Abstract

We propose what is to our knowledge a novel technique for filtering a two-dimensional multichannel color image based on its interpretation as a three-dimensional (3D) signal and the application of a 3D Fourier transform. The color image is considered to have the two usual spatial coordinates with the color distribution as the third dimension of the signal. This approach permits the 3D generalization of the usual phase-only filter and phase correlation, and color pattern recognition can be performed by means of a 3D correlation. We analyze two cases: whitening only along the color Fourier spectrum and whitening the whole 3D Fourier spectrum. We study the transformation induced in the color content of the image by the whitening of the color Fourier spectrum and how it affects the correlation distribution. In particular it is demonstrated that the whitening of the 3D Fourier spectrum improves the recognition performance of the correlation.

© 2003 Optical Society of America

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References

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  1. F. T. S. Yu, “Color image recognition by spectral-spatial matched filtering,” Opt. Eng. 23, 690–695 (1984).
    [CrossRef]
  2. M. S. Millán, J. Campos, C. Ferreira, M. J. Yzuel, “Matched filter and phase-only filter performance in colour image recognition,” Opt. Commun. 73, 277–284 (1989).
    [CrossRef]
  3. F. T. S. Yu, Z. Yang, K. Pan, “Polychromatic target identification with a color liquid crystal-TV based joint transform correlator,” Appl. Opt. 33, 2170–2172 (1994).
    [CrossRef] [PubMed]
  4. M.-L. Hsieh, K. Y. Hsu, H. Zhai, “Color image recognition by use of a joint transform correlator of three liquid-crystal televisions,” Appl. Opt. 41, 1500–1504 (2002).
    [CrossRef] [PubMed]
  5. L. P. Yaroslavsky, “The theory of optimal methods for localization of objects in pictures,” in E. Wolf, ed., Progress in Optics, XXXII (1993).
  6. M. Guillaume, Ph. Réfrégier, J. Campos, V. Lashin, “Detection theory approach to multichannel pattern location,” Opt. Lett. 22, 1887–1889 (1997).
    [CrossRef]
  7. M. S. Alam, C. N. Wai, “Color pattern recognition using fringe adjusted joint transform correlator,” Opt. Eng. 40, 2407–2413 (2001).
    [CrossRef]
  8. K. Yamaba, Y. Miyake, “Color character recognition method based on human perception,” Opt. Eng. 32, 33–40 (1993).
    [CrossRef]
  9. M. S. Millán, M. Corbalán, J. Romero, M. J. Yzuel, “Optical pattern recognition based on color vision models,” Opt. Lett. 20, 1722–1724 (1995).
    [CrossRef] [PubMed]
  10. M. Corbalán, M. S. Millán, M. J. Yzuel, “Color pattern recognition with CIELAB coordinates,” Opt. Eng. 41, 130–138 (2002).
    [CrossRef]
  11. I. Moreno, V. Kober, V. Lashin, J. Campos, L. P. Yaroslavsky, M. J. Yzuel, “Color pattern recognition with circular component whitening,” Opt. Lett. 21, 498–500 (1996).
    [CrossRef] [PubMed]
  12. V. Kober, V. Lashin, I. Moreno, J. Campos, L. P. Yaroslavsky, M. J. Yzuel, “Color component transformations for optical pattern recognition,” J. Opt. Soc. Am. A 14, 2656–2669 (1997).
    [CrossRef]
  13. E. Badiqué, N. Ohyama, T. Honda, J. Tsujiuchi, “Color image correlation for spatial/spectral recognition and increased selectivity,” Opt. Commun. 68, 91–96 (1988).
    [CrossRef]
  14. A. L. Thornton, S. J. Sangwine, “Colour object location using complex coding in the frequency domain,” in Proceedings of the IEE 5th International Conference on Image Processing and Its Applications (Heriot-Watt University, Edimburgh, UK, 1995), pp. 820–824.
    [CrossRef]
  15. A. McCabe, T. Caelli, G. West, A. Reeves, “Theory of spatiochromatic image encoding and feature extraction,” J. Opt. Soc. Am. A 17, 1744–1754 (2000).
    [CrossRef]
  16. S. J. Sangwine, “Fourier transforms of colour images using quaternion or hypercomplex numbers,” Electron. Lett. 32, 1979–1980 (1996).
    [CrossRef]
  17. S. J. Sangwine, “Colour image edge detector based on quaternion convolution,” Electron. Lett. 34, 969–971 (1998).
    [CrossRef]
  18. J. Nicolás, M. J. Yzuel, J. Campos, “Color pattern recognition by three-dimensional correlation,” Opt. Commun. 184, 335–343 (2000).
    [CrossRef]
  19. J. Nicolás, M. J. Yzuel, J. Campos, “Colour information as a third dimension in Fourier transform and correlation,” in Proceedings 15th ICPR Barcelona, Spain, A. Sanfeliu, J. J. Villanueva, M. Vanrell, R. Alquézar, J. Crowley, Y. Shirai, eds. (IEEE Computer Society, Los Alamitos, 2000) pp. 515–518.
  20. J. L. Horner, P. D. Gianino, “Phase-only matched filter,” Appl. Opt. 23, 812–816 (1984).
    [CrossRef]
  21. J. J. Pearson, D. C. Hines, S. Golosman, C. D. Kuglin, “Video-rate image correlation processor,” Proc. SPIE 119, 197–205 (1977).
    [CrossRef]
  22. O. K. Ersoy, M. Zeng, “Nonlinear matched filtering,” J. Opt. Soc. Am. A 6, 636–648 (1989).
    [CrossRef]
  23. Q. Chen, M. Defrise, F. Deconinck, “Symmetric phase-only matched filtering of Fourier-Mellin transforms for image registration and recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 1156–1168 (1994).
    [CrossRef]
  24. R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1992).

