Abstract

The two-dimensional in-plane displacement and strain calculation problem through digital image processing methods has been studied extensively in the past three decades. Out of the various algorithms developed, the Newton–Raphson partial differential correction method performs the best quality wise and is the most widely used in practical applications despite its higher computational cost. The work presented in this paper improves the original algorithm by including adaptive spatial regularization in the minimization process used to obtain the motion data. Results indicate improvements in the strain accuracy for both small and large strains. The improvements become even more significant when employing small displacement and strain window sizes, making the new method highly suitable for situations where the underlying strain data presents both slow and fast spatial variations or contains highly localized discontinuities.

© 2010 Optical Society of America

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  1. W. H. Peters and W. F. Ranson, “Digital imaging techniques in experimental stress-analysis,” Opt. Eng. 21, 427–431 (1982).
  2. M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vis. Comput. 1, 133–139 (1983).
    [CrossRef]
  3. C.-H. Teng, S.-H. Lai, Y.-S. Chen, and W.-H. Hsu, “Accurate optical flow computation under non-uniform brightness variations,” Comput. Vis. Image Underst. 97, 315–346(2005).
    [CrossRef]
  4. W. H. Peters, W. F. Ranson, M. A. Sutton, T. C. Chu, and J. Anderson, “Applications of digital correlation methods to rigid body mechanics,” Opt. Eng. 22, 738–742 (1983).
  5. T. C. Chu, W. F. Ranson, M. A. Sutton, and W. H. Peters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
    [CrossRef]
  6. H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters, “Digital image correlation using Newton-Raphson method of partial differential correction,” Exp. Mech. 29, 261–267(1989).
    [CrossRef]
  7. G. Vendroux and W. G. Knauss, “Submicron deformation field measurements: part 2. Improved digital image correlation,” Exp. Mech. 38, 86–92 (1998).
    [CrossRef]
  8. H. Lu and P. D. Cary, “Deformation measurements by digital image correlation: implementation of a second-order displacement gradient,” Exp. Mech. 40, 393–400 (2000).
    [CrossRef]
  9. 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]
  10. C. Cofaru, W. Philips, and W. Van Paepegem, “Evaluation of digital image correlation techniques using realistic ground truth speckle images,” Meas. Sci. Technol. 21, 055102(2010).
    [CrossRef]
  11. M. A. Sutton, J.-J. Orteu, and H. W. Schreier, Image Correlation for Shape, Motion and Deformation Measurements (Springer, 2009).
  12. B. Pan, K-M. Qian, H-M. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
    [CrossRef]
  13. M. Ye, R. M. Haralick, and L. G. Shapiro, “Estimating piecewise-smooth optical flow with global matching and graduated optimization,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1625–1630 (2003).
    [CrossRef]
  14. G. Le Besnerais and F. Champagnat, “B-spline image model for energy minimization-based optical flow estimation,” IEEE Trans. Image Process. 15, 3201–3206 (2006).
    [CrossRef]
  15. J.-D. Kim and J. Kim, “Effective nonlinear approach for optical flow estimation,” Signal Process. 81, 2249–2252 (2001).
    [CrossRef]
  16. M. J. Black and P. Anandan, “The robust estimation of multiple motions: parametric and piecewise-smooth flow fields,” Comput. Vis. Image Underst. 63, 75–104 (1996).
    [CrossRef]
  17. Y.-H. Kim, A. M. Martìnez, and A. C. Kak, “Robust motion estimation under varying illumination,” Image Vis. Comput. 23, 365–375 (2005).
    [CrossRef]
  18. J. Weickert and C. Schnorr, “Variational optic flow computation with a spatio-temporal smoothness constraint,” J. Math. Imaging Vision 14, 245–255 (2001).
    [CrossRef]
  19. A. Bruhn, J. Weickert, and C. Schnorr, “Lucas/Kanade meets Horn/Schunck: combining local and global optic flow methods,” Int. J. Comput. Vis. 61, 1 (2005).
    [CrossRef]
  20. J. F. Cárdenas-García and J. J. E. Verhaegh, “Catalogue of Moiré fringes for a bi-axially-loaded infinite plate with a hole,” Mech. Res. Commun. 26, 641–648 (1999).
    [CrossRef]
  21. B. Pan, A. Asundi, H.-M. Xie, and J. X. Gao, “Digital image correlation using iterative least squares and pointwise least squares for displacement field and strain field measurements,” Opt. Lasers Eng. 47, 865–874 (2009).
    [CrossRef]

