Abstract

The physical contrast of simple images such as sinusoidal gratings or a single patch of light on a uniform background is well defined and agrees with the perceived contrast, but this is not so for complex images. Most definitions assign a single contrast value to the whole image, but perceived contrast may vary greatly across the image. Human contrast sensitivity is a function of spatial frequency; therefore the spatial frequency content of an image should be considered in the definition of contrast. In this paper a definition of local band-limited contrast in images is proposed that assigns a contrast value to every point in the image as a function of the spatial frequency band. For each frequency band, the contrast is defined as the ratio of the bandpass-filtered image at that frequency to the low-pass image filtered to an octave below the same frequency (local luminance mean). This definition raises important implications regarding the perception of contrast in complex images and is helpful in understanding the effects of image-processing algorithms on the perceived contrast. A pyramidal image-contrast structure based on this definition is useful in simulating nonlinear, threshold characteristics of spatial vision in both normal observers and the visually impaired.

© 1990 Optical Society of America

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    [CrossRef]
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  47. The pyramidal image transform used here is conceptually identical to any of the commonly used pyramids of bandpass-filtered images. Since for our application images of equal size are used at all bands, we avoided the common approach of subsampling the images recursively, filtering, and then unsampling the reduced size images, instead; all filtering was done in the frequency domain. Thus the content of our final images in the pyramid of image scales was identical to the images that would be calculated by upsampling images obtained on a pyramid of image resolution.
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    [CrossRef]

1989 (6)

J. P. Thomas, “Independent processing of suprathreshold spatial gratings as a function of their separation in spatial frequency,” J. Opt. Soc. Am. A 6, 1102–1111 (1989).
[CrossRef] [PubMed]

G. S. Rubin, G. E. Legge, “Psychophysics of reading. VI. The role of contrast in low vision,” Vision Res. 29, 79–91 (1989).
[CrossRef]

J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the human visual field with emphasis on the low spatial frequency range,” Vision Res. 29, 1133–1151 (1989).
[CrossRef]

A. Toet, L. G. van Ruyven, J. M. Valeton, “Merging thermal and visual images by contrast pyramid,” Opt. Eng. 28, 789–792 (1989).
[CrossRef]

R. W. Bowen, J. Pokorny, V. C. Smith, “Sawtooth contrast sensitivity: decrements have the edge,” Vision Res. 298, 1501–1509 (1989).

E. Peli, “Hilbert transform pairs mechanisms,” Invest. Ophthalmol. Vis. Sci. 30, 110 (1989).

1988 (6)

M. W. Cannon, S. C. Fullenkamp, “Perceived contrast and stimulus size: experiment and simulation,” Vision Res. 28, 695–709 (1988).
[CrossRef] [PubMed]

M. C. Morrone, D. C. Burr, “Feature detection in human vision: a phase-dependent energy model,” Proc. R. Soc. London Ser. B 235, 221–245 (1988).
[CrossRef]

J. G. Robson, “Linear and non-linear operations in the visual system,” Invest. Ophthalmol. Vis. Sci. 29, 117 (1988).

T. B. Lawton, “Improved word recognition for observers with age-related maculopathies using compensation filters,” Clin. Vision Sci. 3, 125–135 (1988).

T. R. Riedl, G. Sperling, “Spatial frequency bands in complex visual stimuli: American Sign Language,” J. Opt. Soc. Am. A 5, 606–616 (1988).
[CrossRef] [PubMed]

D. S. Loshin, T. A. Banton, “Local contrast requirements for Facial recognition in patients with central field defects,” Invest. Ophthalmol. Vis. Sci. Suppl. 29, 43 (1988).

