Abstract

Digitized records of terrain scenes were produced using a technique of photographic colorimetry. Each record consisted of three tristimulus images (X,Y, and Z) which were analyzed for their color statistics, spatial frequency content, and image correlation. Interactions between color and space were examined using a cone receptor transformation. It is shown that the scene amplitude spectra follow an approximate reciprocal variation with frequency, and that the correlation function can be described by a one-step autoregressive model. The results are discussed in terms of methods for optimum image coding in human and machine vision.

© 1987 Optical Society of America

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  1. R. W. Burnham, R. M. Hanes, C. J. Bartleson, Color: A Guide to Basic Facts and Concepts (Wiley, New York, 1963).
  2. C. R. Ingling, E. Martinez-Uriegas, “The Relationship Between Spectral Sensitivity and Spatial Sensitivity for the Primate r-g X-Channel,” Vision Res. 23, 1495 (1983).
    [CrossRef] [PubMed]
  3. I. R. Moorhead, G. J. Burton, “Visual Processing of Colour and Spatial Structure,” in preparation.A summary of the work was given by I. R. Moorhead, “Human Colour Vision and Natural Images,” in Colour in Information Technology and Visual Displays (IERE, London, Publication No. 61, 1985).
  4. E. L. Krinov, “Spectral Reflectance Properties of Natural Formations,” Translated by G. Belkov. National Research Council of Canada, Technical Translation TT-439 (1947).
  5. G. Wyszecki, W. S. Stiles, Color Science (Wiley, London, 1967).
  6. R. Gafvert, W. Lloyd, J. Kavanaugh, “Target Signature Technology. Statistical Sets,” Interim Technical Report No. 2, Wright-Patterson AFB, Contract F33615-69-C-1455 (1968).
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    [CrossRef] [PubMed]
  8. E. R. Kretzmer, “Statistics of Television Signals,” Bell Syst. Tech. J. 31, 751 (1952).
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  10. A. Gagalowicz, S. de Ma, “Synthesis of Natural Textures,” in Proceedings, Sixth International Conference on Pattern Recognition, Munich (Oct. 1982).
  11. A. P. Pentland, “Fractal-Based Description of Natural Scenes,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-6, 661 (1984).
    [CrossRef]
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  13. S. E. Jenkins, “Colour Determination of Australian Foliage from Reversal Film,” Technical Note 381, Materials Research Laboratories, Victoria, Australia (Dec.1975).
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    [CrossRef]
  15. T. N. Wiesel, D. H. Hubel, “Spatial and Chromatic Interactions in the Lateral Geniculate Body of the Rhesus Monkey,” J. Neurophysiol. 29, 1115 (1966).
    [PubMed]
  16. W. E. K. Middleton, Vision Through the Atmosphere (Oxford U. P., London, 1958).
  17. L. M. Biberman, Perception of Displayed Information (Plenum, New York, 1973).
    [CrossRef]
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    [CrossRef]
  19. L. C. Thomson, W. D. Wright, “The Colour Sensitivity of the Retina Within the Central Fovea of Man,” J. Physiol. London 105, 316 (1947).
    [PubMed]
  20. J. J. Vos, P. L. Walraven, “On the Derivation of the Foveal Receptor Primaries,” Vision Res. 11, 799 (1970).
    [CrossRef]
  21. K. H. Ruddock, “The Physics of Colour Vision,” Contemp. Phys. 12, 229 (1971).
    [CrossRef]
  22. G. Buchsbaum, A. Gottschalk, “Trichromacy, Opponent Colours Coding and Optimum Colour Information Transmission in the Retina,” Proc. R. Soc. London Ser. B 220, 89 (1983).
    [CrossRef]
  23. J. W. Cooley, J. W. Tukey, “An Algorithm for the Machine Calculation of Complex Fourier Series,” Math. Comp. 19, 297 (1965).
    [CrossRef]
  24. E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, NJ, 1974).
  25. G. J. Burton, N. D. Haig, I. R. Moorhead, “A Self-Similar Stack Model for Human and Machine Vision,” Biol. Cybern. 53, 397 (1986).
    [CrossRef] [PubMed]
  26. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).
  27. J. Makhoul, “Linear Prediction: A Tutorial Review,” Proc. IEEE 63, 561 (1975).
    [CrossRef]
  28. R. L. Kashyap, P. M. Lapsa, “Synthesis and Estimation of Random Fields Using Long-Correlation Models,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-6, 800 (1984).
    [CrossRef]
  29. D. H. Hubel, T. N. Wiessel, “Receptive Fields, Binocular Interaction and Functional Architecture in the Cat’s Visual Cortex,” J. Physiol. London 160, 106 (1962).
  30. M. V. Srinivasan, S. B. Laughlin, A. Dubs, “Predictive Coding: A Fresh View of Inhibition in the Retina,” Proc. R. Soc. London Ser. B 216, 427 (1982).
    [CrossRef]
  31. M. B. Sachs, J. Nachmias, J. G. Robson, “Spatial Frequency Channels in Human Vision,” J. Opt. Soc. Am. 61, 1176 (1971).
    [CrossRef] [PubMed]
  32. B. Sakitt, H. B. Barlow, “A Model for Economical Encoding of the Visual Image in Cerebral Cortex,” Biol. Cybern. 43, 97 (1982).
    [CrossRef] [PubMed]
  33. A. B. Watson, “Detection and Recognition of Simple Spatial Forms,” in Physical and Biological Processing of Images, O. J. Braddick, A. C. Sleigh, Eds. (Springer-Verlag, New York, 1983).
    [CrossRef]
  34. A. K. Jain, “Advances in Mathematical Models for Image Processing,” Proc. IEEE 69, 502 (1981).
    [CrossRef]
  35. J. J. Koenderink, A. J. van Doom, “Visual Detection of Spatial Contrast; Influence of Location in the Visual Field, Target Extent and Illumination Level,” Biol. Cybern. 30, 157 (1978).
    [CrossRef] [PubMed]
  36. B. G. Bender, “Spatial Interactions Between the Red- and Green-Sensitive Colour Mechanisms of the Human Visual System,” Vision Res. 13, 2205 (1973).
    [CrossRef] [PubMed]
  37. G. von Bekesy, “Neutral Inhibitory Units of the Eye and Skin. Quantitative Description of Contrast Phenomena,” J. Opt. Soc. Am. 50, 1060 (1960).
    [CrossRef]
  38. C. Blakemore, F. W. Campbell, “On the Existence of Neurones in the Human Visual System Selectively Sensitive to the Orientation and Size of Retinal Images,” J. Physiol. London 203, 237 (1969).
    [PubMed]
  39. A. Y. Maudarbocus, K. H. Ruddock, “Non-Linearity of Visual Signals in Relation to Shape-Sensitive Adaptation Processes,” Vision Res. 13, 1713 (1973).
    [CrossRef] [PubMed]
  40. P. J. Burt, “Fast Filter Transforms for Image Processing,” Comput. Graphics Image Process. 16, 20 (1981).
    [CrossRef]
  41. A. R. Robertson, “The CIE 1976 Color-Difference Formulae,” Color Res. Appl. 2, 7 (1977).

