Abstract

High-throughput processing of parallel-beam X-ray tomography at synchrotron facilities is lacking a reliable and robust method to determine the center of rotation in an automated fashion, i.e. without the need for a human scorer. Well-known techniques based on center of mass calculation, image registration, or reconstruction evaluation work well under favourable conditions but they fail in cases where samples are larger than field of view, when the projections show low signal-to-noise, or when optical defects dominate the contrast. Here we propose an alternative technique which is based on the Fourier analysis of the sinogram. Our technique shows excellent performance particularly on challenging data.

© 2014 Optical Society of America

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References

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  1. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1988).
  2. B. Zitová and J. Flusser, “Image registration methods: a survey,” Image Vis. Comput. 21(11), 977–1000 (2003).
    [CrossRef]
  3. M. Yang, H. Gao, X. Li, F. Meng, and D. Wei, “A new method to determine the center of rotation shift in 2D-CT scanning system using image cross correlation,” NDT Int. 46, 48–54 (2012).
    [CrossRef]
  4. A. Brunetti and F. de Carlo, “A robust procedure for determination of center of rotation in tomography,” Proc. SPIE 5535, 652–659 (2004).
    [CrossRef]
  5. T. Donath, F. Beckmann, and A. Schreyer, “Automated determination of the center of rotation in tomography data,” J. Opt. Soc. Am. A 23(5), 1048–1057 (2006).
    [CrossRef] [PubMed]
  6. D. S. G. Azevedo, D. J. Schneberk, J. P. Fitch, and H. E. Martz, “Calculation of the rotational centers in computed tomography sinograms,” IEEE Trans. Nucl. Sci. 37(4), 1525–1540 (1990).
    [CrossRef]
  7. P. R. Edholm, R. M. Lewitt, and B. Lindholm, “Novel properties of the Fourier decomposition of the sinogram,” Proc. SPIE 671, 8–18 (1986).
    [CrossRef]
  8. K. Pearson, “Contributions to the mathematical theory of evolution, III, Regression, Heredity, and Panmixia,” Philos. Trans. R. Soc. Lond. Ser. A 187, 253–318 (1896).
    [CrossRef]
  9. C. Spearman, “The proof and measurement of association between two things,” Am. J. Psychol. 15(1), 72–101 (1904).
    [CrossRef] [PubMed]
  10. C. D. Kuglin and D. C. Hines, “The phase correlation image alignment method,” in IEEE 1975 Conference on Cybernetics and Society, New York (1975), pp. 163–165.
  11. V. Argyriou and T. Vlachos, “Estimation of sub-pixel motion using gradient cross-correlation,” Electron. Lett. 39(13), 980–982 (2003).
    [CrossRef]
  12. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
    [CrossRef]
  13. T. M. Lehmann, C. Gönner, and K. Spitzer, “Survey: Interpolation methods in medical image processing,” IEEE Trans. Med. Imaging 18(11), 1049–1075 (1999).
    [CrossRef] [PubMed]
  14. Wolfram Research, Inc., Mathematica, Version 9.0, Champaign, IL, 2013.
  15. R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice-Hall, 2002).

2012 (1)

M. Yang, H. Gao, X. Li, F. Meng, and D. Wei, “A new method to determine the center of rotation shift in 2D-CT scanning system using image cross correlation,” NDT Int. 46, 48–54 (2012).
[CrossRef]

2006 (1)

2004 (1)

A. Brunetti and F. de Carlo, “A robust procedure for determination of center of rotation in tomography,” Proc. SPIE 5535, 652–659 (2004).
[CrossRef]

2003 (2)

B. Zitová and J. Flusser, “Image registration methods: a survey,” Image Vis. Comput. 21(11), 977–1000 (2003).
[CrossRef]

V. Argyriou and T. Vlachos, “Estimation of sub-pixel motion using gradient cross-correlation,” Electron. Lett. 39(13), 980–982 (2003).
[CrossRef]

1999 (1)

T. M. Lehmann, C. Gönner, and K. Spitzer, “Survey: Interpolation methods in medical image processing,” IEEE Trans. Med. Imaging 18(11), 1049–1075 (1999).
[CrossRef] [PubMed]