2002

2001

M. S. Alam, C. N. Wai, “Color pattern recognition using fringe adjusted joint transform correlator,” Opt. Eng. 40, 2407–2413 (2001).
[CrossRef]

2000

J. Nicolás, M. J. Yzuel, J. Campos, “Color pattern recognition by three-dimensional correlation,” Opt. Commun. 184, 335–343 (2000).
[CrossRef]

A. McCabe, T. Caelli, G. West, A. Reeves, “Theory of spatiochromatic image encoding and feature extraction,” J. Opt. Soc. Am. A 17, 1744–1754 (2000).
[CrossRef]

1998

S. J. Sangwine, “Colour image edge detector based on quaternion convolution,” Electron. Lett. 34, 969–971 (1998).
[CrossRef]

1997

1996

S. J. Sangwine, “Fourier transforms of colour images using quaternion or hypercomplex numbers,” Electron. Lett. 32, 1979–1980 (1996).
[CrossRef]

I. Moreno, V. Kober, V. Lashin, J. Campos, L. P. Yaroslavsky, M. J. Yzuel, “Color pattern recognition with circular component whitening,” Opt. Lett. 21, 498–500 (1996).
[CrossRef] [PubMed]

1995

1994

Q. Chen, M. Defrise, F. Deconinck, “Symmetric phase-only matched filtering of Fourier-Mellin transforms for image registration and recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 1156–1168 (1994).
[CrossRef]

F. T. S. Yu, Z. Yang, K. Pan, “Polychromatic target identification with a color liquid crystal-TV based joint transform correlator,” Appl. Opt. 33, 2170–2172 (1994).
[CrossRef] [PubMed]

1993

K. Yamaba, Y. Miyake, “Color character recognition method based on human perception,” Opt. Eng. 32, 33–40 (1993).
[CrossRef]

1989

M. S. Millán, J. Campos, C. Ferreira, M. J. Yzuel, “Matched filter and phase-only filter performance in colour image recognition,” Opt. Commun. 73, 277–284 (1989).
[CrossRef]

O. K. Ersoy, M. Zeng, “Nonlinear matched filtering,” J. Opt. Soc. Am. A 6, 636–648 (1989).
[CrossRef]

1988

E. Badiqué, N. Ohyama, T. Honda, J. Tsujiuchi, “Color image correlation for spatial/spectral recognition and increased selectivity,” Opt. Commun. 68, 91–96 (1988).
[CrossRef]