1986 (1)

G. J. Burton, N. D. Haig, I. R. Moorhead, “A Self-Similar Stack Model for Human and Machine Vision,” Biol. Cybern. 53, 397 (1986).
[CrossRef] [PubMed]

1984 (2)

R. L. Kashyap, P. M. Lapsa, “Synthesis and Estimation of Random Fields Using Long-Correlation Models,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-6, 800 (1984).
[CrossRef]

A. P. Pentland, “Fractal-Based Description of Natural Scenes,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-6, 661 (1984).
[CrossRef]

1983 (2)

C. R. Ingling, E. Martinez-Uriegas, “The Relationship Between Spectral Sensitivity and Spatial Sensitivity for the Primate r-g X-Channel,” Vision Res. 23, 1495 (1983).
[CrossRef] [PubMed]

G. Buchsbaum, A. Gottschalk, “Trichromacy, Opponent Colours Coding and Optimum Colour Information Transmission in the Retina,” Proc. R. Soc. London Ser. B 220, 89 (1983).
[CrossRef]

1982 (2)

M. V. Srinivasan, S. B. Laughlin, A. Dubs, “Predictive Coding: A Fresh View of Inhibition in the Retina,” Proc. R. Soc. London Ser. B 216, 427 (1982).
[CrossRef]

B. Sakitt, H. B. Barlow, “A Model for Economical Encoding of the Visual Image in Cerebral Cortex,” Biol. Cybern. 43, 97 (1982).
[CrossRef] [PubMed]

1981 (2)

A. K. Jain, “Advances in Mathematical Models for Image Processing,” Proc. IEEE 69, 502 (1981).
[CrossRef]

P. J. Burt, “Fast Filter Transforms for Image Processing,” Comput. Graphics Image Process. 16, 20 (1981).
[CrossRef]

1978 (1)

J. J. Koenderink, A. J. van Doom, “Visual Detection of Spatial Contrast; Influence of Location in the Visual Field, Target Extent and Illumination Level,” Biol. Cybern. 30, 157 (1978).
[CrossRef] [PubMed]

1977 (1)

A. R. Robertson, “The CIE 1976 Color-Difference Formulae,” Color Res. Appl. 2, 7 (1977).

1975 (1)