1995 (1)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

1990 (1)

D. S. G. Azevedo, D. J. Schneberk, J. P. Fitch, and H. E. Martz, “Calculation of the rotational centers in computed tomography sinograms,” IEEE Trans. Nucl. Sci. 37(4), 1525–1540 (1990).
[CrossRef]

1986 (1)

P. R. Edholm, R. M. Lewitt, and B. Lindholm, “Novel properties of the Fourier decomposition of the sinogram,” Proc. SPIE 671, 8–18 (1986).
[CrossRef]

1904 (1)

C. Spearman, “The proof and measurement of association between two things,” Am. J. Psychol. 15(1), 72–101 (1904).
[CrossRef] [PubMed]

1896 (1)

K. Pearson, “Contributions to the mathematical theory of evolution, III, Regression, Heredity, and Panmixia,” Philos. Trans. R. Soc. Lond. Ser. A 187, 253–318 (1896).
[CrossRef]

Argyriou, V.

V. Argyriou and T. Vlachos, “Estimation of sub-pixel motion using gradient cross-correlation,” Electron. Lett. 39(13), 980–982 (2003).
[CrossRef]

Azevedo, D. S. G.

D. S. G. Azevedo, D. J. Schneberk, J. P. Fitch, and H. E. Martz, “Calculation of the rotational centers in computed tomography sinograms,” IEEE Trans. Nucl. Sci. 37(4), 1525–1540 (1990).
[CrossRef]

Beckmann, F.

Brunetti, A.

A. Brunetti and F. de Carlo, “A robust procedure for determination of center of rotation in tomography,” Proc. SPIE 5535, 652–659 (2004).
[CrossRef]

de Carlo, F.

A. Brunetti and F. de Carlo, “A robust procedure for determination of center of rotation in tomography,” Proc. SPIE 5535, 652–659 (2004).
[CrossRef]

Donath, T.

Edholm, P. R.

P. R. Edholm, R. M. Lewitt, and B. Lindholm, “Novel properties of the Fourier decomposition of the sinogram,” Proc. SPIE 671, 8–18 (1986).
[CrossRef]

Fitch, J. P.

D. S. G. Azevedo, D. J. Schneberk, J. P. Fitch, and H. E. Martz, “Calculation of the rotational centers in computed tomography sinograms,” IEEE Trans. Nucl. Sci. 37(4), 1525–1540 (1990).
[CrossRef]

Flusser, J.

B. Zitová and J. Flusser, “Image registration methods: a survey,” Image Vis. Comput. 21(11), 977–1000 (2003).
[CrossRef]

Gao, H.

M. Yang, H. Gao, X. Li, F. Meng, and D. Wei, “A new method to determine the center of rotation shift in 2D-CT scanning system using image cross correlation,” NDT Int. 46, 48–54 (2012).
[CrossRef]

Gönner, C.

T. M. Lehmann, C. Gönner, and K. Spitzer, “Survey: Interpolation methods in medical image processing,” IEEE Trans. Med. Imaging 18(11), 1049–1075 (1999).
[CrossRef] [PubMed]

Kohn, V.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

Kuznetsov, S.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

Lehmann, T. M.

T. M. Lehmann, C. Gönner, and K. Spitzer, “Survey: Interpolation methods in medical image processing,” IEEE Trans. Med. Imaging 18(11), 1049–1075 (1999).
[CrossRef] [PubMed]

Lewitt, R. M.

P. R. Edholm, R. M. Lewitt, and B. Lindholm, “Novel properties of the Fourier decomposition of the sinogram,” Proc. SPIE 671, 8–18 (1986).
[CrossRef]

Li, X.

M. Yang, H. Gao, X. Li, F. Meng, and D. Wei, “A new method to determine the center of rotation shift in 2D-CT scanning system using image cross correlation,” NDT Int. 46, 48–54 (2012).
[CrossRef]

Lindholm, B.

P. R. Edholm, R. M. Lewitt, and B. Lindholm, “Novel properties of the Fourier decomposition of the sinogram,” Proc. SPIE 671, 8–18 (1986).
[CrossRef]

Martz, H. E.