2010 (1)

C. Cofaru, W. Philips, and W. Van Paepegem, “Evaluation of digital image correlation techniques using realistic ground truth speckle images,” Meas. Sci. Technol. 21, 055102(2010).
[CrossRef]

2009 (2)

B. Pan, K-M. Qian, H-M. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
[CrossRef]

B. Pan, A. Asundi, H.-M. Xie, and J. X. Gao, “Digital image correlation using iterative least squares and pointwise least squares for displacement field and strain field measurements,” Opt. Lasers Eng. 47, 865–874 (2009).
[CrossRef]

2006 (2)

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]

G. Le Besnerais and F. Champagnat, “B-spline image model for energy minimization-based optical flow estimation,” IEEE Trans. Image Process. 15, 3201–3206 (2006).
[CrossRef]

2005 (3)

Y.-H. Kim, A. M. Martìnez, and A. C. Kak, “Robust motion estimation under varying illumination,” Image Vis. Comput. 23, 365–375 (2005).
[CrossRef]

A. Bruhn, J. Weickert, and C. Schnorr, “Lucas/Kanade meets Horn/Schunck: combining local and global optic flow methods,” Int. J. Comput. Vis. 61, 1 (2005).
[CrossRef]

C.-H. Teng, S.-H. Lai, Y.-S. Chen, and W.-H. Hsu, “Accurate optical flow computation under non-uniform brightness variations,” Comput. Vis. Image Underst. 97, 315–346(2005).
[CrossRef]

2003 (1)

M. Ye, R. M. Haralick, and L. G. Shapiro, “Estimating piecewise-smooth optical flow with global matching and graduated optimization,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1625–1630 (2003).
[CrossRef]

2001 (2)

J.-D. Kim and J. Kim, “Effective nonlinear approach for optical flow estimation,” Signal Process. 81, 2249–2252 (2001).
[CrossRef]

J. Weickert and C. Schnorr, “Variational optic flow computation with a spatio-temporal smoothness constraint,” J. Math. Imaging Vision 14, 245–255 (2001).
[CrossRef]

2000 (1)

H. Lu and P. D. Cary, “Deformation measurements by digital image correlation: implementation of a second-order displacement gradient,” Exp. Mech. 40, 393–400 (2000).
[CrossRef]

1999 (1)

J. F. Cárdenas-García and J. J. E. Verhaegh, “Catalogue of Moiré fringes for a bi-axially-loaded infinite plate with a hole,” Mech. Res. Commun. 26, 641–648 (1999).
[CrossRef]

1998 (1)

G. Vendroux and W. G. Knauss, “Submicron deformation field measurements: part 2. Improved digital image correlation,” Exp. Mech. 38, 86–92 (1998).
[CrossRef]

1996 (1)

M. J. Black and P. Anandan, “The robust estimation of multiple motions: parametric and piecewise-smooth flow fields,” Comput. Vis. Image Underst. 63, 75–104 (1996).
[CrossRef]

1989 (1)

H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters, “Digital image correlation using Newton-Raphson method of partial differential correction,” Exp. Mech. 29, 261–267(1989).
[CrossRef]

1985 (1)

T. C. Chu, W. F. Ranson, M. A. Sutton, and W. H. Peters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

1983 (2)

W. H. Peters, W. F. Ranson, M. A. Sutton, T. C. Chu, and J. Anderson, “Applications of digital correlation methods to rigid body mechanics,” Opt. Eng. 22, 738–742 (1983).

