Abstract

The interpolation algorithm plays an essential role in the digital image correlation (DIC) technique for shape, deformation, and motion measurements with subpixel accuracies. At the present, little effort has been made to improve the interpolation methods used in DIC. In this Letter, a family of recursive interpolation schemes based on B-spline representation and its inverse gradient weighting version is employed to enhance the accuracy of DIC analysis. Theories are introduced, and simulation results are presented to illustrate the effectiveness of the method as compared with the common bicubic interpolation.

© 2011 Optical Society of America

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References

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  1. W. Sharpe, Handbook of Experimental Solid Mechanics (Springer, 2008).
    [CrossRef]
  2. M. Sutton, J. Orteu, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements (Springer, 2009).
  3. B. Pan, H. Xie, and Z. Wang, Appl. Opt. 49, 5501 (2010).
    [CrossRef] [PubMed]
  4. W. Tong, Opt. Lett. 36, 763 (2011).
    [CrossRef] [PubMed]
  5. H. Hou and H. Andrews, IEEE Trans. Acoust. Speech Signal Process. 26, 508 (1978).
    [CrossRef]
  6. M. Unser, A. Aldroubi, and M. Eden, IEEE Trans. Pattern Anal. Mach. Intell. 13, 277 (1991).
    [CrossRef]
  7. M. Unser, IEEE Signal Proc. Mag. 16 (6), 22 (1999).
    [CrossRef]
  8. T. Blu, P. Thevenaz, and M. Unser, IEEE Trans. Image Process. 10, 1069 (2001).
    [CrossRef]
  9. A. Gotchev, K. Egiazarian, J. Vesma, and T. Saramaki, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Vol.  3 (IEEE, 2001), pp. 1865–1868.
  10. J. Hwang and H. Lee, IEEE Signal Process. Lett. 11, 359 (2004).
    [CrossRef]
  11. B. Pan, H. Xie, B. Xu, and F. Dai, Meas. Sci. Technol. 17, 1615 (2006).
    [CrossRef]

2011

2010

2009

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

2008

W. Sharpe, Handbook of Experimental Solid Mechanics (Springer, 2008).
[CrossRef]

2006

B. Pan, H. Xie, B. Xu, and F. Dai, Meas. Sci. Technol. 17, 1615 (2006).
[CrossRef]

2004

J. Hwang and H. Lee, IEEE Signal Process. Lett. 11, 359 (2004).
[CrossRef]

2001

T. Blu, P. Thevenaz, and M. Unser, IEEE Trans. Image Process. 10, 1069 (2001).
[CrossRef]

A. Gotchev, K. Egiazarian, J. Vesma, and T. Saramaki, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Vol.  3 (IEEE, 2001), pp. 1865–1868.

1999

M. Unser, IEEE Signal Proc. Mag. 16 (6), 22 (1999).
[CrossRef]

1991

M. Unser, A. Aldroubi, and M. Eden, IEEE Trans. Pattern Anal. Mach. Intell. 13, 277 (1991).
[CrossRef]

1978

H. Hou and H. Andrews, IEEE Trans. Acoust. Speech Signal Process. 26, 508 (1978).
[CrossRef]

Aldroubi, A.

M. Unser, A. Aldroubi, and M. Eden, IEEE Trans. Pattern Anal. Mach. Intell. 13, 277 (1991).
[CrossRef]

Andrews, H.

H. Hou and H. Andrews, IEEE Trans. Acoust. Speech Signal Process. 26, 508 (1978).
[CrossRef]

Blu, T.

T. Blu, P. Thevenaz, and M. Unser, IEEE Trans. Image Process. 10, 1069 (2001).
[CrossRef]

Dai, F.

B. Pan, H. Xie, B. Xu, and F. Dai, Meas. Sci. Technol. 17, 1615 (2006).
[CrossRef]

Eden, M.

M. Unser, A. Aldroubi, and M. Eden, IEEE Trans. Pattern Anal. Mach. Intell. 13, 277 (1991).
[CrossRef]

Egiazarian, K.

A. Gotchev, K. Egiazarian, J. Vesma, and T. Saramaki, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Vol.  3 (IEEE, 2001), pp. 1865–1868.

Gotchev, A.

A. Gotchev, K. Egiazarian, J. Vesma, and T. Saramaki, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Vol.  3 (IEEE, 2001), pp. 1865–1868.

Hou, H.

H. Hou and H. Andrews, IEEE Trans. Acoust. Speech Signal Process. 26, 508 (1978).
[CrossRef]

Hwang, J.

J. Hwang and H. Lee, IEEE Signal Process. Lett. 11, 359 (2004).
[CrossRef]

Lee, H.