1984

F. T. S. Yu, “Color image recognition by spectral-spatial matched filtering,” Opt. Eng. 23, 690–695 (1984).
[CrossRef]

J. L. Horner, P. D. Gianino, “Phase-only matched filter,” Appl. Opt. 23, 812–816 (1984).
[CrossRef]

1977

J. J. Pearson, D. C. Hines, S. Golosman, C. D. Kuglin, “Video-rate image correlation processor,” Proc. SPIE 119, 197–205 (1977).
[CrossRef]

Alam, M. S.

M. S. Alam, C. N. Wai, “Color pattern recognition using fringe adjusted joint transform correlator,” Opt. Eng. 40, 2407–2413 (2001).
[CrossRef]

Badiqué, E.

E. Badiqué, N. Ohyama, T. Honda, J. Tsujiuchi, “Color image correlation for spatial/spectral recognition and increased selectivity,” Opt. Commun. 68, 91–96 (1988).
[CrossRef]

Caelli, T.

Campos, J.

J. Nicolás, M. J. Yzuel, J. Campos, “Color pattern recognition by three-dimensional correlation,” Opt. Commun. 184, 335–343 (2000).
[CrossRef]

V. Kober, V. Lashin, I. Moreno, J. Campos, L. P. Yaroslavsky, M. J. Yzuel, “Color component transformations for optical pattern recognition,” J. Opt. Soc. Am. A 14, 2656–2669 (1997).
[CrossRef]

M. Guillaume, Ph. Réfrégier, J. Campos, V. Lashin, “Detection theory approach to multichannel pattern location,” Opt. Lett. 22, 1887–1889 (1997).
[CrossRef]

I. Moreno, V. Kober, V. Lashin, J. Campos, L. P. Yaroslavsky, M. J. Yzuel, “Color pattern recognition with circular component whitening,” Opt. Lett. 21, 498–500 (1996).
[CrossRef] [PubMed]

M. S. Millán, J. Campos, C. Ferreira, M. J. Yzuel, “Matched filter and phase-only filter performance in colour image recognition,” Opt. Commun. 73, 277–284 (1989).
[CrossRef]

J. Nicolás, M. J. Yzuel, J. Campos, “Colour information as a third dimension in Fourier transform and correlation,” in Proceedings 15th ICPR Barcelona, Spain, A. Sanfeliu, J. J. Villanueva, M. Vanrell, R. Alquézar, J. Crowley, Y. Shirai, eds. (IEEE Computer Society, Los Alamitos, 2000) pp. 515–518.

Chen, Q.

Q. Chen, M. Defrise, F. Deconinck, “Symmetric phase-only matched filtering of Fourier-Mellin transforms for image registration and recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 1156–1168 (1994).
[CrossRef]

Corbalán, M.

M. Corbalán, M. S. Millán, M. J. Yzuel, “Color pattern recognition with CIELAB coordinates,” Opt. Eng. 41, 130–138 (2002).
[CrossRef]

M. S. Millán, M. Corbalán, J. Romero, M. J. Yzuel, “Optical pattern recognition based on color vision models,” Opt. Lett. 20, 1722–1724 (1995).
[CrossRef] [PubMed]

Deconinck, F.

Q. Chen, M. Defrise, F. Deconinck, “Symmetric phase-only matched filtering of Fourier-Mellin transforms for image registration and recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 1156–1168 (1994).
[CrossRef]

Defrise, M.

Q. Chen, M. Defrise, F. Deconinck, “Symmetric phase-only matched filtering of Fourier-Mellin transforms for image registration and recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 1156–1168 (1994).
[CrossRef]

Ersoy, O. K.

Ferreira, C.

M. S. Millán, J. Campos, C. Ferreira, M. J. Yzuel, “Matched filter and phase-only filter performance in colour image recognition,” Opt. Commun. 73, 277–284 (1989).
[CrossRef]

Gianino, P. D.

Golosman, S.

