky-Golay digital differentiator in digital image correlation," Opt. Eng. 46, 033601 (2007).
[CrossRef]

B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, "Performance of sub-pixel registration algorithms in digital image correlation," Meas. Sci. Technol. 17, 1615-1621 (2006).
[CrossRef]

Xu, B. Q.

B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, "Performance of sub-pixel registration algorithms in digital image correlation," Meas. Sci. Technol. 17, 1615-1621 (2006).
[CrossRef]

Yoneyama, S.

S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, "Lens distortion correction for digital image correlation by measuring rigid body displacement," Opt. Eng. 45, 023602 (2006).
[CrossRef]

Zhang, D. S.

D. S. Zhang, M. Luo, and D. D. Arola, "Displacement/strain measurements using an optical microscope and digital image correlation," Opt. Eng. 45, 033605 (2006).
[CrossRef]

Exp. Mech.

H. W. Schreier and M. A. Sutton, "Systematic errors in digital image correlation due to undermatched subset shape functions," Exp. Mech. 42, 303-310 (2002).
[CrossRef]

Z. Y. Wang, H. Q. Li, J. W. Tong, and J. T. Ruan, "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 (2007).
[CrossRef]

Meas. Sci. Technol.

B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, "Performance of sub-pixel registration algorithms in digital image correlation," Meas. Sci. Technol. 17, 1615-1621 (2006).
[CrossRef]

Opt. Eng.

D. S. Zhang, M. Luo, and D. D. Arola, "Displacement/strain measurements using an optical microscope and digital image correlation," Opt. Eng. 45, 033605 (2006).
[CrossRef]

S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, "Lens distortion correction for digital image correlation by measuring rigid body displacement," Opt. Eng. 45, 023602 (2006).
[CrossRef]

H. W. Schreier, J. R. Braasch, and M. A. Sutton, "Systematic errors in digital image correlation caused by intensity interpolation," Opt. Eng. 39, 2915-2921 (2000).
[CrossRef]

B. Pan, H. M. Xie, Z. Q. Guo, and T. Hua, "Full-field strain measurement using a two-dimensional Savitzky-Golay digital differentiator in digital image correlation," Opt. Eng. 46, 033601 (2007).
[CrossRef]

Opt. Lasers Eng.

Y. F. Sun and H. J. Pang, "Study of optimal subset size in digital image correlation of speckle pattern images," Opt. Lasers Eng. 45, 967-974 (2007).
[CrossRef]

Strain.

W. Tong, "An evaluation of digital image correlation criteria for strain mapping applications," Strain. 41, 167-175 (2005).
[CrossRef]

Other

M. A. Sutton, S. R. McNeill, J. D. Helm, and Y. J. Chao, "Advances in two-dimensional and three-dimensional computer vision," in Topics in Applied Physics, 1st ed., P. K. Rastogi, ed., (Springer, Berlin: Springer, 2000) 323-372.

http://www.correlatedsolutions.com.

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Figures (9)

Fig. 1.
Fig. 1.

Schematic figure of reference and target (or deformed) subsets in DIC

Fig. 2.
Fig. 2.

Standard deviation for displacements as a function of SSSIG and the variance of image noise, assume that H=1.

Fig. 3.
Fig. 3.

Flowchart of the algorithm for optimal selection of subset size.

Fig. 4.
Fig. 4.

Three reference images used in the experimental validation

Fig. 5.
Fig. 5.

Standard deviation of u-displacement (left) and v-displacement (right) for the three sets of image pair vs. the subset size.

Fig. 6.
Fig. 6.

Standard deviation of the u-displacements and v-displacements vs. SSSIG for: (a) image pair A, (b)image pair B, and (c) image pair C; the data ranges have been truncated for comparison purpose.

Fig. 7.
Fig. 7.

Statistical distribution of deviation of u-displacement (left) and v-displacement (right) vs. SSSIG for image pair A.

Fig. 8.
Fig. 8.

Statistical distribution of deviation of u-displacement (left) and v-displacement (right) vs. SSSIG for image pair B.

Fig. 9.
Fig. 9.

Statistical distribution of deviation of u-displacement (left) and v-displacement (right) vs. SSSIG for image pair C.

Tables (2)

Tables Icon

Table 1. Calculated value of C g x , g y 2 for six different points of three speckle image with subset of 11×11 pixels

Tables Icon

Table 2. Calculated displacements with optimal subset size under a SSSIG threshold of 1×105

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

C ( Δ u , Δ v ) = x = M x = M y = M y = M [ f ( x , y ) g ( x , y ) ] 2
x = x + u = x + u 0 + Δ u , y = y + v = y + v 0 + Δ v
g ( x + u 0 + Δ u , y + v 0 + Δ v )
= g ( x + u 0 , y + v 0 ) + Δ u · g x ( x + u 0 , y + v 0 ) + Δ v · g y ( x + u 0 , y + v 0 )
C ( Δ u ) = 0 , C ( Δ v ) = 0
[ Δ u Δ v ] = [ ( g x ) 2 ( g x . g y ) ( g x . g y ) ( g y ) 2 ] 1 [ [ ( f g ) · g x ] [ ( f g ) · g y ] ]
Δ u = ( g y ) 2 [ ( f g ) · g x ] ( g x . g y ) [ ( f g ) · g y ] ( g x ) 2 ( g y ) 2 ( ( g x . g y ) ) 2
Δ v = ( g x ) 2 [ ( f g ) · g y ] ( g x . g y ) [ ( f g ) · g x ] ( g x ) 2 ( g y ) 2 ( ( g x . g y ) ) 2
f ( x , y ) = f ( x , y ) + η 1 ( x , y ) , g ( x , y ) = g ( x , y ) + η 2 ( x , y )
Δ u = ( g y ) 2 [ ( f g η ) · g x ] ( g x . g y ) [ ( f g η ) · g y ] ( g x ) 2 ( g y ) 2 ( ( g x . g y ) ) 2
Δ v = ( g x ) 2 [ ( f g η ) · g y ] ( g x . g y ) [ ( f g η ) · g x ] ( g x ) 2 ( g y ) 2 ( ( g x . g y ) ) 2
Δ u = ( g y ) 2 [ ( f g η ) · g x ] ( g x . g y ) [ ( f g η ) · g y ] ( g x ) 2 ( g y ) 2 ( ( g x . g y ) ) 2
Δ v = ( g x ) 2 [ ( f g η ) · g y ] ( g x . g y ) [ ( f g η ) · g x ] ( g x ) 2 ( g y ) 2 ( ( g x . g y ) ) 2
E ( Δ u ) = Δ u , E ( Δ v ) = Δ v
D ( Δ u ) = H ( g x ) 2 · D ( η )
D ( Δ v ) = H ( g y ) 2 · D ( η )
H = 1 + C g x , g y 2 ( 1 C g x , g y 2 ) 2
C g x , g y 2 = ( ( g x · g y ) ) 2 ( g x ) 2 ( g y ) 2
σ ( Δ u ) ( D ( η ) ( f x ) 2 ) 1 2
σ ( Δ v ) ( D ( η ) ( f y ) 2 ) 1 2
σ = 1 N 1 i = 1 N d i 2

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