Abstract

A backward linear digital image correlation algorithm was introduced to obtain subpixel image registration without noise-induced bias for an image set consisting of a noise-free reference image and a number of noisy current images. Furthermore, a correction procedure using additional reference images (generated by offsetting the original image to displacement increments of either half-pixels or even quarter-pixels) was proposed to reduce subpixel approximation bias in the analysis. Numerical results of six sets of synthetic images showed that the proposed algorithm was effective in improving the accuracy of subpixel image registration.

© 2011 Optical Society of America

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References

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  1. B. D. Lucas and T. Kanade, in Proceedings of the 7th International Joint Conference on Artificial Intelligence (IJCAI 1981), P.K.Hayes, ed. (1981), Vol. 2, pp. 674–679.
  2. J. L. Barron, D. J. Fleet, and S. S. Beauchemin, Int. J. Comput. Vis. 12, 43 (1994).
    [CrossRef]
  3. S. Baker and I. Matthews, Int. J. Comput. Vision 56, 221 (2004).
    [CrossRef]
  4. W. Tong, Strain 41, 167 (2005).
    [CrossRef]
  5. D. G. Bailey, A. Gilman, and R. Browne, in Proceedings/TENCON, IEEE Region 10 Annual International Conference (2005).
  6. Y. Q. Wang, M. A. Sutton, H. A. Bruck, and H. W. Schreier, Strain 45, 160 (2009).
    [CrossRef]
  7. W. Tong, H. Yao, and Y. Xuan, “An improved error evaluation in one-dimensional deformation measurements by linear digital image correlation,” Exp. Mech., doi:10.1007/s11340-010-9423-6, to be published.

2009 (1)

Y. Q. Wang, M. A. Sutton, H. A. Bruck, and H. W. Schreier, Strain 45, 160 (2009).
[CrossRef]

2005 (1)

W. Tong, Strain 41, 167 (2005).
[CrossRef]

2004 (1)

S. Baker and I. Matthews, Int. J. Comput. Vision 56, 221 (2004).
[CrossRef]

1994 (1)

J. L. Barron, D. J. Fleet, and S. S. Beauchemin, Int. J. Comput. Vis. 12, 43 (1994).
[CrossRef]

Bailey, D. G.

D. G. Bailey, A. Gilman, and R. Browne, in Proceedings/TENCON, IEEE Region 10 Annual International Conference (2005).

Baker, S.

S. Baker and I. Matthews, Int. J. Comput. Vision 56, 221 (2004).
[CrossRef]

Barron, J. L.

J. L. Barron, D. J. Fleet, and S. S. Beauchemin, Int. J. Comput. Vis. 12, 43 (1994).
[CrossRef]

Beauchemin, S. S.

J. L. Barron, D. J. Fleet, and S. S. Beauchemin, Int. J. Comput. Vis. 12, 43 (1994).
[CrossRef]

Browne, R.

D. G. Bailey, A. Gilman, and R. Browne, in Proceedings/TENCON, IEEE Region 10 Annual International Conference (2005).

Bruck, H. A.

Y. Q. Wang, M. A. Sutton, H. A. Bruck, and H. W. Schreier, Strain 45, 160 (2009).
[CrossRef]

Fleet, D. J.

J. L. Barron, D. J. Fleet, and S. S. Beauchemin, Int. J. Comput. Vis. 12, 43 (1994).
[CrossRef]

Gilman, A.

D. G. Bailey, A. Gilman, and R. Browne, in Proceedings/TENCON, IEEE Region 10 Annual International Conference (2005).

Kanade, T.

B. D. Lucas and T. Kanade, in Proceedings of the 7th International Joint Conference on Artificial Intelligence (IJCAI 1981), P.K.Hayes, ed. (1981), Vol. 2, pp. 674–679.

Lucas, B. D.

B. D. Lucas and T. Kanade, in Proceedings of the 7th International Joint Conference on Artificial Intelligence (IJCAI 1981), P.K.Hayes, ed. (1981), Vol. 2, pp. 674–679.

Matthews, I.

S. Baker and I. Matthews, Int. J. Comput. Vision 56, 221 (2004).
[CrossRef]

Schreier, H. W.

Y. Q. Wang, M. A. Sutton, H. A. Bruck, and H. W. Schreier, Strain 45, 160 (2009).
[CrossRef]

Sutton, M. A.

Y. Q. Wang, M. A. Sutton, H. A. Bruck, and H. W. Schreier, Strain 45, 160 (2009).
[CrossRef]

Tong, W.