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vis. Comput. 1, 133–139 (1983).
[CrossRef]

1982 (1)

W. H. Peters and W. F. Ranson, “Digital imaging techniques in experimental stress-analysis,” Opt. Eng. 21, 427–431 (1982).

Anandan, P.

M. J. Black and P. Anandan, “The robust estimation of multiple motions: parametric and piecewise-smooth flow fields,” Comput. Vis. Image Underst. 63, 75–104 (1996).
[CrossRef]

Anderson, J.

W. H. Peters, W. F. Ranson, M. A. Sutton, T. C. Chu, and J. Anderson, “Applications of digital correlation methods to rigid body mechanics,” Opt. Eng. 22, 738–742 (1983).

Asundi, A.

B. Pan, K-M. Qian, H-M. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
[CrossRef]

B. Pan, A. Asundi, H.-M. Xie, and J. X. Gao, “Digital image correlation using iterative least squares and pointwise least squares for displacement field and strain field measurements,” Opt. Lasers Eng. 47, 865–874 (2009).
[CrossRef]

Black, M. J.

M. J. Black and P. Anandan, “The robust estimation of multiple motions: parametric and piecewise-smooth flow fields,” Comput. Vis. Image Underst. 63, 75–104 (1996).
[CrossRef]

Bruck, H. A.

H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters, “Digital image correlation using Newton-Raphson method of partial differential correction,” Exp. Mech. 29, 261–267(1989).
[CrossRef]

Bruhn, A.

A. Bruhn, J. Weickert, and C. Schnorr, “Lucas/Kanade meets Horn/Schunck: combining local and global optic flow methods,” Int. J. Comput. Vis. 61, 1 (2005).
[CrossRef]

Cárdenas-García, J. F.

J. F. Cárdenas-García and J. J. E. Verhaegh, “Catalogue of Moiré fringes for a bi-axially-loaded infinite plate with a hole,” Mech. Res. Commun. 26, 641–648 (1999).
[CrossRef]

Cary, P. D.

H. Lu and P. D. Cary, “Deformation measurements by digital image correlation: implementation of a second-order displacement gradient,” Exp. Mech. 40, 393–400 (2000).
[CrossRef]

Champagnat, F.

G. Le Besnerais and F. Champagnat, “B-spline image model for energy minimization-based optical flow estimation,” IEEE Trans. Image Process. 15, 3201–3206 (2006).
[CrossRef]

Chen, Y.-S.

C.-H. Teng, S.-H. Lai, Y.-S. Chen, and W.-H. Hsu, “Accurate optical flow computation under non-uniform brightness variations,” Comput. Vis. Image Underst. 97, 315–346(2005).
[CrossRef]

Chu, T. C.

T. C. Chu, W. F. Ranson, M. A. Sutton, and W. H. Peters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

W. H. Peters, W. F. Ranson, M. A. Sutton, T. C. Chu, and J. Anderson, “Applications of digital correlation methods to rigid body mechanics,” Opt. Eng. 22, 738–742 (1983).

Cofaru, C.

C. Cofaru, W. Philips, and W. Van Paepegem, “Evaluation of digital image correlation techniques using realistic ground truth speckle images,” Meas. Sci. Technol. 21, 055102(2010).
[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]

Gao, J. X.

B. Pan, A. Asundi, H.-M. Xie, and J. X. Gao, “Digital image correlation using iterative least squares and pointwise least squares for displacement field and strain field measurements,” Opt. Lasers Eng. 47, 865–874 (2009).
[CrossRef]

Haralick, R. M.

M. Ye, R. M. Haralick, and L. G. Shapiro, “Estimating piecewise-smooth optical flow with global matching and graduated optimization,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1625–1630 (2003).
[CrossRef]

Hsu, W.-H.

C.-H. Teng, S.-H. Lai, Y.-S. Chen, and W.-H. Hsu, “Accurate optical flow computation under non-uniform brightness variations,” Comput. Vis. Image Underst. 97, 315–346(2005).
[CrossRef]

Kak, A. C.