J. Hwang and H. Lee, IEEE Signal Process. Lett. 11, 359 (2004).
[CrossRef]

Orteu, J.

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

Pan, B.

B. Pan, H. Xie, and Z. Wang, Appl. Opt. 49, 5501 (2010).
[CrossRef] [PubMed]

B. Pan, H. Xie, B. Xu, and F. Dai, Meas. Sci. Technol. 17, 1615 (2006).
[CrossRef]

Saramaki, T.

A. Gotchev, K. Egiazarian, J. Vesma, and T. Saramaki, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Vol.  3 (IEEE, 2001), pp. 1865–1868.

Schreier, H.

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

Sharpe, W.

W. Sharpe, Handbook of Experimental Solid Mechanics (Springer, 2008).
[CrossRef]

Sutton, M.

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

Thevenaz, P.

T. Blu, P. Thevenaz, and M. Unser, IEEE Trans. Image Process. 10, 1069 (2001).
[CrossRef]

Tong, W.

Unser, M.

T. Blu, P. Thevenaz, and M. Unser, IEEE Trans. Image Process. 10, 1069 (2001).
[CrossRef]

M. Unser, IEEE Signal Proc. Mag. 16 (6), 22 (1999).
[CrossRef]

M. Unser, A. Aldroubi, and M. Eden, IEEE Trans. Pattern Anal. Mach. Intell. 13, 277 (1991).
[CrossRef]

Vesma, J.

A. Gotchev, K. Egiazarian, J. Vesma, and T. Saramaki, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Vol.  3 (IEEE, 2001), pp. 1865–1868.

Wang, Z.

Xie, H.

B. Pan, H. Xie, and Z. Wang, Appl. Opt. 49, 5501 (2010).
[CrossRef] [PubMed]

B. Pan, H. Xie, B. Xu, and F. Dai, Meas. Sci. Technol. 17, 1615 (2006).
[CrossRef]

Xu, B.

B. Pan, H. Xie, B. Xu, and F. Dai, Meas. Sci. Technol. 17, 1615 (2006).
[CrossRef]

Appl. Opt.

IEEE Signal Proc. Mag.

M. Unser, IEEE Signal Proc. Mag. 16 (6), 22 (1999).
[CrossRef]

IEEE Signal Process. Lett.

J. Hwang and H. Lee, IEEE Signal Process. Lett. 11, 359 (2004).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process.

H. Hou and H. Andrews, IEEE Trans. Acoust. Speech Signal Process. 26, 508 (1978).
[CrossRef]

IEEE Trans. Image Process.

T. Blu, P. Thevenaz, and M. Unser, IEEE Trans. Image Process. 10, 1069 (2001).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

M. Unser, A. Aldroubi, and M. Eden, IEEE Trans. Pattern Anal. Mach. Intell. 13, 277 (1991).
[CrossRef]

Meas. Sci. Technol.

B. Pan, H. Xie, B. Xu, and F. Dai, Meas. Sci. Technol. 17, 1615 (2006).
[CrossRef]

Opt. Lett.

Other

W. Sharpe, Handbook of Experimental Solid Mechanics (Springer, 2008).
[CrossRef]

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

A. Gotchev, K. Egiazarian, J. Vesma, and T. Saramaki, in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Vol.  3 (IEEE, 2001), pp. 1865–1868.

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Figures (4)

Fig. 1
Fig. 1

Block diagram of B-spline interpolation.

Fig. 2
Fig. 2

RMSE of displacements obtained by using various interpolation algorithms.

Fig. 3
Fig. 3

Reference and deformed images.

Fig. 4
Fig. 4

RMSE of displacements obtained by using inverse gradient weighting version of the cubic B-spline.

Tables (1)

Tables Icon

Table 1 RMSE Yielded by Various Interpolation Algorithms for Displacements with Large Shear Strains

Equations (4)

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

21 z 1 4 1 ( 1 z 1 z ) ( 1 z 1 z 1 ) ,
β 3 ( x ) = { | x | 3 2 x 2 + | x | 14 + 13 21 , 0 | x | 1 | x | 3 6 + x 2 85 42 | x | + 29 11 , 1 | x | 2 0 , otherwise .
H l = 1 1 + a | f i f i 1 | H r = 1 1 + a | f i + 2 f i + 1 | D = H l ( 1 s ) + H r s ,
I r ( x , y ) = k = 1 n A k exp ( ( ( x x k ) 2 + ( y y k ) 2 ) / R 2 ) I t ( x , y ) = k = 1 n A k exp ( ( ( x x k u 0 u x x u y y ) 2 + ( y y k v 0 v x x v y y ) 2 ) / R 2 ) ,

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