Abstract

Phase dominance is a phenomenon that has been widely observed in imaging, visual perception, and other technical areas. Here we show for general images that phase dominance, in terms of exchanging the spectral amplitude and phase of two images, is simply explained by the expected mean square error.

© 2009 Optical Society of America

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References

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  1. G. N. Ramachandran and R. Srinivasan, Fourier Methods in Crystallography (Wiley, 1970).
  2. T. S. Huang, J. W. Burnett, and A. G. Deczky, IEEE Trans. Acoust., Speech, Signal Process. ASSP-23, 529 (1975).
    [CrossRef]
  3. W. A. Pearlman and R. M. Gray, IEEE Trans. Inf. Theory IT-24, 683 (1978).
    [CrossRef]
  4. A. V. Oppenheim and J. S. Lim, Proc. IEEE 69, 529 (1981).
    [CrossRef]
  5. L. N. Piotrowski and F. W. Campbell, Perception 11, 337 (1982).
    [CrossRef] [PubMed]
  6. R. P. Millane and W. H. Hsiao, J. Opt. Soc. Am. A 20, 753 (2003).
    [CrossRef]
  7. R. J. Read, in Methods in Enzymology, C.W.Carter and R.M.Sweet, eds. (Academic, 1997), Vol. 277, pp. 110-128.
    [CrossRef] [PubMed]
  8. E. Lattman and D. DeRosier, Acta Crystallogr., Sect. A: Found. Crystallogr. 64, 341 (2008).
    [CrossRef]
  9. W. H. Hsiao and R. P. Millane, J. Opt. Soc. Am. A 23, 1823 (2006).
    [CrossRef]
  10. D. J. Field, J. Opt. Soc. Am. A 4, 2379 (1987).
    [CrossRef] [PubMed]
  11. A. van der Schaaf and J. H. van Hateren, Vision Res. 36, 2759 (1996).
    [CrossRef] [PubMed]
  12. W. H. Hsiao and R. P. Millane, J. Opt. Soc. Am. A 22, 1789 (2005).
    [CrossRef]

2008 (1)

E. Lattman and D. DeRosier, Acta Crystallogr., Sect. A: Found. Crystallogr. 64, 341 (2008).
[CrossRef]

2006 (1)

2005 (1)

2003 (1)

1996 (1)

A. van der Schaaf and J. H. van Hateren, Vision Res. 36, 2759 (1996).
[CrossRef] [PubMed]

1987 (1)

1982 (1)

L. N. Piotrowski and F. W. Campbell, Perception 11, 337 (1982).
[CrossRef] [PubMed]

1981 (1)

A. V. Oppenheim and J. S. Lim, Proc. IEEE 69, 529 (1981).
[CrossRef]

1978 (1)

W. A. Pearlman and R. M. Gray, IEEE Trans. Inf. Theory IT-24, 683 (1978).
[CrossRef]

1975 (1)

T. S. Huang, J. W. Burnett, and A. G. Deczky, IEEE Trans. Acoust., Speech, Signal Process. ASSP-23, 529 (1975).
[CrossRef]

Burnett, J. W.

T. S. Huang, J. W. Burnett, and A. G. Deczky, IEEE Trans. Acoust., Speech, Signal Process. ASSP-23, 529 (1975).
[CrossRef]

Campbell, F. W.

L. N. Piotrowski and F. W. Campbell, Perception 11, 337 (1982).
[CrossRef] [PubMed]

Deczky, A. G.

T. S. Huang, J. W. Burnett, and A. G. Deczky, IEEE Trans. Acoust., Speech, Signal Process. ASSP-23, 529 (1975).
[CrossRef]

DeRosier, D.

E. Lattman and D. DeRosier, Acta Crystallogr., Sect. A: Found. Crystallogr. 64, 341 (2008).
[CrossRef]

Field, D. J.

Gray, R. M.

W. A. Pearlman and R. M. Gray, IEEE Trans. Inf. Theory IT-24, 683 (1978).
[CrossRef]

Hsiao, W. H.

Huang, T. S.

T. S. Huang, J. W. Burnett, and A. G. Deczky, IEEE Trans. Acoust., Speech, Signal Process. ASSP-23, 529 (1975).
[CrossRef]

Lattman, E.

E. Lattman and D. DeRosier, Acta Crystallogr., Sect. A: Found. Crystallogr. 64, 341 (2008).
[CrossRef]

Lim, J. S.

A. V. Oppenheim and J. S. Lim, Proc. IEEE 69, 529 (1981).
[CrossRef]

Millane, R. P.

Oppenheim, A. V.

A. V. Oppenheim and J. S. Lim, Proc. IEEE 69, 529 (1981).
[CrossRef]

Pearlman, W. A.

