Abstract

Color images degraded by defocusing and chromatism are restored using different digital models and linear filtering techniques. The restoration process for color images is properly performed through the filters associated with three transfer functions for tristimulus values. However, the use of three monochromatic OTFs corresponding to the maxima of the color receiver is also discussed for different cases of wavelength-dependent aberrations, since it enables a significant reduction in the computer processing time.

© 1988 Optical Society of America

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References

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  1. C. E. Mancill, “Digital Color Image Restoration,” USCIPI Report 630 (1975).
  2. R. A. Wallis, “Film Recording of Digital Color Images,” USCIPI Report 570 (1975).
  3. J. Bescos, I. Glaser, A. A. Sawchuk, “Restoration of Color Images Degraded by Chromatic Aberration,” Appl. Opt. 19, 3869 (1980).
    [CrossRef] [PubMed]
  4. J. Santamaría, A. Plaza, J. Bescos, “Color Image Enhancement by White Light Spatial Filtering,” Opt. Commun. 45, 244 (1983).
    [CrossRef]
  5. J. Bescos, J. Santamaría, “Formation of Colour Images. Optical Transfer Functions for the Tristimulus Values,” Photogr. Sci. Eng. 6, 355 (1977).
  6. J. Bescos, J. Santamaría, “Colour Based Quality Parameters for White Light Imagery,” Opt. Acta 28, 43 (1981).
    [CrossRef]
  7. G. Wyszecki, W. S. Stiles, Colour Science (Wiley, New York, 1967).
  8. M. J. Yzuel, J. Santamaría, “Polychromatic Optical Image. Diffraction Limited System and Influence of the Longitudinal Chromatic Aberration,” Opt. Acta 22, 673 (1975).
    [CrossRef]
  9. M. J. Yzuel, J. Bescos, “Polychromatic Off-Axis Optical Image. Influence of the Transverse Chromatic Aberration,” Opt. Acta 22, 913 (1976).
    [CrossRef]
  10. L. R. Berriel, J. Bescos, A. Santisteban, “Image Restoration for a Defocused Optical System,” Appl. Opt. 22, 2772 (1983).
    [CrossRef] [PubMed]

1983

J. Santamaría, A. Plaza, J. Bescos, “Color Image Enhancement by White Light Spatial Filtering,” Opt. Commun. 45, 244 (1983).
[CrossRef]

L. R. Berriel, J. Bescos, A. Santisteban, “Image Restoration for a Defocused Optical System,” Appl. Opt. 22, 2772 (1983).
[CrossRef] [PubMed]

1981

J. Bescos, J. Santamaría, “Colour Based Quality Parameters for White Light Imagery,” Opt. Acta 28, 43 (1981).
[CrossRef]

1980

1977

J. Bescos, J. Santamaría, “Formation of Colour Images. Optical Transfer Functions for the Tristimulus Values,” Photogr. Sci. Eng. 6, 355 (1977).

1976

M. J. Yzuel, J. Bescos, “Polychromatic Off-Axis Optical Image. Influence of the Transverse Chromatic Aberration,” Opt. Acta 22, 913 (1976).
[CrossRef]

1975

M. J. Yzuel, J. Santamaría, “Polychromatic Optical Image. Diffraction Limited System and Influence of the Longitudinal Chromatic Aberration,” Opt. Acta 22, 673 (1975).
[CrossRef]

Berriel, L. R.

Bescos, J.

L. R. Berriel, J. Bescos, A. Santisteban, “Image Restoration for a Defocused Optical System,” Appl. Opt. 22, 2772 (1983).
[CrossRef] [PubMed]

J. Santamaría, A. Plaza, J. Bescos, “Color Image Enhancement by White Light Spatial Filtering,” Opt. Commun. 45, 244 (1983).
[CrossRef]

J. Bescos, J. Santamaría, “Colour Based Quality Parameters for White Light Imagery,” Opt. Acta 28, 43 (1981).
[CrossRef]

J. Bescos, I. Glaser, A. A. Sawchuk, “Restoration of Color Images Degraded by Chromatic Aberration,” Appl. Opt. 19, 3869 (1980).
[CrossRef] [PubMed]

J. Bescos, J. Santamaría, “Formation of Colour Images. Optical Transfer Functions for the Tristimulus Values,” Photogr. Sci. Eng. 6, 355 (1977).

M. J. Yzuel, J. Bescos, “Polychromatic Off-Axis Optical Image. Influence of the Transverse Chromatic Aberration,” Opt. Acta 22, 913 (1976).
[CrossRef]

Glaser, I.

Mancill, C. E.

C. E. Mancill, “Digital Color Image Restoration,” USCIPI Report 630 (1975).

Plaza, A.

J. Santamaría, A. Plaza, J. Bescos, “Color Image Enhancement by White Light Spatial Filtering,” Opt. Commun. 45, 244 (1983).
[CrossRef]

Santamaría, J.

J. Santamaría, A. Plaza, J. Bescos, “Color Image Enhancement by White Light Spatial Filtering,” Opt. Commun. 45, 244 (1983).
[CrossRef]

J. Bescos, J. Santamaría, “Colour Based Quality Parameters for White Light Imagery,” Opt. Acta 28, 43 (1981).
[CrossRef]

J. Bescos, J. Santamaría, “Formation of Colour Images. Optical Transfer Functions for the Tristimulus Values,” Photogr. Sci. Eng. 6, 355 (1977).