Y.-H. Kim, A. M. Martìnez, and A. C. Kak, “Robust motion estimation under varying illumination,” Image Vis. Comput. 23, 365–375 (2005).
[CrossRef]

Kim, J.

J.-D. Kim and J. Kim, “Effective nonlinear approach for optical flow estimation,” Signal Process. 81, 2249–2252 (2001).
[CrossRef]

Kim, J.-D.

J.-D. Kim and J. Kim, “Effective nonlinear approach for optical flow estimation,” Signal Process. 81, 2249–2252 (2001).
[CrossRef]

Kim, Y.-H.

Y.-H. Kim, A. M. Martìnez, and A. C. Kak, “Robust motion estimation under varying illumination,” Image Vis. Comput. 23, 365–375 (2005).
[CrossRef]

Knauss, W. G.

G. Vendroux and W. G. Knauss, “Submicron deformation field measurements: part 2. Improved digital image correlation,” Exp. Mech. 38, 86–92 (1998).
[CrossRef]

Lai, S.-H.

C.-H. Teng, S.-H. Lai, Y.-S. Chen, and W.-H. Hsu, “Accurate optical flow computation under non-uniform brightness variations,” Comput. Vis. Image Underst. 97, 315–346(2005).
[CrossRef]

Le Besnerais, G.

G. Le Besnerais and F. Champagnat, “B-spline image model for energy minimization-based optical flow estimation,” IEEE Trans. Image Process. 15, 3201–3206 (2006).
[CrossRef]

Lu, H.

H. Lu and P. D. Cary, “Deformation measurements by digital image correlation: implementation of a second-order displacement gradient,” Exp. Mech. 40, 393–400 (2000).
[CrossRef]

Martìnez, A. M.

Y.-H. Kim, A. M. Martìnez, and A. C. Kak, “Robust motion estimation under varying illumination,” Image Vis. Comput. 23, 365–375 (2005).
[CrossRef]

McNeill, S. R.

H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters, “Digital image correlation using Newton-Raphson method of partial differential correction,” Exp. Mech. 29, 261–267(1989).
[CrossRef]

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vis. Comput. 1, 133–139 (1983).
[CrossRef]

Orteu, J.-J.

M. A. Sutton, J.-J. Orteu, and H. W. Schreier, Image Correlation for Shape, Motion and Deformation Measurements (Springer, 2009).

Pan, B.

B. Pan, A. Asundi, H.-M. Xie, and J. X. Gao, “Digital image correlation using iterative least squares and pointwise least squares for displacement field and strain field measurements,” Opt. Lasers Eng. 47, 865–874 (2009).
[CrossRef]

B. Pan, K-M. Qian, H-M. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
[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]

Peters, W. H.

H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters, “Digital image correlation using Newton-Raphson method of partial differential correction,” Exp. Mech. 29, 261–267(1989).
[CrossRef]

T. C. Chu, W. F. Ranson, M. A. Sutton, and W. H. Peters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vis. Comput. 1, 133–139 (1983).
[CrossRef]

W. H. Peters, W. F. Ranson, M. A. Sutton, T. C. Chu, and J. Anderson, “Applications of digital correlation methods to rigid body mechanics,” Opt. Eng. 22, 738–742 (1983).

W. H. Peters and W. F. Ranson, “Digital imaging techniques in experimental stress-analysis,” Opt. Eng. 21, 427–431 (1982).

Philips, W.

C. Cofaru, W. Philips, and W. Van Paepegem, “Evaluation of digital image correlation techniques using realistic ground truth speckle images,” Meas. Sci. Technol. 21, 055102(2010).
[CrossRef]

Qian, K-M.

B. Pan, K-M. Qian, H-M. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
[CrossRef]

Ranson, W. F.

T. C. Chu, W. F. Ranson, M. A. Sutton, and W. H. Peters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vis. Comput. 1, 133–139 (1983).
[CrossRef]

W. H. Peters, W. F. Ranson, M. A. Sutton, T. C. Chu, and J. Anderson, “Applications of digital correlation methods to rigid body mechanics,” Opt. Eng. 22, 738–742 (1983).