1987 (5)

1985 (4)

G. E. Legge, G. S. Rubin, D. G. Pelli, M. M. Schleske, “Psychophysics of reading. II. Low vision,” Vision Res. 25, 253–266 (1985).
[CrossRef]

M. W. Cannon, “Perceived contrast in the fovea and periphery,” J. Opt. Soc. Am. A 2, 1760–1768 (1985).
[CrossRef] [PubMed]

G. Westheimer, “The oscilloscopic view: retinal illuminance and contrast of point and line targets,” Vision Res. 25, 1097–1103 (1985).
[CrossRef] [PubMed]

M. Hubner, I. Rentschler, W. Encke, “Hidden-face recognition: comparing foveal and extrafoveal performance,” Hum. Neurobiol. 4, 1–7 (1985).
[PubMed]

1984 (3)

G. S. Rubin, K. Siegel, “Recognition of low-pass filtered faces and letters,” Invest. Ophthalmol. Vis. Sci. Suppl. 25, 71 (1984).

D. R. Badcock, “Spatial phase or luminance profile discrimination?” Vision Res. 24, 613–623 (1984).
[CrossRef] [PubMed]

E. Peli, T. Peli, “Image enhancement for the visually impaired,” Opt. Eng. 23, 47–51 (1984).
[CrossRef]

1983 (3)

A. B. Watson, H. B. Barlow, J. G. Robson, “What does the eye see best?” Nature (London) 302, 419–422 (1983).
[CrossRef]

A. Fiorentini, L. Maffei, G. Sandini, “The role of high spatial frequencies in face perception,” Perception 12, 195–201 (1983).
[CrossRef] [PubMed]

R. F. Hess, A. Bradley, L. Piotrowski, “Contrast-coding in amblyopia. I. Differences in the neural basis of human amblyopia,” Proc. R. Soc. London Ser. B 217, 309–330 (1983).
[CrossRef]

1982 (3)

J. D. Briers, A. F. Fercher, “Retinal blood-flow visualization by means of laser speckle photography,” Invest. Ophthalmol. Vis. Sci. 22, 255–259 (1982).
[PubMed]

R. Sekuler, C. Owsley, L. Hutman, “Assessing spatial vision of older people,” Am. J. Optom. Physiol. Opt. 59, 961–968 (1982).
[CrossRef] [PubMed]

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

1981 (2)

C. Owsley, R. Sekuler, C. Boldt, “Aging and low-contrast vision: face perception,” Invest. Ophthalmol. Vis. Sci. 21, 362–365 (1981).
[PubMed]

B. L. Lundh, G. Derefeldt, S. Nyberg, G. Lennerstrand, “Picture simulation of contrast sensitivity in organic and functional amblyopia,” Acta Ophthalmol. 59, 774–783 (1981).

1977 (1)

D. H. Kelly, “Visual contrast sensitivity,” Opt. Acta 24, 107–129 (1977).
[CrossRef]

1975 (2)

M. A. Georgeson, G. D. Sullivan, “Contrast constancy: deblurring in human vision by spatial frequency channels,” J. Physiol. (London) 252, 627–656 (1975).

C. F. Stromeyer, S. Klein, “Evidence against narrowband spatial frequency channels in human vision: the detectability of frequency modulated gratings,” Vision Res. 15, 899–910 (1975).
[CrossRef]

Albrecht, D. G.

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

Arend, L.

E. Peli, R. Goldstein, G. Young, L. Arend, “Contrast sensitivity functions for analysis and simulation of visual perception,” in Digest of the Topical Meeting on Noninvasive Assessment of the Visual System (Optical Society of America, Washington, D.C., 1990).

Badcock, D. R.

D. R. Badcock, “Spatial phase or luminance profile discrimination?” Vision Res. 24, 613–623 (1984).
[CrossRef] [PubMed]

Banton, T. A.

D. S. Loshin, T. A. Banton, “Local contrast requirements for Facial recognition in patients with central field defects,” Invest. Ophthalmol. Vis. Sci. Suppl. 29, 43 (1988).

Barlow, H. B.

A. B. Watson, H. B. Barlow, J. G. Robson, “What does the eye see best?” Nature (London) 302, 419–422 (1983).
[CrossRef]

Boldt, C.

C. Owsley, R. Sekuler, C. Boldt, “Aging and low-contrast vision: face perception,” Invest. Ophthalmol. Vis. Sci. 21, 362–365 (1981).
[PubMed]

Bowen, R. W.