D. S. G. Azevedo, D. J. Schneberk, J. P. Fitch, and H. E. Martz, “Calculation of the rotational centers in computed tomography sinograms,” IEEE Trans. Nucl. Sci. 37(4), 1525–1540 (1990).
[CrossRef]

Meng, F.

M. Yang, H. Gao, X. Li, F. Meng, and D. Wei, “A new method to determine the center of rotation shift in 2D-CT scanning system using image cross correlation,” NDT Int. 46, 48–54 (2012).
[CrossRef]

Pearson, K.

K. Pearson, “Contributions to the mathematical theory of evolution, III, Regression, Heredity, and Panmixia,” Philos. Trans. R. Soc. Lond. Ser. A 187, 253–318 (1896).
[CrossRef]

Schelokov, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

Schneberk, D. J.

D. S. G. Azevedo, D. J. Schneberk, J. P. Fitch, and H. E. Martz, “Calculation of the rotational centers in computed tomography sinograms,” IEEE Trans. Nucl. Sci. 37(4), 1525–1540 (1990).
[CrossRef]

Schreyer, A.

Snigirev, A.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

Snigireva, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

Spearman, C.

C. Spearman, “The proof and measurement of association between two things,” Am. J. Psychol. 15(1), 72–101 (1904).
[CrossRef] [PubMed]

Spitzer, K.

T. M. Lehmann, C. Gönner, and K. Spitzer, “Survey: Interpolation methods in medical image processing,” IEEE Trans. Med. Imaging 18(11), 1049–1075 (1999).
[CrossRef] [PubMed]

Vlachos, T.

V. Argyriou and T. Vlachos, “Estimation of sub-pixel motion using gradient cross-correlation,” Electron. Lett. 39(13), 980–982 (2003).
[CrossRef]

Wei, D.

M. Yang, H. Gao, X. Li, F. Meng, and D. Wei, “A new method to determine the center of rotation shift in 2D-CT scanning system using image cross correlation,” NDT Int. 46, 48–54 (2012).
[CrossRef]

Yang, M.

M. Yang, H. Gao, X. Li, F. Meng, and D. Wei, “A new method to determine the center of rotation shift in 2D-CT scanning system using image cross correlation,” NDT Int. 46, 48–54 (2012).
[CrossRef]

Zitová, B.

B. Zitová and J. Flusser, “Image registration methods: a survey,” Image Vis. Comput. 21(11), 977–1000 (2003).
[CrossRef]

Am. J. Psychol. (1)

C. Spearman, “The proof and measurement of association between two things,” Am. J. Psychol. 15(1), 72–101 (1904).
[CrossRef] [PubMed]

Electron. Lett. (1)

V. Argyriou and T. Vlachos, “Estimation of sub-pixel motion using gradient cross-correlation,” Electron. Lett. 39(13), 980–982 (2003).
[CrossRef]

IEEE Trans. Med. Imaging (1)

T. M. Lehmann, C. Gönner, and K. Spitzer, “Survey: Interpolation methods in medical image processing,” IEEE Trans. Med. Imaging 18(11), 1049–1075 (1999).
[CrossRef] [PubMed]

IEEE Trans. Nucl. Sci. (1)

D. S. G. Azevedo, D. J. Schneberk, J. P. Fitch, and H. E. Martz, “Calculation of the rotational centers in computed tomography sinograms,” IEEE Trans. Nucl. Sci. 37(4), 1525–1540 (1990).
[CrossRef]

Image Vis. Comput. (1)

B. Zitová and J. Flusser, “Image registration methods: a survey,” Image Vis. Comput. 21(11), 977–1000 (2003).
[CrossRef]

J. Opt. Soc. Am. A (1)

NDT Int. (1)

M. Yang, H. Gao, X. Li, F. Meng, and D. Wei, “A new method to determine the center of rotation shift in 2D-CT scanning system using image cross correlation,” NDT Int. 46, 48–54 (2012).
[CrossRef]

Philos. Trans. R. Soc. Lond. Ser. A (1)

K. Pearson, “Contributions to the mathematical theory of evolution, III, Regression, Heredity, and Panmixia,” Philos. Trans. R. Soc. Lond. Ser. A 187, 253–318 (1896).
[CrossRef]

Proc. SPIE (2)

A. Brunetti and F. de Carlo, “A robust procedure for determination of center of rotation in tomography,” Proc. SPIE 5535, 652–659 (2004).
[CrossRef]

P. R. Edholm, R. M. Lewitt, and B. Lindholm, “Novel properties of the Fourier decomposition of the sinogram,” Proc. SPIE 671, 8–18 (1986).
[CrossRef]

Rev. Sci. Instrum. (1)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

Other (4)

Wolfram Research, Inc., Mathematica, Version 9.0, Champaign, IL, 2013.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice-Hall, 2002).