J. Makhoul, “Linear Prediction: A Tutorial Review,” Proc. IEEE 63, 561 (1975).
[CrossRef]

1973 (2)

B. G. Bender, “Spatial Interactions Between the Red- and Green-Sensitive Colour Mechanisms of the Human Visual System,” Vision Res. 13, 2205 (1973).
[CrossRef] [PubMed]

A. Y. Maudarbocus, K. H. Ruddock, “Non-Linearity of Visual Signals in Relation to Shape-Sensitive Adaptation Processes,” Vision Res. 13, 1713 (1973).
[CrossRef] [PubMed]

1971 (2)

1970 (1)

J. J. Vos, P. L. Walraven, “On the Derivation of the Foveal Receptor Primaries,” Vision Res. 11, 799 (1970).
[CrossRef]

1969 (1)

C. Blakemore, F. W. Campbell, “On the Existence of Neurones in the Human Visual System Selectively Sensitive to the Orientation and Size of Retinal Images,” J. Physiol. London 203, 237 (1969).
[PubMed]

1966 (1)

T. N. Wiesel, D. H. Hubel, “Spatial and Chromatic Interactions in the Lateral Geniculate Body of the Rhesus Monkey,” J. Neurophysiol. 29, 1115 (1966).
[PubMed]

1965 (1)

J. W. Cooley, J. W. Tukey, “An Algorithm for the Machine Calculation of Complex Fourier Series,” Math. Comp. 19, 297 (1965).
[CrossRef]

1962 (1)

D. H. Hubel, T. N. Wiessel, “Receptive Fields, Binocular Interaction and Functional Architecture in the Cat’s Visual Cortex,” J. Physiol. London 160, 106 (1962).

1960 (1)

1952 (2)

W. R. J. Brown, “Statistics of Color-Matching Data,” J. Opt. Soc. Am. 42, 252 (1952).
[CrossRef]

E. R. Kretzmer, “Statistics of Television Signals,” Bell Syst. Tech. J. 31, 751 (1952).

1949 (1)

1947 (1)

L. C. Thomson, W. D. Wright, “The Colour Sensitivity of the Retina Within the Central Fovea of Man,” J. Physiol. London 105, 316 (1947).
[PubMed]

1942 (1)

Barlow, H. B.

B. Sakitt, H. B. Barlow, “A Model for Economical Encoding of the Visual Image in Cerebral Cortex,” Biol. Cybern. 43, 97 (1982).
[CrossRef] [PubMed]

Bartleson, C. J.

R. W. Burnham, R. M. Hanes, C. J. Bartleson, Color: A Guide to Basic Facts and Concepts (Wiley, New York, 1963).

Bender, B. G.

B. G. Bender, “Spatial Interactions Between the Red- and Green-Sensitive Colour Mechanisms of the Human Visual System,” Vision Res. 13, 2205 (1973).
[CrossRef] [PubMed]

Biberman, L. M.

L. M. Biberman, Perception of Displayed Information (Plenum, New York, 1973).
[CrossRef]

Blakemore, C.

C. Blakemore, F. W. Campbell, “On the Existence of Neurones in the Human Visual System Selectively Sensitive to the Orientation and Size of Retinal Images,” J. Physiol. London 203, 237 (1969).
[PubMed]

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

Brigham, E. O.

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, NJ, 1974).

Brown, W. R. J.

Buchsbaum, G.

G. Buchsbaum, A. Gottschalk, “Trichromacy, Opponent Colours Coding and Optimum Colour Information Transmission in the Retina,” Proc. R. Soc. London Ser. B 220, 89 (1983).
[CrossRef]

Burnham, R. W.

R. W. Burnham, R. M. Hanes, C. J. Bartleson, Color: A Guide to Basic Facts and Concepts (Wiley, New York, 1963).

Burt, P. J.

P. J. Burt, “Fast Filter Transforms for Image Processing,” Comput. Graphics Image Process. 16, 20 (1981).
[CrossRef]

Burton, G. J.

G. J. Burton, N. D. Haig, I. R. Moorhead, “A Self-Similar Stack Model for Human and Machine Vision,” Biol. Cybern. 53, 397 (1986).
[CrossRef] [PubMed]

I. R. Moorhead, G. J. Burton, “Visual Processing of Colour and Spatial Structure,” in preparation.A summary of the work was given by I. R. Moorhead, “Human Colour Vision and Natural Images,” in Colour in Information Technology and Visual Displays (IERE, London, Publication No. 61, 1985).

Campbell, F. W.

C. Blakemore, F. W. Campbell, “On the Existence of Neurones in the Human Visual System Selectively Sensitive to the Orientation and Size of Retinal Images,” J. Physiol. London 203, 237 (1969).
[PubMed]

Carlson, C. R.