J. J. Pearson, D. C. Hines, S. Golosman, C. D. Kuglin, “Video-rate image correlation processor,” Proc. SPIE 119, 197–205 (1977).
[CrossRef]

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1992).

Guillaume, M.

Hines, D. C.

J. J. Pearson, D. C. Hines, S. Golosman, C. D. Kuglin, “Video-rate image correlation processor,” Proc. SPIE 119, 197–205 (1977).
[CrossRef]

Honda, T.

E. Badiqué, N. Ohyama, T. Honda, J. Tsujiuchi, “Color image correlation for spatial/spectral recognition and increased selectivity,” Opt. Commun. 68, 91–96 (1988).
[CrossRef]

Horner, J. L.

Hsieh, M.-L.

Hsu, K. Y.

Kober, V.

Kuglin, C. D.

J. J. Pearson, D. C. Hines, S. Golosman, C. D. Kuglin, “Video-rate image correlation processor,” Proc. SPIE 119, 197–205 (1977).
[CrossRef]

Lashin, V.

McCabe, A.

Millán, M. S.

M. Corbalán, M. S. Millán, M. J. Yzuel, “Color pattern recognition with CIELAB coordinates,” Opt. Eng. 41, 130–138 (2002).
[CrossRef]

M. S. Millán, M. Corbalán, J. Romero, M. J. Yzuel, “Optical pattern recognition based on color vision models,” Opt. Lett. 20, 1722–1724 (1995).
[CrossRef] [PubMed]

M. S. Millán, J. Campos, C. Ferreira, M. J. Yzuel, “Matched filter and phase-only filter performance in colour image recognition,” Opt. Commun. 73, 277–284 (1989).
[CrossRef]

Miyake, Y.

K. Yamaba, Y. Miyake, “Color character recognition method based on human perception,” Opt. Eng. 32, 33–40 (1993).
[CrossRef]

Moreno, I.

Nicolás, J.

J. Nicolás, M. J. Yzuel, J. Campos, “Color pattern recognition by three-dimensional correlation,” Opt. Commun. 184, 335–343 (2000).
[CrossRef]

J. Nicolás, M. J. Yzuel, J. Campos, “Colour information as a third dimension in Fourier transform and correlation,” in Proceedings 15th ICPR Barcelona, Spain, A. Sanfeliu, J. J. Villanueva, M. Vanrell, R. Alquézar, J. Crowley, Y. Shirai, eds. (IEEE Computer Society, Los Alamitos, 2000) pp. 515–518.

Ohyama, N.

E. Badiqué, N. Ohyama, T. Honda, J. Tsujiuchi, “Color image correlation for spatial/spectral recognition and increased selectivity,” Opt. Commun. 68, 91–96 (1988).
[CrossRef]

Pan, K.

Pearson, J. J.

J. J. Pearson, D. C. Hines, S. Golosman, C. D. Kuglin, “Video-rate image correlation processor,” Proc. SPIE 119, 197–205 (1977).
[CrossRef]

Reeves, A.

Réfrégier, Ph.

Romero, J.

Sangwine, S. J.

S. J. Sangwine, “Colour image edge detector based on quaternion convolution,” Electron. Lett. 34, 969–971 (1998).
[CrossRef]

S. J. Sangwine, “Fourier transforms of colour images using quaternion or hypercomplex numbers,” Electron. Lett. 32, 1979–1980 (1996).
[CrossRef]

A. L. Thornton, S. J. Sangwine, “Colour object location using complex coding in the frequency domain,” in Proceedings of the IEE 5th International Conference on Image Processing and Its Applications (Heriot-Watt University, Edimburgh, UK, 1995), pp. 820–824.
[CrossRef]

Thornton, A. L.

A. L. Thornton, S. J. Sangwine, “Colour object location using complex coding in the frequency domain,” in Proceedings of the IEE 5th International Conference on Image Processing and Its Applications (Heriot-Watt University, Edimburgh, UK, 1995), pp. 820–824.
[CrossRef]

Tsujiuchi, J.

E. Badiqué, N. Ohyama, T. Honda, J. Tsujiuchi, “Color image correlation for spatial/spectral recognition and increased selectivity,” Opt. Commun. 68, 91–96 (1988).
[CrossRef]

Wai, C. N.