C. D. Kuglin and D. C. Hines, “The phase correlation image alignment method,” in IEEE 1975 Conference on Cybernetics and Society, New York (1975), pp. 163–165.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1988).

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Figures (10)

Fig. 1
Fig. 1

Schematics of parallel-beam X-ray tomography.

Fig. 2
Fig. 2

Reconstruction artifacts with a mispositioned CoR. (a) Correct position. (b) displaced 1 pixel to the left. (c) displaced 1 pixel to the right.

Fig. 3
Fig. 3

Fixed artifacts in the detection system in X-ray projections: (a) Taken at 0°; (b) Taken at 180°.

Fig. 4
Fig. 4

(a) Modification of Shepp-Logan phantom [1]. Its estimated [0; 2π] sinogram and its Fourier transform in three cases: (b) and (e) Correct alignment; (c) and (f) 5 pixels misalignment; (d) and (g) 10 pixels misalignment.

Fig. 5
Fig. 5

Recorded x-ray 2D-projections of a sample made from polymer spheres: (a) At 0° ; (b) At 180°. (c) The corresponding sinogram at the height indicated by white lines.

Fig. 6
Fig. 6

Results from CoR calculation for different techniques: (a) Image registration methods; (b) Reconstruction based methods; (c) Our sinogram Fourier metric method. Dashed lines indicate the CoR as determined by a human scorer.

Fig. 7
Fig. 7

(a) 2D projection of Magnesium Phosphate cement sample, flat-field corrected, exhibiting low contrast. (b) Sinogram at the middle of the projection showing intense vertical streaks from detector defects. (c) Part of a reconstructed slice used for visual inspection at the correct CoR.

Fig. 8
Fig. 8

Results of CoR calculation from different techniques: (a) Image registration methods; (b) Reconstruction based methods; (c) Proposed sinogram Fourier metric method. Dashed lines indicate the CoR as determined by the human scorer.

Fig. 9
Fig. 9

(a) Estimated full revolution sinogram. (b) 2D projection indicating the position for the sinogram (white line). (c) Magnification of the sinogram inside white box at nearest whole number alignment above the correct fractional location of CoR. (d) As in (c) but below the correct fractional location of the CoR. (e) as (c) but at correct fractional position of the CoR.

Fig. 10
Fig. 10

Sinogram Fourier metrics, QsF, for alignment of sinogram-halves in fractional pixel units: (a) Using cubic interpolation; (b) Using linear interpolation.

Equations (13)

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

P( t,θ )= f( x,y )δ( xcosθ+ysinθt )dxdy .
P ^ ( u,ν )= 0 2π P( t,θ )exp[ i( ut+νθ ) ]dt dθ
| ν || u |r
Q SF = | P ^ ( u,ν ) |M( u,ν )dudν M( u,ν )dudν
M( u,ν )={ 0: | ν || u |r 1: else .
CoR=HCoI+ s 0 2 .
Q P =1 i,j ( P ij P ¯ )( P ij s P ¯ s ) i,j ( P ij P ¯ ) 2 i,j ( P ij s P ¯ s ) 2
Q S = k=1 K [ R( P k )R( P k s ) ] 2 K( K 2 1 )/6
P pc = F 1 [ F[ P ]×F [ P s ] | F[ P ]×F [ P s ] | ]
P i,j =( P j+1,i P j1,i )+i( P j,i+1 P j,i1 )
Q SA = i,j N | f( x i , y j ) | θ m M i N P( t i , θ m ) /M ,
Q SN = i,j N f( x i , y j )w[ f( x i , y j ) ] θ m M i N P( t i , θ m ) /M
w( α )={ 1:α<0 0:α0 .

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