M. J. Yzuel, J. Santamaría, “Polychromatic Optical Image. Diffraction Limited System and Influence of the Longitudinal Chromatic Aberration,” Opt. Acta 22, 673 (1975).
[CrossRef]

Santisteban, A.

Sawchuk, A. A.

Stiles, W. S.

G. Wyszecki, W. S. Stiles, Colour Science (Wiley, New York, 1967).

Wallis, R. A.

R. A. Wallis, “Film Recording of Digital Color Images,” USCIPI Report 570 (1975).

Wyszecki, G.

G. Wyszecki, W. S. Stiles, Colour Science (Wiley, New York, 1967).

Yzuel, M. J.

M. J. Yzuel, J. Bescos, “Polychromatic Off-Axis Optical Image. Influence of the Transverse Chromatic Aberration,” Opt. Acta 22, 913 (1976).
[CrossRef]

M. J. Yzuel, J. Santamaría, “Polychromatic Optical Image. Diffraction Limited System and Influence of the Longitudinal Chromatic Aberration,” Opt. Acta 22, 673 (1975).
[CrossRef]

Appl. Opt.

Opt. Acta

J. Bescos, J. Santamaría, “Colour Based Quality Parameters for White Light Imagery,” Opt. Acta 28, 43 (1981).
[CrossRef]

M. J. Yzuel, J. Santamaría, “Polychromatic Optical Image. Diffraction Limited System and Influence of the Longitudinal Chromatic Aberration,” Opt. Acta 22, 673 (1975).
[CrossRef]

M. J. Yzuel, J. Bescos, “Polychromatic Off-Axis Optical Image. Influence of the Transverse Chromatic Aberration,” Opt. Acta 22, 913 (1976).
[CrossRef]

Opt. Commun.

J. Santamaría, A. Plaza, J. Bescos, “Color Image Enhancement by White Light Spatial Filtering,” Opt. Commun. 45, 244 (1983).
[CrossRef]

Photogr. Sci. Eng.

J. Bescos, J. Santamaría, “Formation of Colour Images. Optical Transfer Functions for the Tristimulus Values,” Photogr. Sci. Eng. 6, 355 (1977).

Other

G. Wyszecki, W. S. Stiles, Colour Science (Wiley, New York, 1967).

C. E. Mancill, “Digital Color Image Restoration,” USCIPI Report 630 (1975).

R. A. Wallis, “Film Recording of Digital Color Images,” USCIPI Report 570 (1975).

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Figures (9)

Fig. 1
Fig. 1

Original digital image: red, green, and blue components, from the left.

Fig. 2
Fig. 2

Tristimulus values of the monitor color channels for different gray levels.

Fig. 3
Fig. 3

Color image components blurred by defocusing through the tristimulus values OTFs: (a) δ0W20 = 0.5 μm; (b) δ0W20 = 1 μm.

Fig. 4
Fig. 4

Top, OTFs for the tristimulus values in the presence of defocusing: δ0W20 = 1 μm. Bottom, Wiener filters corresponding to OTFs for tristimulus values (top).

Fig. 5
Fig. 5

Restored image of the defocused image of Fig. 3(b) using OTFs for tristimulus values.

Fig. 6
Fig. 6

Colour Image Restoration. (a) Original Digital Image. (b) Defocused Image by δ0W20 = 1 μm. (c) Restored Image from the Defocused one (b).

Fig. 7
Fig. 7

Color image components blurred by the longitudinal chromatism of a single lens.

Fig. 8
Fig. 8

Top, OTFs for tristimulus values in the presence of longitudinal chromatism of a single lens. Bottom, monochromatic OTFs corresponding to the maxima of the color receiver for the same chromatism.

Fig. 9
Fig. 9

Top, restored components of the image of Fig. 7 through the filters of the OTFs for the tristimulus values shown in Fig. 8 (top). Bottom, restored components of the image of Fig. 7 through the filters of the monochromatic OTFs shown in Fig. 8 (bottom).

Equations (5)

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X I ( x , y ) = X O ( x , y ) D X ( x x , y y ) d x d y , Y I ( x , y ) = Y O ( x , y ) D Y ( x x , y y ) d x d y , Z I ( x , y ) = Z O ( x , y ) D Z ( x x , y y ) d x d y ,
X ˆ I ( u , υ ) = X ˆ O ( u , υ ) H X ( u , υ ) , Y ˆ I ( u , υ ) = Y ˆ O ( u , υ ) H Y ( u , υ ) , Z ˆ I ( u , υ ) = Z ˆ O ( u , υ ) H Z ( u , υ ) ,
H X ( u , υ ) = S ( λ ) H λ ( u , υ ) x ¯ λ d λ S ( λ ) x ¯ λ d λ , H Y ( u , υ ) = S ( λ ) H λ ( u , υ ) y ¯ λ d λ S ( λ ) y ¯ λ d λ , H Z ( u , υ ) = S ( λ ) H λ ( u , υ ) z ¯ λ d λ S ( λ ) z ¯ λ d λ .
( 1 H X 1 H Y 1 H Z ) ,
W X ( u , υ ) = H * X ( u , υ ) | H X ( u , υ ) | 2 + ϕ n ( u , υ ) / ϕ f ( u , υ ) , W Y ( u , υ ) = H * Y ( u , υ ) | H Y ( u , υ ) | 2 + ϕ n ( u , υ ) / ϕ f ( u , υ ) , W Z ( u , υ ) = H * Z ( u , υ ) | H Z ( u , υ ) | 2 + ϕ n ( u , υ ) / ϕ f ( u , υ ) ,

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