Abstract

Recently, the use of three-dimensional correlation for multichannel pattern recognition has been introduced. In this work we propose the use of circular harmonic components with this new technique to obtain invariance under target rotations. The differences between this method and the previous use of circular harmonic filters for multichannel images are discussed. Also the problem of determining the proper center is studied and, to our knowledge, a new and more understandable criterion to locate it is introduced. Some simulation results to verify the successful operation of the method are included.

© 2003 Optical Society of America

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  1. F. T. S. Yu, T. H. Chao, “Color signal correlation detected by matched spatial filtering,” Appl. Phys. B 32, 1–6 (1983).
    [CrossRef]
  2. F. T. S. Yu, B. Javidi, “Experiments on real-time polychromatic signal detection by matched spatial filtering,” Opt. Commun. 56, 384–388 (1986).
    [CrossRef]
  3. M. S. Millan, J. Campos, C. Ferreira, M. Yzuel, “Matched filter and phase only filter performance in color image recognition,” Opt. Commun. 73, 277–284 (1989).
    [CrossRef]
  4. 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]
  5. C. Ferreira, M. S. Millan, M. J. Yzuel, J. Campos, “Experimental results in color pattern recognition by multichannel matched filter,” Opt. Eng. 31, 2231–2238 (1992).
    [CrossRef]
  6. J. García, J. Campos, C. Ferreira, “Multichannel colour pattern recognition using a minimum average correlation energy filter,” Pure Appl. Opt. 3, 221–224 (1994).
    [CrossRef]
  7. M. S. Millan, M. J. Yzuel, J. Campos, C. Ferreira, “Different strategies in optical recognition of polychromatic images,” Appl. Opt. 31, 2560–2567 (1992).
    [CrossRef] [PubMed]
  8. J. García, C. Ferreira, J. Campos, S. Bosch, M. S. Millán, M. J. Yzuel, “Multichannel rotation invariant pattern recognition for polychromatic objects using circular harmonic filters,” Opt. Commun. 91, 425–432 (1992).
    [CrossRef]
  9. J. García, J. Campos, C. Ferreira, “Circular-harmonic minimum average correlation energy filter for color pattern recognition,” Appl. Opt. 33, 2180–2187 (1994).
    [CrossRef] [PubMed]
  10. J. Nicolás, M. J. Yzuel, J. Campos, “Colour pattern recognition by three-dimensional correlation,” Opt. Commun. 184, 335–343 (2000).
    [CrossRef]
  11. Y. Yang, Y.-N. Hsu, H. H. Arsenault, “Optimum circular symmetrical filters and their uses in optical pattern recognition,” Opt. Acta 29, 627–644 (1982).
    [CrossRef]
  12. Y.-N. Hsu, H. H. Arsenault, “Optical pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4016–4019 (1982).
    [CrossRef] [PubMed]
  13. L. Leclerc, Y. Sheng, H. H. Arsenault, “Rotation invariant phase-only and binary phase-only correlation,” Appl. Opt. 28, 1251–1256 (1982).
    [CrossRef]
  14. J. Rosen, J. Shamir, “Circular harmonic phase-only filters for efficient rotation-invariant pattern recognition,” Appl. Opt. 27, 2895–2899 (1988).
    [CrossRef] [PubMed]
  15. L. Leclerc, Y. Sheng, H. H. Arsenault, “Circular harmonic covariance filters for rotation invariant object recognition and discrimination,” Opt. Commun. 85, 299–305 (1991).
    [CrossRef]
  16. O. Gualdrón, H. H. Arsenault, “Phase-derived circular harmonic filter,” Opt. Commun. 104, 32–34 (1993).
    [CrossRef]
  17. O. Gualdrón, H. H. Arsenault, “Improved invariant pattern recognition methods,” in Real Time Optical Information Processing. B. Javidi, J. Horner, eds., Academic, San Diego, Calif., 1994, pp. 89–113.
  18. O. Gualdrón, H. H. Arsenault, “Optimum rotation-invariant filter for disjoint-noise scenes,” Appl. Opt. 35, 2507–2513 (1996).
    [CrossRef] [PubMed]
  19. Y. Sheng, H. H. Arsenault, “Method for determining expansion centers and predicting sidelobe levels for circular harmonic filters,” J. Opt. Soc. Am. A 4, 1793–1797 (1987).
    [CrossRef]
  20. G. Premont, Y. Sheng, “Fast design of circular harmonic filters using simulated annealing,” Appl. Opt. 32, 3116–3121 (1993).
    [CrossRef]
  21. P. García-Martínez, J. García, C. Ferreira, “A new criterion for determining the expansion center for circular-harmonic filters,” Opt. Commun. 117, 399–405 (1995).
    [CrossRef]