J. J. Mezrich, C. R. Carlson, R. W. Cohen, “Image Descriptors for Displays,” Technical Report to Office of Naval Research, contract N00014-74-C-0184 (Jan.1977).

Cohen, R. W.

J. J. Mezrich, C. R. Carlson, R. W. Cohen, “Image Descriptors for Displays,” Technical Report to Office of Naval Research, contract N00014-74-C-0184 (Jan.1977).

Cooley, J. W.

J. W. Cooley, J. W. Tukey, “An Algorithm for the Machine Calculation of Complex Fourier Series,” Math. Comp. 19, 297 (1965).
[CrossRef]

de Ma, S.

A. Gagalowicz, S. de Ma, “Synthesis of Natural Textures,” in Proceedings, Sixth International Conference on Pattern Recognition, Munich (Oct. 1982).

Dubs, A.

M. V. Srinivasan, S. B. Laughlin, A. Dubs, “Predictive Coding: A Fresh View of Inhibition in the Retina,” Proc. R. Soc. London Ser. B 216, 427 (1982).
[CrossRef]

Gafvert, R.

R. Gafvert, W. Lloyd, J. Kavanaugh, “Target Signature Technology. Statistical Sets,” Interim Technical Report No. 2, Wright-Patterson AFB, Contract F33615-69-C-1455 (1968).

Gagalowicz, A.

A. Gagalowicz, S. de Ma, “Synthesis of Natural Textures,” in Proceedings, Sixth International Conference on Pattern Recognition, Munich (Oct. 1982).

Gottschalk, A.

G. Buchsbaum, A. Gottschalk, “Trichromacy, Opponent Colours Coding and Optimum Colour Information Transmission in the Retina,” Proc. R. Soc. London Ser. B 220, 89 (1983).
[CrossRef]

Haig, N. D.

G. J. Burton, N. D. Haig, I. R. Moorhead, “A Self-Similar Stack Model for Human and Machine Vision,” Biol. Cybern. 53, 397 (1986).
[CrossRef] [PubMed]

Hanes, R. M.

R. W. Burnham, R. M. Hanes, C. J. Bartleson, Color: A Guide to Basic Facts and Concepts (Wiley, New York, 1963).

Hecht, S.

Hendley, C. D.

Hubel, D. H.

T. N. Wiesel, D. H. Hubel, “Spatial and Chromatic Interactions in the Lateral Geniculate Body of the Rhesus Monkey,” J. Neurophysiol. 29, 1115 (1966).
[PubMed]

D. H. Hubel, T. N. Wiessel, “Receptive Fields, Binocular Interaction and Functional Architecture in the Cat’s Visual Cortex,” J. Physiol. London 160, 106 (1962).

Ingling, C. R.

C. R. Ingling, E. Martinez-Uriegas, “The Relationship Between Spectral Sensitivity and Spatial Sensitivity for the Primate r-g X-Channel,” Vision Res. 23, 1495 (1983).
[CrossRef] [PubMed]

Jain, A. K.

A. K. Jain, “Advances in Mathematical Models for Image Processing,” Proc. IEEE 69, 502 (1981).
[CrossRef]

Jenkins, S. E.

S. E. Jenkins, “Colour Determination of Australian Foliage from Reversal Film,” Technical Note 381, Materials Research Laboratories, Victoria, Australia (Dec.1975).

Kashyap, R. L.

R. L. Kashyap, P. M. Lapsa, “Synthesis and Estimation of Random Fields Using Long-Correlation Models,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-6, 800 (1984).
[CrossRef]

Kavanaugh, J.

R. Gafvert, W. Lloyd, J. Kavanaugh, “Target Signature Technology. Statistical Sets,” Interim Technical Report No. 2, Wright-Patterson AFB, Contract F33615-69-C-1455 (1968).

Koenderink, J. J.

J. J. Koenderink, A. J. van Doom, “Visual Detection of Spatial Contrast; Influence of Location in the Visual Field, Target Extent and Illumination Level,” Biol. Cybern. 30, 157 (1978).
[CrossRef] [PubMed]

Kretzmer, E. R.

E. R. Kretzmer, “Statistics of Television Signals,” Bell Syst. Tech. J. 31, 751 (1952).

Krinov, E. L.

E. L. Krinov, “Spectral Reflectance Properties of Natural Formations,” Translated by G. Belkov. National Research Council of Canada, Technical Translation TT-439 (1947).

Lapsa, P. M.

R. L. Kashyap, P. M. Lapsa, “Synthesis and Estimation of Random Fields Using Long-Correlation Models,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-6, 800 (1984).
[CrossRef]

Laughlin, S. B.