R. W. Bowen, J. Pokorny, V. C. Smith, “Sawtooth contrast sensitivity: decrements have the edge,” Vision Res. 298, 1501–1509 (1989).

Bradley, A.

R. F. Hess, A. Bradley, L. Piotrowski, “Contrast-coding in amblyopia. I. Differences in the neural basis of human amblyopia,” Proc. R. Soc. London Ser. B 217, 309–330 (1983).
[CrossRef]

Briers, J. D.

J. D. Briers, A. F. Fercher, “Retinal blood-flow visualization by means of laser speckle photography,” Invest. Ophthalmol. Vis. Sci. 22, 255–259 (1982).
[PubMed]

Burr, D. C.

M. C. Morrone, D. C. Burr, “Feature detection in human vision: a phase-dependent energy model,” Proc. R. Soc. London Ser. B 235, 221–245 (1988).
[CrossRef]

Cannon, M. W.

M. W. Cannon, S. C. Fullenkamp, “Perceived contrast and stimulus size: experiment and simulation,” Vision Res. 28, 695–709 (1988).
[CrossRef] [PubMed]

M. W. Cannon, “Perceived contrast in the fovea and periphery,” J. Opt. Soc. Am. A 2, 1760–1768 (1985).
[CrossRef] [PubMed]

De Valois, R. L.

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

Derefeldt, G.

B. L. Lundh, G. Derefeldt, S. Nyberg, G. Lennerstrand, “Picture simulation of contrast sensitivity in organic and functional amblyopia,” Acta Ophthalmol. 59, 774–783 (1981).

Encke, W.

M. Hubner, I. Rentschler, W. Encke, “Hidden-face recognition: comparing foveal and extrafoveal performance,” Hum. Neurobiol. 4, 1–7 (1985).
[PubMed]

Enroth-Cugell, C.

R. Shapley, C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” in Progress in Retinal Research, N. N. Osborne, ed. (Pergamon, Oxford, 1984), Vol. 3, pp. 263–343.
[CrossRef]

Fercher, A. F.

J. D. Briers, A. F. Fercher, “Retinal blood-flow visualization by means of laser speckle photography,” Invest. Ophthalmol. Vis. Sci. 22, 255–259 (1982).
[PubMed]

Field, D. J.

Fiorentini, A.

A. Fiorentini, L. Maffei, G. Sandini, “The role of high spatial frequencies in face perception,” Perception 12, 195–201 (1983).
[CrossRef] [PubMed]

Fullenkamp, S. C.

M. W. Cannon, S. C. Fullenkamp, “Perceived contrast and stimulus size: experiment and simulation,” Vision Res. 28, 695–709 (1988).
[CrossRef] [PubMed]

Georgeson, M. A.

M. A. Georgeson, G. D. Sullivan, “Contrast constancy: deblurring in human vision by spatial frequency channels,” J. Physiol. (London) 252, 627–656 (1975).

Ginsburg, A. P.

A. P. Ginsburg, “Visual information processing based on spatial filters constrained by biological data,” Ph.D. dissertation, Aerospace Medical Research Laboratory Rep. AMRL-TR-78-129 (University of Cambridge, Cambridge, 1978).

Goldstein, R.

E. Peli, R. Goldstein, G. Young, L. Arend, “Contrast sensitivity functions for analysis and simulation of visual perception,” in Digest of the Topical Meeting on Noninvasive Assessment of the Visual System (Optical Society of America, Washington, D.C., 1990).

Goldstein, R. B.

E. Peli, R. B. Goldstein, “Contrast in images,” in Visual Communication and Image Processing ’88, T. R. Hsing, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1001, 521–528 (1988).

Hess, R. F.

J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the human visual field with emphasis on the low spatial frequency range,” Vision Res. 29, 1133–1151 (1989).
[CrossRef]

R. F. Hess, J. S. Pointer, “Evidence for spatially local computations underlying discrimination of periodic patterns in fovea and periphery,” Vision Res. 27, 1343–1360 (1987).
[CrossRef] [PubMed]

R. F. Hess, A. Bradley, L. Piotrowski, “Contrast-coding in amblyopia. I. Differences in the neural basis of human amblyopia,” Proc. R. Soc. London Ser. B 217, 309–330 (1983).
[CrossRef]

Hilsenrath, O. A.