2000

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

1996

1995

P. García-Martínez, J. García, C. Ferreira, “A new criterion for determining the expansion center for circular-harmonic filters,” Opt. Commun. 117, 399–405 (1995).
[CrossRef]

1994

1993

O. Gualdrón, H. H. Arsenault, “Phase-derived circular harmonic filter,” Opt. Commun. 104, 32–34 (1993).
[CrossRef]

G. Premont, Y. Sheng, “Fast design of circular harmonic filters using simulated annealing,” Appl. Opt. 32, 3116–3121 (1993).
[CrossRef]

1992

M. S. Millan, M. J. Yzuel, J. Campos, C. Ferreira, “Different strategies in optical recognition of polychromatic images,” Appl. Opt. 31, 2560–2567 (1992).
[CrossRef] [PubMed]

J. García, C. Ferreira, J. Campos, S. Bosch, M. S. Millán, M. J. Yzuel, “Multichannel rotation invariant pattern recognition for polychromatic objects using circular harmonic filters,” Opt. Commun. 91, 425–432 (1992).
[CrossRef]

C. Ferreira, M. S. Millan, M. J. Yzuel, J. Campos, “Experimental results in color pattern recognition by multichannel matched filter,” Opt. Eng. 31, 2231–2238 (1992).
[CrossRef]

1991

L. Leclerc, Y. Sheng, H. H. Arsenault, “Circular harmonic covariance filters for rotation invariant object recognition and discrimination,” Opt. Commun. 85, 299–305 (1991).
[CrossRef]

1989

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

1988

1987

1986

F. T. S. Yu, B. Javidi, “Experiments on real-time polychromatic signal detection by matched spatial filtering,” Opt. Commun. 56, 384–388 (1986).
[CrossRef]

1983

F. T. S. Yu, T. H. Chao, “Color signal correlation detected by matched spatial filtering,” Appl. Phys. B 32, 1–6 (1983).
[CrossRef]

1982

Arsenault, H. H.

O. Gualdrón, H. H. Arsenault, “Optimum rotation-invariant filter for disjoint-noise scenes,” Appl. Opt. 35, 2507–2513 (1996).
[CrossRef] [PubMed]

O. Gualdrón, H. H. Arsenault, “Phase-derived circular harmonic filter,” Opt. Commun. 104, 32–34 (1993).
[CrossRef]

L. Leclerc, Y. Sheng, H. H. Arsenault, “Circular harmonic covariance filters for rotation invariant object recognition and discrimination,” Opt. Commun. 85, 299–305 (1991).
[CrossRef]

Y. Sheng, H. H. Arsenault, “Method for determining expansion centers and predicting sidelobe levels for circular harmonic filters,” J. Opt. Soc. Am. A 4, 1793–1797 (1987).
[CrossRef]

Y. Yang, Y.-N. Hsu, H. H. Arsenault, “Optimum circular symmetrical filters and their uses in optical pattern recognition,” Opt. Acta 29, 627–644 (1982).
[CrossRef]

Y.-N. Hsu, H. H. Arsenault, “Optical pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4016–4019 (1982).
[CrossRef] [PubMed]

L. Leclerc, Y. Sheng, H. H. Arsenault, “Rotation invariant phase-only and binary phase-only correlation,” Appl. Opt. 28, 1251–1256 (1982).
[CrossRef]

O. Gualdrón, H. H. Arsenault, “Improved invariant pattern recognition methods,” in Real Time Optical Information Processing. B. Javidi, J. Horner, eds., Academic, San Diego, Calif., 1994, pp. 89–113.

Bosch, S.

J. García, C. Ferreira, J. Campos, S. Bosch, M. S. Millán, M. J. Yzuel, “Multichannel rotation invariant pattern recognition for polychromatic objects using circular harmonic filters,” Opt. Commun. 91, 425–432 (1992).
[CrossRef]

Campos, J.