M. V. Srinivasan, S. B. Laughlin, A. Dubs, “Predictive Coding: A Fresh View of Inhibition in the Retina,” Proc. R. Soc. London Ser. B 216, 427 (1982).
[CrossRef]

Lloyd, W.

R. Gafvert, W. Lloyd, J. Kavanaugh, “Target Signature Technology. Statistical Sets,” Interim Technical Report No. 2, Wright-Patterson AFB, Contract F33615-69-C-1455 (1968).

MacAdam, D. L.

Makhoul, J.

J. Makhoul, “Linear Prediction: A Tutorial Review,” Proc. IEEE 63, 561 (1975).
[CrossRef]

Martinez-Uriegas, E.

C. R. Ingling, E. Martinez-Uriegas, “The Relationship Between Spectral Sensitivity and Spatial Sensitivity for the Primate r-g X-Channel,” Vision Res. 23, 1495 (1983).
[CrossRef] [PubMed]

Maudarbocus, A. Y.

A. Y. Maudarbocus, K. H. Ruddock, “Non-Linearity of Visual Signals in Relation to Shape-Sensitive Adaptation Processes,” Vision Res. 13, 1713 (1973).
[CrossRef] [PubMed]

Mezrich, J. J.

J. J. Mezrich, C. R. Carlson, R. W. Cohen, “Image Descriptors for Displays,” Technical Report to Office of Naval Research, contract N00014-74-C-0184 (Jan.1977).

Middleton, W. E. K.

W. E. K. Middleton, Vision Through the Atmosphere (Oxford U. P., London, 1958).

Moorhead, I. R.

G. J. Burton, N. D. Haig, I. R. Moorhead, “A Self-Similar Stack Model for Human and Machine Vision,” Biol. Cybern. 53, 397 (1986).
[CrossRef] [PubMed]

I. R. Moorhead, G. J. Burton, “Visual Processing of Colour and Spatial Structure,” in preparation.A summary of the work was given by I. R. Moorhead, “Human Colour Vision and Natural Images,” in Colour in Information Technology and Visual Displays (IERE, London, Publication No. 61, 1985).

Nachmias, J.

Pentland, A. P.

A. P. Pentland, “Fractal-Based Description of Natural Scenes,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-6, 661 (1984).
[CrossRef]

Pratt, W. K.

W. K. Pratt, Digital Image Processing (Wiley, New York, 1978).

Robertson, A. R.

A. R. Robertson, “The CIE 1976 Color-Difference Formulae,” Color Res. Appl. 2, 7 (1977).

Robson, J. G.

Ruddock, K. H.

A. Y. Maudarbocus, K. H. Ruddock, “Non-Linearity of Visual Signals in Relation to Shape-Sensitive Adaptation Processes,” Vision Res. 13, 1713 (1973).
[CrossRef] [PubMed]

K. H. Ruddock, “The Physics of Colour Vision,” Contemp. Phys. 12, 229 (1971).
[CrossRef]

Sachs, M. B.

Sakitt, B.

B. Sakitt, H. B. Barlow, “A Model for Economical Encoding of the Visual Image in Cerebral Cortex,” Biol. Cybern. 43, 97 (1982).
[CrossRef] [PubMed]

Srinivasan, M. V.

M. V. Srinivasan, S. B. Laughlin, A. Dubs, “Predictive Coding: A Fresh View of Inhibition in the Retina,” Proc. R. Soc. London Ser. B 216, 427 (1982).
[CrossRef]

Stiles, W. S.

G. Wyszecki, W. S. Stiles, Color Science (Wiley, London, 1967).

Thomson, L. C.

L. C. Thomson, W. D. Wright, “The Colour Sensitivity of the Retina Within the Central Fovea of Man,” J. Physiol. London 105, 316 (1947).
[PubMed]

Tukey, J. W.

J. W. Cooley, J. W. Tukey, “An Algorithm for the Machine Calculation of Complex Fourier Series,” Math. Comp. 19, 297 (1965).
[CrossRef]

van Doom, A. J.

J. J. Koenderink, A. J. van Doom, “Visual Detection of Spatial Contrast; Influence of Location in the Visual Field, Target Extent and Illumination Level,” Biol. Cybern. 30, 157 (1978).
[CrossRef] [PubMed]

von Bekesy, G.

Vos, J. J.

J. J. Vos, P. L. Walraven, “On the Derivation of the Foveal Receptor Primaries,” Vision Res. 11, 799 (1970).
[CrossRef]

Walraven, P. L.

J. J. Vos, P. L. Walraven, “On the Derivation of the Foveal Receptor Primaries,” Vision Res. 11, 799 (1970).
[CrossRef]

Watson, A. B.