O. A. Hilsenrath, Y. Y. Zeevi, “Adaptive two-dimensional neighborhood sensitivity control by a one-dimensional process,” in Visual Communication and Image Processing ’88, T. R. Hsing, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1001, 717–723 (1988).

Hubner, M.

M. Hubner, I. Rentschler, W. Encke, “Hidden-face recognition: comparing foveal and extrafoveal performance,” Hum. Neurobiol. 4, 1–7 (1985).
[PubMed]

Huntley, D. T.

P. S. Schenker, D. R. Urangst, T. F. Knaak, D. T. Huntley, W. R. Patterson, “Pyramidal normalization filter: visual model with application to image understanding,” in Real Time Signal Processing V, J. Trimble, ed., Proc. Soc. Photo-Opt. Instrum. Eng.341, 99–108 (1982).
[CrossRef]

Hutman, L.

R. Sekuler, C. Owsley, L. Hutman, “Assessing spatial vision of older people,” Am. J. Optom. Physiol. Opt. 59, 961–968 (1982).
[CrossRef] [PubMed]

Kelly, D. H.

D. H. Kelly, “Visual contrast sensitivity,” Opt. Acta 24, 107–129 (1977).
[CrossRef]

Klein, S.

C. F. Stromeyer, S. Klein, “Evidence against narrowband spatial frequency channels in human vision: the detectability of frequency modulated gratings,” Vision Res. 15, 899–910 (1975).
[CrossRef]

Knaak, T. F.

P. S. Schenker, D. R. Urangst, T. F. Knaak, D. T. Huntley, W. R. Patterson, “Pyramidal normalization filter: visual model with application to image understanding,” in Real Time Signal Processing V, J. Trimble, ed., Proc. Soc. Photo-Opt. Instrum. Eng.341, 99–108 (1982).
[CrossRef]

Lawton, T. B.

T. B. Lawton, “Improved word recognition for observers with age-related maculopathies using compensation filters,” Clin. Vision Sci. 3, 125–135 (1988).

Legge, G. E.

G. S. Rubin, G. E. Legge, “Psychophysics of reading. VI. The role of contrast in low vision,” Vision Res. 29, 79–91 (1989).
[CrossRef]

G. E. Legge, G. S. Rubin, D. G. Pelli, M. M. Schleske, “Psychophysics of reading. II. Low vision,” Vision Res. 25, 253–266 (1985).
[CrossRef]

Lennerstrand, G.

B. L. Lundh, G. Derefeldt, S. Nyberg, G. Lennerstrand, “Picture simulation of contrast sensitivity in organic and functional amblyopia,” Acta Ophthalmol. 59, 774–783 (1981).

Loshin, D. S.

D. S. Loshin, T. A. Banton, “Local contrast requirements for Facial recognition in patients with central field defects,” Invest. Ophthalmol. Vis. Sci. Suppl. 29, 43 (1988).

Lundh, B. L.

B. L. Lundh, G. Derefeldt, S. Nyberg, G. Lennerstrand, “Picture simulation of contrast sensitivity in organic and functional amblyopia,” Acta Ophthalmol. 59, 774–783 (1981).

Maffei, L.

A. Fiorentini, L. Maffei, G. Sandini, “The role of high spatial frequencies in face perception,” Perception 12, 195–201 (1983).
[CrossRef] [PubMed]

Merker, B.

E. L. Schwartz, B. Merker, E. Wolfson, A. Shaw, “Applications of computer graphics and image processing to 2D and 3D modeling of the functional architecture of visual cortex,” in Digest of Meeting on Computer Graphics and Applications (Institute of Electrical and Electronics Engineers, New York, 1988), pp. 12–23.

E. L. Schwartz, B. Merker, “Computer-aided neuroanatomy differential geometry of cortical surfaces and on optimal flattening algorithm,” in Digest of Meeting on Computer Graphics and Applications (Institute of Electrical and Electronics Engineers, New York, 1986), pp. 36–49.
[CrossRef]

Michelson, A. A.