W. H. Peters and W. F. Ranson, “Digital imaging techniques in experimental stress-analysis,” Opt. Eng. 21, 427–431 (1982).

Schnorr, C.

A. Bruhn, J. Weickert, and C. Schnorr, “Lucas/Kanade meets Horn/Schunck: combining local and global optic flow methods,” Int. J. Comput. Vis. 61, 1 (2005).
[CrossRef]

J. Weickert and C. Schnorr, “Variational optic flow computation with a spatio-temporal smoothness constraint,” J. Math. Imaging Vision 14, 245–255 (2001).
[CrossRef]

Schreier, H. W.

M. A. Sutton, J.-J. Orteu, and H. W. Schreier, Image Correlation for Shape, Motion and Deformation Measurements (Springer, 2009).

Shapiro, L. G.

M. Ye, R. M. Haralick, and L. G. Shapiro, “Estimating piecewise-smooth optical flow with global matching and graduated optimization,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1625–1630 (2003).
[CrossRef]

Sutton, M. A.

H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters, “Digital image correlation using Newton-Raphson method of partial differential correction,” Exp. Mech. 29, 261–267(1989).
[CrossRef]

T. C. Chu, W. F. Ranson, M. A. Sutton, and W. H. Peters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vis. Comput. 1, 133–139 (1983).
[CrossRef]

W. H. Peters, W. F. Ranson, M. A. Sutton, T. C. Chu, and J. Anderson, “Applications of digital correlation methods to rigid body mechanics,” Opt. Eng. 22, 738–742 (1983).

M. A. Sutton, J.-J. Orteu, and H. W. Schreier, Image Correlation for Shape, Motion and Deformation Measurements (Springer, 2009).

Teng, C.-H.

C.-H. Teng, S.-H. Lai, Y.-S. Chen, and W.-H. Hsu, “Accurate optical flow computation under non-uniform brightness variations,” Comput. Vis. Image Underst. 97, 315–346(2005).
[CrossRef]

Van Paepegem, W.

C. Cofaru, W. Philips, and W. Van Paepegem, “Evaluation of digital image correlation techniques using realistic ground truth speckle images,” Meas. Sci. Technol. 21, 055102(2010).
[CrossRef]

Vendroux, G.

G. Vendroux and W. G. Knauss, “Submicron deformation field measurements: part 2. Improved digital image correlation,” Exp. Mech. 38, 86–92 (1998).
[CrossRef]

Verhaegh, J. J. E.

J. F. Cárdenas-García and J. J. E. Verhaegh, “Catalogue of Moiré fringes for a bi-axially-loaded infinite plate with a hole,” Mech. Res. Commun. 26, 641–648 (1999).
[CrossRef]

Weickert, J.

A. Bruhn, J. Weickert, and C. Schnorr, “Lucas/Kanade meets Horn/Schunck: combining local and global optic flow methods,” Int. J. Comput. Vis. 61, 1 (2005).
[CrossRef]

J. Weickert and C. Schnorr, “Variational optic flow computation with a spatio-temporal smoothness constraint,” J. Math. Imaging Vision 14, 245–255 (2001).
[CrossRef]

Wolters, W. J.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vis. Comput. 1, 133–139 (1983).
[CrossRef]

Xie, H.-M.

B. Pan, A. Asundi, H.-M. Xie, and J. X. Gao, “Digital image correlation using iterative least squares and pointwise least squares for displacement field and strain field measurements,” Opt. Lasers Eng. 47, 865–874 (2009).
[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]

Xie, H-M.

B. Pan, K-M. Qian, H-M. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
[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]

Ye, M.