A. B. Watson, “Detection and Recognition of Simple Spatial Forms,” in Physical and Biological Processing of Images, O. J. Braddick, A. C. Sleigh, Eds. (Springer-Verlag, New York, 1983).
[CrossRef]

Wiesel, T. N.

T. N. Wiesel, D. H. Hubel, “Spatial and Chromatic Interactions in the Lateral Geniculate Body of the Rhesus Monkey,” J. Neurophysiol. 29, 1115 (1966).
[PubMed]

Wiessel, T. N.

D. H. Hubel, T. N. Wiessel, “Receptive Fields, Binocular Interaction and Functional Architecture in the Cat’s Visual Cortex,” J. Physiol. London 160, 106 (1962).

Wright, W. D.

L. C. Thomson, W. D. Wright, “The Colour Sensitivity of the Retina Within the Central Fovea of Man,” J. Physiol. London 105, 316 (1947).
[PubMed]

Wyszecki, G.

G. Wyszecki, W. S. Stiles, Color Science (Wiley, London, 1967).

Bell Syst. Tech. J. (1)

E. R. Kretzmer, “Statistics of Television Signals,” Bell Syst. Tech. J. 31, 751 (1952).

Biol. Cybern. (3)

G. J. Burton, N. D. Haig, I. R. Moorhead, “A Self-Similar Stack Model for Human and Machine Vision,” Biol. Cybern. 53, 397 (1986).
[CrossRef] [PubMed]

B. Sakitt, H. B. Barlow, “A Model for Economical Encoding of the Visual Image in Cerebral Cortex,” Biol. Cybern. 43, 97 (1982).
[CrossRef] [PubMed]

J. J. Koenderink, A. J. van Doom, “Visual Detection of Spatial Contrast; Influence of Location in the Visual Field, Target Extent and Illumination Level,” Biol. Cybern. 30, 157 (1978).
[CrossRef] [PubMed]

Color Res. Appl. (1)

A. R. Robertson, “The CIE 1976 Color-Difference Formulae,” Color Res. Appl. 2, 7 (1977).

Comput. Graphics Image Process. (1)

P. J. Burt, “Fast Filter Transforms for Image Processing,” Comput. Graphics Image Process. 16, 20 (1981).
[CrossRef]

Contemp. Phys. (1)

K. H. Ruddock, “The Physics of Colour Vision,” Contemp. Phys. 12, 229 (1971).
[CrossRef]

IEEE Trans. Pattern Anal. Machine Intell. (2)

A. P. Pentland, “Fractal-Based Description of Natural Scenes,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-6, 661 (1984).
[CrossRef]

R. L. Kashyap, P. M. Lapsa, “Synthesis and Estimation of Random Fields Using Long-Correlation Models,” IEEE Trans. Pattern Anal. Machine Intell. PAMI-6, 800 (1984).
[CrossRef]

J. Neurophysiol. (1)

T. N. Wiesel, D. H. Hubel, “Spatial and Chromatic Interactions in the Lateral Geniculate Body of the Rhesus Monkey,” J. Neurophysiol. 29, 1115 (1966).
[PubMed]

J. Opt. Soc. Am. (5)

J. Physiol. London (3)

C. Blakemore, F. W. Campbell, “On the Existence of Neurones in the Human Visual System Selectively Sensitive to the Orientation and Size of Retinal Images,” J. Physiol. London 203, 237 (1969).
[PubMed]

D. H. Hubel, T. N. Wiessel, “Receptive Fields, Binocular Interaction and Functional Architecture in the Cat’s Visual Cortex,” J. Physiol. London 160, 106 (1962).

L. C. Thomson, W. D. Wright, “The Colour Sensitivity of the Retina Within the Central Fovea of Man,” J. Physiol. London 105, 316 (1947).
[PubMed]

Math. Comp. (1)

J. W. Cooley, J. W. Tukey, “An Algorithm for the Machine Calculation of Complex Fourier Series,” Math. Comp. 19, 297 (1965).
[CrossRef]

Proc. IEEE (2)

J. Makhoul, “Linear Prediction: A Tutorial Review,” Proc. IEEE 63, 561 (1975).
[CrossRef]

A. K. Jain, “Advances in Mathematical Models for Image Processing,” Proc. IEEE 69, 502 (1981).
[CrossRef]

Proc. R. Soc. London Ser. B (2)

M. V. Srinivasan, S. B. Laughlin, A. Dubs, “Predictive Coding: A Fresh View of Inhibition in the Retina,” Proc. R. Soc. London Ser. B 216, 427 (1982).
[CrossRef]

G. Buchsbaum, A. Gottschalk, “Trichromacy, Opponent Colours Coding and Optimum Colour Information Transmission in the Retina,” Proc. R. Soc. London Ser. B 220, 89 (1983).
[CrossRef]