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

J. García, J. Campos, C. Ferreira, “Circular-harmonic minimum average correlation energy filter for color pattern recognition,” Appl. Opt. 33, 2180–2187 (1994).
[CrossRef] [PubMed]

J. García, J. Campos, C. Ferreira, “Multichannel colour pattern recognition using a minimum average correlation energy filter,” Pure Appl. Opt. 3, 221–224 (1994).
[CrossRef]

J. García, C. Ferreira, J. Campos, S. Bosch, M. S. Millán, M. J. Yzuel, “Multichannel rotation invariant pattern recognition for polychromatic objects using circular harmonic filters,” Opt. Commun. 91, 425–432 (1992).
[CrossRef]

C. Ferreira, M. S. Millan, M. J. Yzuel, J. Campos, “Experimental results in color pattern recognition by multichannel matched filter,” Opt. Eng. 31, 2231–2238 (1992).
[CrossRef]

M. S. Millan, M. J. Yzuel, J. Campos, C. Ferreira, “Different strategies in optical recognition of polychromatic images,” Appl. Opt. 31, 2560–2567 (1992).
[CrossRef] [PubMed]

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

Chao, T. H.

F. T. S. Yu, T. H. Chao, “Color signal correlation detected by matched spatial filtering,” Appl. Phys. B 32, 1–6 (1983).
[CrossRef]

Ferreira, C.

P. García-Martínez, J. García, C. Ferreira, “A new criterion for determining the expansion center for circular-harmonic filters,” Opt. Commun. 117, 399–405 (1995).
[CrossRef]

J. García, J. Campos, C. Ferreira, “Multichannel colour pattern recognition using a minimum average correlation energy filter,” Pure Appl. Opt. 3, 221–224 (1994).
[CrossRef]

J. García, J. Campos, C. Ferreira, “Circular-harmonic minimum average correlation energy filter for color pattern recognition,” Appl. Opt. 33, 2180–2187 (1994).
[CrossRef] [PubMed]

M. S. Millan, M. J. Yzuel, J. Campos, C. Ferreira, “Different strategies in optical recognition of polychromatic images,” Appl. Opt. 31, 2560–2567 (1992).
[CrossRef] [PubMed]

J. García, C. Ferreira, J. Campos, S. Bosch, M. S. Millán, M. J. Yzuel, “Multichannel rotation invariant pattern recognition for polychromatic objects using circular harmonic filters,” Opt. Commun. 91, 425–432 (1992).
[CrossRef]

C. Ferreira, M. S. Millan, M. J. Yzuel, J. Campos, “Experimental results in color pattern recognition by multichannel matched filter,” Opt. Eng. 31, 2231–2238 (1992).
[CrossRef]

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

García, J.

P. García-Martínez, J. García, C. Ferreira, “A new criterion for determining the expansion center for circular-harmonic filters,” Opt. Commun. 117, 399–405 (1995).
[CrossRef]

J. García, J. Campos, C. Ferreira, “Multichannel colour pattern recognition using a minimum average correlation energy filter,” Pure Appl. Opt. 3, 221–224 (1994).
[CrossRef]

J. García, J. Campos, C. Ferreira, “Circular-harmonic minimum average correlation energy filter for color pattern recognition,” Appl. Opt. 33, 2180–2187 (1994).
[CrossRef] [PubMed]

J. García, C. Ferreira, J. Campos, S. Bosch, M. S. Millán, M. J. Yzuel, “Multichannel rotation invariant pattern recognition for polychromatic objects using circular harmonic filters,” Opt. Commun. 91, 425–432 (1992).
[CrossRef]

García-Martínez, P.

P. García-Martínez, J. García, C. Ferreira, “A new criterion for determining the expansion center for circular-harmonic filters,” Opt. Commun. 117, 399–405 (1995).
[CrossRef]

Gualdrón, O.

O. Gualdrón, H. H. Arsenault, “Optimum rotation-invariant filter for disjoint-noise scenes,” Appl. Opt. 35, 2507–2513 (1996).
[CrossRef] [PubMed]

O. Gualdrón, H. H. Arsenault, “Phase-derived circular harmonic filter,” Opt. Commun. 104, 32–34 (1993).
[CrossRef]

O. Gualdrón, H. H. Arsenault, “Improved invariant pattern recognition methods,” in Real Time Optical Information Processing. B. Javidi, J. Horner, eds., Academic, San Diego, Calif., 1994, pp. 89–113.

Hsu, Y.-N.

Y.-N. Hsu, H. H. Arsenault, “Optical pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4016–4019 (1982).
[CrossRef] [PubMed]

Y. Yang, Y.-N. Hsu, H. H. Arsenault, “Optimum circular symmetrical filters and their uses in optical pattern recognition,” Opt. Acta 29, 627–644 (1982).
[CrossRef]

Javidi, B.

F. T. S. Yu, B. Javidi, “Experiments on real-time polychromatic signal detection by matched spatial filtering,” Opt. Commun. 56, 384–388 (1986).
[CrossRef]

Leclerc, L.