W. A. Pearlman and R. M. Gray, IEEE Trans. Inf. Theory IT-24, 683 (1978).
[CrossRef]

Piotrowski, L. N.

L. N. Piotrowski and F. W. Campbell, Perception 11, 337 (1982).
[CrossRef] [PubMed]

Ramachandran, G. N.

G. N. Ramachandran and R. Srinivasan, Fourier Methods in Crystallography (Wiley, 1970).

Read, R. J.

R. J. Read, in Methods in Enzymology, C.W.Carter and R.M.Sweet, eds. (Academic, 1997), Vol. 277, pp. 110-128.
[CrossRef] [PubMed]

Srinivasan, R.

G. N. Ramachandran and R. Srinivasan, Fourier Methods in Crystallography (Wiley, 1970).

van der Schaaf, A.

A. van der Schaaf and J. H. van Hateren, Vision Res. 36, 2759 (1996).
[CrossRef] [PubMed]

van Hateren, J. H.

A. van der Schaaf and J. H. van Hateren, Vision Res. 36, 2759 (1996).
[CrossRef] [PubMed]

Acta Crystallogr., Sect. A: Found. Crystallogr. (1)

E. Lattman and D. DeRosier, Acta Crystallogr., Sect. A: Found. Crystallogr. 64, 341 (2008).
[CrossRef]

IEEE Trans. Acoust., Speech, Signal Process. (1)

T. S. Huang, J. W. Burnett, and A. G. Deczky, IEEE Trans. Acoust., Speech, Signal Process. ASSP-23, 529 (1975).
[CrossRef]

IEEE Trans. Inf. Theory (1)

W. A. Pearlman and R. M. Gray, IEEE Trans. Inf. Theory IT-24, 683 (1978).
[CrossRef]

J. Opt. Soc. Am. A (4)

Perception (1)

L. N. Piotrowski and F. W. Campbell, Perception 11, 337 (1982).
[CrossRef] [PubMed]

Proc. IEEE (1)

A. V. Oppenheim and J. S. Lim, Proc. IEEE 69, 529 (1981).
[CrossRef]

Vision Res. (1)

A. van der Schaaf and J. H. van Hateren, Vision Res. 36, 2759 (1996).
[CrossRef] [PubMed]

Other (2)

G. N. Ramachandran and R. Srinivasan, Fourier Methods in Crystallography (Wiley, 1970).

R. J. Read, in Methods in Enzymology, C.W.Carter and R.M.Sweet, eds. (Academic, 1997), Vol. 277, pp. 110-128.
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

(a), (b) Original images with similar power spectra. (c), (d) Composite images constructed (c) from the spectral amplitude of (b) and the phase of (a), and (d) from the spectral amplitude of (a) and the phase of (b).

Fig. 2
Fig. 2

Degree of phase dominance R = 2 E p as a function of Δ γ .

Fig. 3
Fig. 3

(a), (b) Original images with different power spectra. (c), (d) Composite images constructed (c) from the spectral amplitude of (b) and the phase of (a), and (d) from the spectral amplitude of (a) and the phase of (b).

Tables (1)

Tables Icon

Table 1 Degree of Phase Dominance R = E a E p for the Images Described

Equations (11)

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E = [ f ̂ ( x , y ) f ( x , y ) ] 2 d x d y = | F ̂ ( u , v ) F ( u , v ) | 2 d u d v ,
E a = 2 | F ( u , v ) | 2 [ 1 1 cos ( Φ G ( u , v ) Φ F ( u , v ) ) ] d u d v ,
E p = [ | F ( u , v ) | | G ( u , v ) | ] 2 d u d v .
E p = 2 2 0 0 2 π | F ( ρ ; φ ) | | G ( ρ ; φ ) | ρ d φ d ρ .
P ( ρ , A ) = ( A σ 2 ( ρ ) ) exp ( A 2 2 σ 2 ( ρ ) ) .
E p = 2 π 2 0 2 σ F ( ρ ) σ G ( ρ ) 2 π ρ d ρ .
E p = 4 π 2 + π 2 0 2 σ F ( ρ ) Δ ( ρ ) 2 π ρ d ρ ,
2 σ 2 ( ρ ) = B ( γ ) ρ γ .
B ( γ ) = 2 γ 2 π ( ρ 2 2 γ ρ 1 2 γ ) , γ 2
= 1 2 π ln ( ρ 2 ρ 1 ) , γ = 2 .
E p = 2 2 π 2 B ( γ F ) B ( γ G ) 4 ( γ F + γ G ) [ ρ 2 2 ( γ F + γ G ) 2 ρ 1 2 ( γ F + γ G ) 2 ] , γ F + γ G 4 = 2 π 2 B ( γ F ) B ( γ G ) ln ( ρ 2 ρ 1 ) , γ F + γ G = 4 ,

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