M. Ye, R. M. Haralick, and L. G. Shapiro, “Estimating piecewise-smooth optical flow with global matching and graduated optimization,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1625–1630 (2003).
[CrossRef]

Comput. Vis. Image Underst. (2)

C.-H. Teng, S.-H. Lai, Y.-S. Chen, and W.-H. Hsu, “Accurate optical flow computation under non-uniform brightness variations,” Comput. Vis. Image Underst. 97, 315–346(2005).
[CrossRef]

M. J. Black and P. Anandan, “The robust estimation of multiple motions: parametric and piecewise-smooth flow fields,” Comput. Vis. Image Underst. 63, 75–104 (1996).
[CrossRef]

Exp. Mech. (4)

T. C. Chu, W. F. Ranson, M. A. Sutton, and W. H. Peters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

H. A. Bruck, S. R. McNeill, M. A. Sutton, and W. H. Peters, “Digital image correlation using Newton-Raphson method of partial differential correction,” Exp. Mech. 29, 261–267(1989).
[CrossRef]

G. Vendroux and W. G. Knauss, “Submicron deformation field measurements: part 2. Improved digital image correlation,” Exp. Mech. 38, 86–92 (1998).
[CrossRef]

H. Lu and P. D. Cary, “Deformation measurements by digital image correlation: implementation of a second-order displacement gradient,” Exp. Mech. 40, 393–400 (2000).
[CrossRef]

IEEE Trans. Image Process. (1)

G. Le Besnerais and F. Champagnat, “B-spline image model for energy minimization-based optical flow estimation,” IEEE Trans. Image Process. 15, 3201–3206 (2006).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

M. Ye, R. M. Haralick, and L. G. Shapiro, “Estimating piecewise-smooth optical flow with global matching and graduated optimization,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1625–1630 (2003).
[CrossRef]

Image Vis. Comput. (2)

Y.-H. Kim, A. M. Martìnez, and A. C. Kak, “Robust motion estimation under varying illumination,” Image Vis. Comput. 23, 365–375 (2005).
[CrossRef]

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vis. Comput. 1, 133–139 (1983).
[CrossRef]

Int. J. Comput. Vis. (1)

A. Bruhn, J. Weickert, and C. Schnorr, “Lucas/Kanade meets Horn/Schunck: combining local and global optic flow methods,” Int. J. Comput. Vis. 61, 1 (2005).
[CrossRef]

J. Math. Imaging Vision (1)

J. Weickert and C. Schnorr, “Variational optic flow computation with a spatio-temporal smoothness constraint,” J. Math. Imaging Vision 14, 245–255 (2001).
[CrossRef]

Meas. Sci. Technol. (3)

B. Pan, K-M. Qian, H-M. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
[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]

C. Cofaru, W. Philips, and W. Van Paepegem, “Evaluation of digital image correlation techniques using realistic ground truth speckle images,” Meas. Sci. Technol. 21, 055102(2010).
[CrossRef]

Mech. Res. Commun. (1)

J. F. Cárdenas-García and J. J. E. Verhaegh, “Catalogue of Moiré fringes for a bi-axially-loaded infinite plate with a hole,” Mech. Res. Commun. 26, 641–648 (1999).
[CrossRef]

Opt. Eng. (2)

W. H. Peters and W. F. Ranson, “Digital imaging techniques in experimental stress-analysis,” Opt. Eng. 21, 427–431 (1982).

W. H. Peters, W. F. Ranson, M. A. Sutton, T. C. Chu, and J. Anderson, “Applications of digital correlation methods to rigid body mechanics,” Opt. Eng. 22, 738–742 (1983).

Opt. Lasers Eng. (1)

B. Pan, A. Asundi, H.-M. Xie, and J. X. Gao, “Digital image correlation using iterative least squares and pointwise least squares for displacement field and strain field measurements,” Opt. Lasers Eng. 47, 865–874 (2009).
[CrossRef]

Signal Process. (1)

J.-D. Kim and J. Kim, “Effective nonlinear approach for optical flow estimation,” Signal Process. 81, 2249–2252 (2001).
[CrossRef]

Other (1)

M. A. Sutton, J.-J. Orteu, and H. W. Schreier, Image Correlation for Shape, Motion and Deformation Measurements (Springer, 2009).

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