Abstract

Three new algorithms for 2D translation image registration to within a small fraction of a pixel that use nonlinear optimization and matrix-multiply discrete Fourier transforms are compared. These algorithms can achieve registration with an accuracy equivalent to that of the conventional fast Fourier transform upsampling approach in a small fraction of the computation time and with greatly reduced memory requirements. Their accuracy and computation time are compared for the purpose of evaluating a translation-invariant error metric.

© 2008 Optical Society of America

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References

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2007

2006

S. T. Thurman and J. R. Fienup, Proc. SPIE 6233, 62330S (2006).
[CrossRef]

2003

B. Zitová and J. Flusser, Image Vis. Comput. 21, 977 (2003).
[CrossRef]

1998

1997

P. Viola and W. M. Wells III, Int. J. Comput. Vis. 24, 137 (1997).
[CrossRef]

J. R. Fienup, Appl. Opt. 36, 8352 (1997).
[CrossRef]

1993

1992

L. G. Brown, ACM Comput. Surv. 24, 325 (1992).
[CrossRef]

1991

M. Irani and S. Peleg, CVGIP: Graph. Models Image Process. 53, 231 (1991).
[CrossRef]

1982

1978

ACM Comput. Surv.

L. G. Brown, ACM Comput. Surv. 24, 325 (1992).
[CrossRef]

Appl. Opt.

CVGIP: Graph. Models Image Process.

M. Irani and S. Peleg, CVGIP: Graph. Models Image Process. 53, 231 (1991).
[CrossRef]

Image Vis. Comput.

B. Zitová and J. Flusser, Image Vis. Comput. 21, 977 (2003).
[CrossRef]

Int. J. Comput. Vis.

P. Viola and W. M. Wells III, Int. J. Comput. Vis. 24, 137 (1997).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Proc. SPIE

S. T. Thurman and J. R. Fienup, Proc. SPIE 6233, 62330S (2006).
[CrossRef]

Other

M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, in Signal Recovery and Synthesis, 2007 OSA Technical Digest Series (Optical Society of America, 2007), SMC3.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77 (Cambridge U. Press, 1992).

H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley, 2004), p. 172.

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Figures (2)

Fig. 1
Fig. 1

(a) Invariant NRMSE estimation E ̂ versus E. (b) Error in estimated image shift Δ r versus upsampling factor κ for E = 0.25 . The dotted curve shows the noiseless maximum error, 1 ( 2 κ ) . For the optimization algorithm, Δ r = 0.0029   pixels (dashed curve).

Fig. 2
Fig. 2

Computation time with respect to (a) image size ( κ = 25 for DFT algorithms) and (b) upsampling factor for 512 × 512 images.

Equations (4)

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E 2 = min α , x 0 , y 0 x , y α g ( x x 0 , y y 0 ) f ( x , y ) 2 x , y f ( x , y ) 2 = 1 max x 0 , y 0 r f g ( x 0 , y 0 ) 2 x , y f ( x , y ) 2 x , y g ( x , y ) 2 ,
r f g ( x 0 , y 0 ) = x , y f ( x , y ) g * ( x x 0 , y y 0 ) = u , v F ( u , v ) G * ( u , v ) exp [ i 2 π ( u x 0 M + v y 0 N ) ] ;
F ( u , v ) = x , y f ( x , y ) M N exp [ i 2 π ( u x M + v y N ) ] ;
r f g ( x 0 , y 0 ) 2 x 0 = 2 Im { r f g ( x 0 , y 0 ) u , v 2 π u M F * ( u , v ) × G ( u , v ) exp [ i 2 π ( u x 0 M + v y 0 N ) ] } ,

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