Vision Res. (4)

J. J. Vos, P. L. Walraven, “On the Derivation of the Foveal Receptor Primaries,” Vision Res. 11, 799 (1970).
[CrossRef]

C. R. Ingling, E. Martinez-Uriegas, “The Relationship Between Spectral Sensitivity and Spatial Sensitivity for the Primate r-g X-Channel,” Vision Res. 23, 1495 (1983).
[CrossRef] [PubMed]

A. Y. Maudarbocus, K. H. Ruddock, “Non-Linearity of Visual Signals in Relation to Shape-Sensitive Adaptation Processes,” Vision Res. 13, 1713 (1973).
[CrossRef] [PubMed]

B. G. Bender, “Spatial Interactions Between the Red- and Green-Sensitive Colour Mechanisms of the Human Visual System,” Vision Res. 13, 2205 (1973).
[CrossRef] [PubMed]

Other (14)

R. W. Burnham, R. M. Hanes, C. J. Bartleson, Color: A Guide to Basic Facts and Concepts (Wiley, New York, 1963).

W. E. K. Middleton, Vision Through the Atmosphere (Oxford U. P., London, 1958).

L. M. Biberman, Perception of Displayed Information (Plenum, New York, 1973).
[CrossRef]

A. B. Watson, “Detection and Recognition of Simple Spatial Forms,” in Physical and Biological Processing of Images, O. J. Braddick, A. C. Sleigh, Eds. (Springer-Verlag, New York, 1983).
[CrossRef]

I. R. Moorhead, G. J. Burton, “Visual Processing of Colour and Spatial Structure,” in preparation.A summary of the work was given by I. R. Moorhead, “Human Colour Vision and Natural Images,” in Colour in Information Technology and Visual Displays (IERE, London, Publication No. 61, 1985).

E. L. Krinov, “Spectral Reflectance Properties of Natural Formations,” Translated by G. Belkov. National Research Council of Canada, Technical Translation TT-439 (1947).

G. Wyszecki, W. S. Stiles, Color Science (Wiley, London, 1967).

R. Gafvert, W. Lloyd, J. Kavanaugh, “Target Signature Technology. Statistical Sets,” Interim Technical Report No. 2, Wright-Patterson AFB, Contract F33615-69-C-1455 (1968).

W. K. Pratt, Digital Image Processing (Wiley, New York, 1978).

S. E. Jenkins, “Colour Determination of Australian Foliage from Reversal Film,” Technical Note 381, Materials Research Laboratories, Victoria, Australia (Dec.1975).

J. J. Mezrich, C. R. Carlson, R. W. Cohen, “Image Descriptors for Displays,” Technical Report to Office of Naval Research, contract N00014-74-C-0184 (Jan.1977).

A. Gagalowicz, S. de Ma, “Synthesis of Natural Textures,” in Proceedings, Sixth International Conference on Pattern Recognition, Munich (Oct. 1982).

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, NJ, 1974).

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

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Figures (11)

Fig. 1
Fig. 1

(A) The CIE 1965 (u′,v′) uniform chromaticity diagram41 showing the spectrum locus with wavelengths indicated. The ranges of values for foliage and earths, measured by Hendley and Hecht,7 are shown by the small closed curves adjacent to the daylight point, D65. The large triangle gives the color gamut for the NTSC color TV standard. Note the large difference between the range occupied by distant terrain scenes and that required for color reception in man-made environments. (B) Part of the chromaticity diagram shown on an enlarged scale. The dots show values from the Hendley and Hecht study and the solid circle gives the daylight point. The open circles show chromaticities for row 4 of the calibration patchwork (see Sec. II.A). The cross gives the approximate coordinates for the patchwork light source (3400 K).

Fig. 2
Fig. 2

Schematic diagram of the optical arrangement used to measure the tristimulus values across selected film areas. The collimated light source, S, was derived from a tungsten-halogen lamp (Atlas 24 V, 150 W), powered by a voltage-stabilized supply (King-shill, type NS3010). The light source illuminated one of the filters in the slide, F. Three color separation filters (R, G, and B) and one neutral filter (N) were fixed in the slide together with neutral trimming filters. The weak milk suspension, M, produced near-uniform illumination across the film plane, P. The film was imaged on the vidicon tube, V, at selected magnifications using the collimating lens, L, and zoom lens, Z.