M. S. Alam, C. N. Wai, “Color pattern recognition using fringe adjusted joint transform correlator,” Opt. Eng. 40, 2407–2413 (2001).
[CrossRef]

West, G.

Woods, R. E.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1992).

Yamaba, K.

K. Yamaba, Y. Miyake, “Color character recognition method based on human perception,” Opt. Eng. 32, 33–40 (1993).
[CrossRef]

Yang, Z.

Yaroslavsky, L. P.

Yu, F. T. S.

Yzuel, M. J.

M. Corbalán, M. S. Millán, M. J. Yzuel, “Color pattern recognition with CIELAB coordinates,” Opt. Eng. 41, 130–138 (2002).
[CrossRef]

J. Nicolás, M. J. Yzuel, J. Campos, “Color pattern recognition by three-dimensional correlation,” Opt. Commun. 184, 335–343 (2000).
[CrossRef]

V. Kober, V. Lashin, I. Moreno, J. Campos, L. P. Yaroslavsky, M. J. Yzuel, “Color component transformations for optical pattern recognition,” J. Opt. Soc. Am. A 14, 2656–2669 (1997).
[CrossRef]

I. Moreno, V. Kober, V. Lashin, J. Campos, L. P. Yaroslavsky, M. J. Yzuel, “Color pattern recognition with circular component whitening,” Opt. Lett. 21, 498–500 (1996).
[CrossRef] [PubMed]

M. S. Millán, M. Corbalán, J. Romero, M. J. Yzuel, “Optical pattern recognition based on color vision models,” Opt. Lett. 20, 1722–1724 (1995).
[CrossRef] [PubMed]

M. S. Millán, J. Campos, C. Ferreira, M. J. Yzuel, “Matched filter and phase-only filter performance in colour image recognition,” Opt. Commun. 73, 277–284 (1989).
[CrossRef]

J. Nicolás, M. J. Yzuel, J. Campos, “Colour information as a third dimension in Fourier transform and correlation,” in Proceedings 15th ICPR Barcelona, Spain, A. Sanfeliu, J. J. Villanueva, M. Vanrell, R. Alquézar, J. Crowley, Y. Shirai, eds. (IEEE Computer Society, Los Alamitos, 2000) pp. 515–518.

Zeng, M.

Zhai, H.

Appl. Opt.

Electron. Lett.

S. J. Sangwine, “Fourier transforms of colour images using quaternion or hypercomplex numbers,” Electron. Lett. 32, 1979–1980 (1996).
[CrossRef]

S. J. Sangwine, “Colour image edge detector based on quaternion convolution,” Electron. Lett. 34, 969–971 (1998).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

Q. Chen, M. Defrise, F. Deconinck, “Symmetric phase-only matched filtering of Fourier-Mellin transforms for image registration and recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 1156–1168 (1994).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

E. Badiqué, N. Ohyama, T. Honda, J. Tsujiuchi, “Color image correlation for spatial/spectral recognition and increased selectivity,” Opt. Commun. 68, 91–96 (1988).
[CrossRef]

J. Nicolás, M. J. Yzuel, J. Campos, “Color pattern recognition by three-dimensional correlation,” Opt. Commun. 184, 335–343 (2000).
[CrossRef]

M. S. Millán, J. Campos, C. Ferreira, M. J. Yzuel, “Matched filter and phase-only filter performance in colour image recognition,” Opt. Commun. 73, 277–284 (1989).
[CrossRef]

Opt. Eng.

M. S. Alam, C. N. Wai, “Color pattern recognition using fringe adjusted joint transform correlator,” Opt. Eng. 40, 2407–2413 (2001).
[CrossRef]

K. Yamaba, Y. Miyake, “Color character recognition method based on human perception,” Opt. Eng. 32, 33–40 (1993).
[CrossRef]

M. Corbalán, M. S. Millán, M. J. Yzuel, “Color pattern recognition with CIELAB coordinates,” Opt. Eng. 41, 130–138 (2002).
[CrossRef]

F. T. S. Yu, “Color image recognition by spectral-spatial matched filtering,” Opt. Eng. 23, 690–695 (1984).
[CrossRef]

Opt. Lett.