W. Tong, Strain 41, 167 (2005).
[CrossRef]

W. Tong, H. Yao, and Y. Xuan, “An improved error evaluation in one-dimensional deformation measurements by linear digital image correlation,” Exp. Mech., doi:10.1007/s11340-010-9423-6, to be published.

Wang, Y. Q.

Y. Q. Wang, M. A. Sutton, H. A. Bruck, and H. W. Schreier, Strain 45, 160 (2009).
[CrossRef]

Xuan, Y.

W. Tong, H. Yao, and Y. Xuan, “An improved error evaluation in one-dimensional deformation measurements by linear digital image correlation,” Exp. Mech., doi:10.1007/s11340-010-9423-6, to be published.

Yao, H.

W. Tong, H. Yao, and Y. Xuan, “An improved error evaluation in one-dimensional deformation measurements by linear digital image correlation,” Exp. Mech., doi:10.1007/s11340-010-9423-6, to be published.

Int. J. Comput. Vis. (1)

J. L. Barron, D. J. Fleet, and S. S. Beauchemin, Int. J. Comput. Vis. 12, 43 (1994).
[CrossRef]

Int. J. Comput. Vision (1)

S. Baker and I. Matthews, Int. J. Comput. Vision 56, 221 (2004).
[CrossRef]

Strain (2)

W. Tong, Strain 41, 167 (2005).
[CrossRef]

Y. Q. Wang, M. A. Sutton, H. A. Bruck, and H. W. Schreier, Strain 45, 160 (2009).
[CrossRef]

Other (3)

W. Tong, H. Yao, and Y. Xuan, “An improved error evaluation in one-dimensional deformation measurements by linear digital image correlation,” Exp. Mech., doi:10.1007/s11340-010-9423-6, to be published.

B. D. Lucas and T. Kanade, in Proceedings of the 7th International Joint Conference on Artificial Intelligence (IJCAI 1981), P.K.Hayes, ed. (1981), Vol. 2, pp. 674–679.

D. G. Bailey, A. Gilman, and R. Browne, in Proceedings/TENCON, IEEE Region 10 Annual International Conference (2005).

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Figures (2)

Fig. 1
Fig. 1

Errors in displacement estimation obtained by forward linear digital image correlation analyses of selected synthetic image sets with a noise-free reference image.

Fig. 2
Fig. 2

Residual errors in displacement estimation obtained by backward linear digital image correlation anal yses of selected synthetic image sets using additional reference images offset (a) at ± 0.5 pixels and (b) at ± 0.25 , ± 0.5 , and ± 0.75 pixels from the original reference image.

Tables (1)

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Table 1 Summary of the Numerical Results

Equations (8)

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C F = i = 1 n [ g ( X i + u + Δ u ) G ( X i ) ] 2 = i = 1 n [ g i * G 0 i ] 2 ,
C FL = i = 1 n [ g ¯ 0 i + Δ g 0 i + ( g ¯ 1 i g ¯ 0 i + Δ g 1 i Δ g 0 i ) ( u + Δ u ) G ¯ 0 i ] 2 ,
Δ u = i = 1 n [ G ¯ 0 i g 0 i ( g 1 i g 0 i ) u ] ( g 1 i g 0 i ) i = 1 n ( g 1 i g 0 i ) 2 .
E FL ( Δ u ) E FL S ( Δ u ) + E FL N ( Δ u ) i = 1 n [ Δ g ¯ i ] S b i n ( b 0 2 + 2 σ 2 ) + ( 1 2 u ) 2 σ 2 b 0 2 + 2 σ 2 ,
Var FL ( Δ u ) [ Std FL ( Δ u ) ] 2 ( 1 2 u + 2 u 2 ) n σ 2 b 0 2 ( b 0 2 + 2 σ 2 ) 2 ,
C BL = i = 1 n [ g ¯ 0 i + Δ g 0 i G ¯ 0 i + ( G ¯ 0 i G ¯ 1 i ) ( u + Δ u ) ] 2 ,
u 1 = u + Δ u = i = 1 n [ G ¯ 0 i g 0 i ] ( G ¯ 0 i G ¯ 1 i ) i = 1 n ( G ¯ 0 i G ¯ 1 i ) 2 .
E BL ( Δ u ) E BL S ( Δ u ) i = 1 n [ Δ G ¯ i ] S B ¯ i n B 0 2 , V a r BL ( Δ u ) = [ S t d BL ( Δ u ) ] 2 1 n σ 2 B 0 2 ,

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