L. Leclerc, Y. Sheng, H. H. Arsenault, “Circular harmonic covariance filters for rotation invariant object recognition and discrimination,” Opt. Commun. 85, 299–305 (1991).
[CrossRef]

L. Leclerc, Y. Sheng, H. H. Arsenault, “Rotation invariant phase-only and binary phase-only correlation,” Appl. Opt. 28, 1251–1256 (1982).
[CrossRef]

Millan, M. S.

C. Ferreira, M. S. Millan, M. J. Yzuel, J. Campos, “Experimental results in color pattern recognition by multichannel matched filter,” Opt. Eng. 31, 2231–2238 (1992).
[CrossRef]

M. S. Millan, M. J. Yzuel, J. Campos, C. Ferreira, “Different strategies in optical recognition of polychromatic images,” Appl. Opt. 31, 2560–2567 (1992).
[CrossRef] [PubMed]

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

Millán, M. S.

J. García, C. Ferreira, J. Campos, S. Bosch, M. S. Millán, M. J. Yzuel, “Multichannel rotation invariant pattern recognition for polychromatic objects using circular harmonic filters,” Opt. Commun. 91, 425–432 (1992).
[CrossRef]

Nicolás, J.

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

Pan, K.

Premont, G.

Rosen, J.

Shamir, J.

Sheng, Y.

Yang, Y.

Y. Yang, Y.-N. Hsu, H. H. Arsenault, “Optimum circular symmetrical filters and their uses in optical pattern recognition,” Opt. Acta 29, 627–644 (1982).
[CrossRef]

Yang, Z.

Yu, F. T. S.

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]

F. T. S. Yu, B. Javidi, “Experiments on real-time polychromatic signal detection by matched spatial filtering,” Opt. Commun. 56, 384–388 (1986).
[CrossRef]

F. T. S. Yu, T. H. Chao, “Color signal correlation detected by matched spatial filtering,” Appl. Phys. B 32, 1–6 (1983).
[CrossRef]

Yzuel, M.

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

Yzuel, M. J.

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

J. García, C. Ferreira, J. Campos, S. Bosch, M. S. Millán, M. J. Yzuel, “Multichannel rotation invariant pattern recognition for polychromatic objects using circular harmonic filters,” Opt. Commun. 91, 425–432 (1992).
[CrossRef]

C. Ferreira, M. S. Millan, M. J. Yzuel, J. Campos, “Experimental results in color pattern recognition by multichannel matched filter,” Opt. Eng. 31, 2231–2238 (1992).
[CrossRef]

M. S. Millan, M. J. Yzuel, J. Campos, C. Ferreira, “Different strategies in optical recognition of polychromatic images,” Appl. Opt. 31, 2560–2567 (1992).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. B

F. T. S. Yu, T. H. Chao, “Color signal correlation detected by matched spatial filtering,” Appl. Phys. B 32, 1–6 (1983).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Acta

Y. Yang, Y.-N. Hsu, H. H. Arsenault, “Optimum circular symmetrical filters and their uses in optical pattern recognition,” Opt. Acta 29, 627–644 (1982).
[CrossRef]

Opt. Commun.

P. García-Martínez, J. García, C. Ferreira, “A new criterion for determining the expansion center for circular-harmonic filters,” Opt. Commun. 117, 399–405 (1995).
[CrossRef]

L. Leclerc, Y. Sheng, H. H. Arsenault, “Circular harmonic covariance filters for rotation invariant object recognition and discrimination,” Opt. Commun. 85, 299–305 (1991).
[CrossRef]

O. Gualdrón, H. H. Arsenault, “Phase-derived circular harmonic filter,” Opt. Commun. 104, 32–34 (1993).
[CrossRef]

F. T. S. Yu, B. Javidi, “Experiments on real-time polychromatic signal detection by matched spatial filtering,” Opt. Commun. 56, 384–388 (1986).
[CrossRef]

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

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

J. García, C. Ferreira, J. Campos, S. Bosch, M. S. Millán, M. J. Yzuel, “Multichannel rotation invariant pattern recognition for polychromatic objects using circular harmonic filters,” Opt. Commun. 91, 425–432 (1992).
[CrossRef]

Opt. Eng.

C. Ferreira, M. S. Millan, M. J. Yzuel, J. Campos, “Experimental results in color pattern recognition by multichannel matched filter,” Opt. Eng. 31, 2231–2238 (1992).
[CrossRef]

Pure Appl. Opt.