Fig. 3
Fig. 3

(A) Comparisons between calculated and measured tristimulus values (X, Y, and Z) for the worst-case least-squares fit. For clarity, the X and Z values are vertically offset by 200 and 400 cd · m−2, respectively. (B) Errors in the corresponding chromaticity coordinates for the 1965 uniform chromaticity space are plotted as the calculated minus the measured values. The just-noticeable-difference ellipse is shown for the appropriate region of color space by the closed curve. Note that this ellipse is three times the size of the McAdam18 color matching ellipse.14

Fig. 4
Fig. 4

(A)–(D) Four records of the terrain data are shown, each containing four images. The upper right, lower left, and lower right images of each record indicate the X, Y, and Z tristimulus values, respectively. The upper left image is the broadband (uncorrected) record containing frame information. For each image, the minimum and maximum tristimulus values were set to give the grey-scale limits of 0 and 255, respectively. Taking (A) as an example, the minimum and maximum values were X = 1550 and 6790, Y = 1750 and 7230, and Z = 870 and 3080 cd · m−2, respectively.

Fig. 5
Fig. 5

Chromaticity coordinates for all pixels in a given image are shown in (u′,v′) space. The squares show the positions of the calibration points for the midrange luminance column on the patchwork (see Sec. II.A). Part of the spectrum locus is shown with wavelengths in the range from 550 to 580 nm and the cross gives the position of the 6500 K (D65) daylight standard. (A) Values are shown for the short-range high-visibility record of Fig. 4(A). The color and spatial statistics for this record are quoted in later sections. (B) Chromaticities are shown by the light grey, dark grey, and black areas for the records in Figs. 4(B), (C), and (D), respectively. Note the overall shift of the clusters toward the blue region of the chromaticity diagram. (C) The frequency histogram for all nineteen images was sliced to give three cumulative frequency contours. The light grey area shows the complete color gamut (100%), the overlaid dark grey areas show the contours containing 75%, and the black area 25%, of the image points.

Fig. 6
Fig. 6

Frequency plots are shown to illustrate the degree of correlation produced in the red-, green-, and blue-sensitive cone receptor system (RGB) of Vos and Walraven.20 Values were obtained from the record in Fig. 4(A). (A), (B), and (C) are plots illustrating the correlation between (R,G), (R,B), and (G,B), respectively. Observe the lower level of correlation for the plots having blue as one component.

Fig. 7
Fig. 7

Fourier amplitude spectra for luminance images (Y values) are shown on logarithmic scales for the record in Fig. 4(A) by lines and for the average results over all nineteen images by circles. Units of frequency are cycles/picture width, for a width of 128 pixels. Values are shown separately for the rows and columns of the images. The oblique straight line, indicated by (1/f), shows the variation when the amplitude is inversely proportional to the spatial frequency f.

Fig. 8
Fig. 8

(A) and (B) Scatter diagrams are plotted to indicate the grey-scale correlation between pairs of image points separated by 1 and 16 pixels, respectively. Values were obtained from the Y image in Fig. 4(A) and represent correlations down columns of the image. The correlation coefficients are 0.976 and 0.531 for (A) and (B), respectively.

Fig. 9
Fig. 9

Correlation coefficients are plotted for point separations in the range of 0–64 pixels. The continuous and broken lines show values obtained from the rows and columns of Fig. 4(A), respectively. The corresponding sample averages are indicated by solid and open circles. Note that the column correlation coefficients are close to zero for large separations, in marked contrast with the large pedestal present for the row values.

Fig. 10
Fig. 10

Fourier amplitude spectra are shown for images transformed to the red, green, and blue cone receptor system of Vos and Walraven.20 The oblique lines indicate a (1/f) amplitude spectrum. (A) shows the row data and (B) the column data. Lines give values derived from the image in Fig. 4(A) and circles show values averaged over all nineteen images.

Fig. 11
Fig. 11

Correlation coefficients are plotted for the RGB cone receptor system. (A) shows the row data and (B) the column data. Continuous and broken lines give values derived from the record in Fig. 4(A) for the green and blue receptors, respectively. Solid and opoen circles show the corresponding sample means. For clarity, results for the red receptors are not plotted because they are almost identical to the corresponding values for the green receptors.

Tables (2)

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Table I Values for Slope (±SE) for Amplitude Spectra

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Table II Values of One-Step Coefficient ρ1, Correlation Length K (Pixels), Constant c, and rms Curve-Fitting Error

Equations (6)

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S = a + b x + c y + d x 2 + e y 2 + f x y ,
X = a + b R + c G + d B + e R 2 + f G 2 + g B 2 + h R G + i R B + j G B ,
B R ( λ ) = B 0 ( λ ) · exp [ - σ ( λ ) R ] + B H ( λ ) · { 1 - exp [ - σ ( λ ) R ] } ,
C ( y ) = I ( x ) · I ( x + y ) · d x ,
C k = i ( I i - I i ) · ( I i + k - I i + k ) / N ,
ρ = ( 1 - c ) ρ 1 k + c ,

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