Proc. SPIE

J. J. Pearson, D. C. Hines, S. Golosman, C. D. Kuglin, “Video-rate image correlation processor,” Proc. SPIE 119, 197–205 (1977).
[CrossRef]

Other

A. L. Thornton, S. J. Sangwine, “Colour object location using complex coding in the frequency domain,” in Proceedings of the IEE 5th International Conference on Image Processing and Its Applications (Heriot-Watt University, Edimburgh, UK, 1995), pp. 820–824.
[CrossRef]

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1992).

L. P. Yaroslavsky, “The theory of optimal methods for localization of objects in pictures,” in E. Wolf, ed., Progress in Optics, XXXII (1993).

J. Nicolás, M. J. Yzuel, J. Campos, “Colour information as a third dimension in Fourier transform and correlation,” in Proceedings 15th ICPR Barcelona, Spain, A. Sanfeliu, J. J. Villanueva, M. Vanrell, R. Alquézar, J. Crowley, Y. Shirai, eds. (IEEE Computer Society, Los Alamitos, 2000) pp. 515–518.

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Figures (6)

Fig. 1
Fig. 1

(a) Color image, (b) image as a continuous 3D function, (c) 3D discrete function that describes the color image in (a).

Fig. 2
Fig. 2

Representation of the colors in a cone according to the values of F C(0) and F C(2) in Eqs. 5(a)5(d).

Fig. 3
Fig. 3

Representation of the colors in Fig. 2. Effect of the whitening of the color Fourier spectrum. A color represented by a point A is transformed onto a color A′ with the same hue, but with unit intensity and unit saturation.

Fig. 4
Fig. 4

(a) Input color image, (b) impulse response image after whitening along the color Fourier spectrum, (c) impulse response image after whitening of the 3D Fourier spectrum, (d, e, f) color autocorrelation of images (a, b, c).

Fig. 5
Fig. 5

3D autocorrelation. The results shown in rows (a), (b), and (c) correspond to the 3D autocorrelation functions of the images shown in Figs. 4(a), 4(b), and 5(c). In each row we represent the three channels (n = 0, 1, 2).

Fig. 6
Fig. 6

(a) Color input scene. A1 is the target to recognize. We represent only the n = 0 channel of the 3D correlation using (b) 3D classical matched filter, (c) POF along the color axis, (d) 3D POF, (e) whitening of the color Fourier spectrum of the scene and 3D POF, (f) whitening of the 3D Fourier spectrum of the scene and 3D POF (pure phase correlation).

Tables (1)

Tables Icon

Table 1 Discrimination Capability for the Different Correlation Methodsa

Equations (16)

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

F3Du, v, m=x=0Dx-1y=0Dy-1n=0N-1 fx, y, n×exp-i2πuxDx+vyDy+mnN,
FCx, y, m=n=0N-1 fx, y, nexp-i2π mnN.
FCx, y, 0=Rx, y+Gx, y+Bx, y, FCx, y, 1=FC*x, y, 2
=Rx, y+Gx, yexp-i 2π3+Bx, yexp+i 2π3,
FCx, y, 2=ηx, y+iξx, y=ρx, yexpiϕx, y,
η=ReFC2=R-G+B2,
ξ=ImFC2=32G-B,
ρ=|FC2|=R2+G2+B2-RG-RB-GB1/2,
tanϕ=ImFC2ReFC2=3G-B2R-G-B.
S1=1-3 MinR, G, BR+G+B.
S2=ρR+G+B=ρI=FC2FC0.
c3Dx, y, n=x=0Dx-1y=0Dy-1n=0N-1 sx, y, no*x-x, y-y, n-n,
c3Dx, y, n=FT3D-1S3Du, v, mO3D*u, v, m,
cCx, y, n=n=0N-1 sx, y, no*x, y, n-n,
cCx, y, n=FTC-1SCx, y, mOC*x, y, m,
DC=1-C1C22,

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