J. García, J. Campos, C. Ferreira, “Multichannel colour pattern recognition using a minimum average correlation energy filter,” Pure Appl. Opt. 3, 221–224 (1994).
[CrossRef]

Other

O. Gualdrón, H. H. Arsenault, “Improved invariant pattern recognition methods,” in Real Time Optical Information Processing. B. Javidi, J. Horner, eds., Academic, San Diego, Calif., 1994, pp. 89–113.

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Figures (6)

Fig. 1
Fig. 1

Basic color patterns used in the first experiment. The top plane is the color scene. The other three planes are the red, green, and blue channels of the scene.

Fig. 2
Fig. 2

Second order circular harmonic components of the target object of the first experiment. The amplitude distribution of the three red, green, and blue channels are represented.

Fig. 3
Fig. 3

Multichannel correlation between the scene in Fig. 1 and the 2nd-order CHF of the cyan-magenta target.

Fig. 4
Fig. 4

n = 0 plane of the 3D correlation between the scene in Fig. 1 and the 2nd-order CHC of the 3D color Fourier transform of the target.

Fig. 5
Fig. 5

(a) Capsule-shaped target used for the second test, (b) modified target after rotation of 180 deg of its green plane.

Fig. 6
Fig. 6

Correlation peak intensities for gradual rotation of the green plane of the target in Fig. 5.

Tables (2)

Tables Icon

Table 1 RGBa Composition Corresponding to the Patterns in Fig. 1

Tables Icon

Table 2 RGBa Composition Corresponding to the Pattern in Fig. 5

Equations (33)

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

fx, y; n=0 ix, y, λSnλdλ.
Fu, v; m=n=0N-1y=0Dy-1x=0Dx-1 fx, y; n×exp-i2πuxDx+vyDy+mnN.
F¯nu, v=y=0Dy-1x=0Dx-1 fx, y; nexp-i2πuxDx+vyDy.
C¯x, y=n=0N-1 |C¯nx, y|2
C¯nx, y=fnx, y * hnx, y.
Cx, y; n=n=0N-1y=0Dy-1x=0Dx-1 fx, y, nh*x+x, y+y, n+n,
Cx, y; n=1DxDyNm=0N-1v=0Dy-1u=0Dx-1 Fu, v; m×H*u, v; mexpi2πuxDx+vyDy+mnN.
Cx, y; n=0=n=0N-1C¯nx, y.
fr, θ=k=-chckr, θ=k=- fkrexpikθ,
fkr=02π fr, θexp-ikθdθ.
F¯ρ, ϕ=k=-chckρ, ϕ=k=-F¯kρexpikϕ,
F¯kρ=2π-jk0 fkrJ02πrρrdr,
H¯kmρ, ϕ=chckF¯mρ, ϕ=F¯kmρexpikϕ,
Hkρ, ϕ; m=chckFρ, ϕ; m=Fkmρexpikϕ.
Fkmρ=02π Fρ, ϕ; mexp-ikϕdϕ.
Fρ, ϕ; m=n=0N-1F¯ρ, ϕ; nexp-i2π mnN,
Fkmρ=n=0N-1F¯knρexp-i2π mnN.
Hkρ, ϕ; m=n=0N-1H¯knρ, ϕexp-i2π mnN=n=0N-1H¯knρ, ϕWNmn,
H¯k=H¯k0, H¯k1,, H¯kN-2, H¯kN-1,
F¯=F¯0, F¯1,, F¯N-2, F¯N-1,
Hk=WNH¯k,
F=WNF¯.
Cx, y; 0=1Nm=0N-1 Fu, v; mH*u, v; m=1N FH*=1NWNF¯WNH¯k*,
Cx, y; 0=F¯H¯k*=m=0N-1C¯kmx, y.
C0, 0; 0=m=0N-1C¯km0, 0expikαm.
Ekx, y=|C¯kx=x, y=y; x, y|2=|fx, y * chckfx-x, y-yx=x,y=y|2.
Ekx, y=|C¯kx=0, y=0; x, y|2=|fx-x, y-y * chckfx-x, y-yx=0, y=0|2.
C¯knxmxn, ymxn=max|C¯knx, y; x, y|.
Dkx, y=n=0N-1xmxn-x2+ymxn-y21/2.
C¯kx, y=n=0N-1max|C¯knx, y|2,  x, y,
|C0, 0|2=|C10, 0|2+|C20, 0|2+|C30, 0|2.
|C0, 0|2=|C10, 0expiπ|2+|C20, 0|2+|C30, 0|2.
|C0, 0; 0|2=|C10, 0expiπ+C20, 0+C30, 0|2

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