A. A. Michelson, Studies in Optics (U. Chicago Press, Chicago, Ill., 1927).

Morrone, M. C.

M. C. Morrone, D. C. Burr, “Feature detection in human vision: a phase-dependent energy model,” Proc. R. Soc. London Ser. B 235, 221–245 (1988).
[CrossRef]

Nyberg, S.

B. L. Lundh, G. Derefeldt, S. Nyberg, G. Lennerstrand, “Picture simulation of contrast sensitivity in organic and functional amblyopia,” Acta Ophthalmol. 59, 774–783 (1981).

Owsley, C.

R. Sekuler, C. Owsley, L. Hutman, “Assessing spatial vision of older people,” Am. J. Optom. Physiol. Opt. 59, 961–968 (1982).
[CrossRef] [PubMed]

C. Owsley, R. Sekuler, C. Boldt, “Aging and low-contrast vision: face perception,” Invest. Ophthalmol. Vis. Sci. 21, 362–365 (1981).
[PubMed]

Patterson, W. R.

P. S. Schenker, D. R. Urangst, T. F. Knaak, D. T. Huntley, W. R. Patterson, “Pyramidal normalization filter: visual model with application to image understanding,” in Real Time Signal Processing V, J. Trimble, ed., Proc. Soc. Photo-Opt. Instrum. Eng.341, 99–108 (1982).
[CrossRef]

Pavel, M.

Peli, E.

E. Peli, “Hilbert transform pairs mechanisms,” Invest. Ophthalmol. Vis. Sci. 30, 110 (1989).

E. Peli, T. Peli, “Image enhancement for the visually impaired,” Opt. Eng. 23, 47–51 (1984).
[CrossRef]

E. Peli, R. Goldstein, G. Young, L. Arend, “Contrast sensitivity functions for analysis and simulation of visual perception,” in Digest of the Topical Meeting on Noninvasive Assessment of the Visual System (Optical Society of America, Washington, D.C., 1990).

E. Peli, R. B. Goldstein, “Contrast in images,” in Visual Communication and Image Processing ’88, T. R. Hsing, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1001, 521–528 (1988).

Peli, T.

E. Peli, T. Peli, “Image enhancement for the visually impaired,” Opt. Eng. 23, 47–51 (1984).
[CrossRef]

Pelli, D. G.

G. E. Legge, G. S. Rubin, D. G. Pelli, M. M. Schleske, “Psychophysics of reading. II. Low vision,” Vision Res. 25, 253–266 (1985).
[CrossRef]

D. G. Pelli, “Reading and contrast adaptation,” in Digest of Topical Meeting on Applied Vision (Optical Society of America, Washington, D.C., 1989), pp. 102–103.

Peterfreund, N.

Y. Y. Zeevi, N. Peterfreund, E. Shlomot, “Pyramidal image representation in nonuniform systems,” in Visual Communications and Image Processing, ’88,T. R. Hsing, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1001, 563–571 (1988).

Piotrowski, L.

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J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the human visual field with emphasis on the low spatial frequency range,” Vision Res. 29, 1133–1151 (1989).
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R. F. Hess, J. S. Pointer, “Evidence for spatially local computations underlying discrimination of periodic patterns in fovea and periphery,” Vision Res. 27, 1343–1360 (1987).
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R. W. Bowen, J. Pokorny, V. C. Smith, “Sawtooth contrast sensitivity: decrements have the edge,” Vision Res. 298, 1501–1509 (1989).

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W. K. Pratt, Digital Image Processing, (Wiley, New York, 1978), pp. 307–344.

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G. S. Rubin, K. Siegel, “Recognition of low-pass filtered faces and letters,” Invest. Ophthalmol. Vis. Sci. Suppl. 25, 71 (1984).

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P. S. Schenker, D. R. Urangst, T. F. Knaak, D. T. Huntley, W. R. Patterson, “Pyramidal normalization filter: visual model with application to image understanding,” in Real Time Signal Processing V, J. Trimble, ed., Proc. Soc. Photo-Opt. Instrum. Eng.341, 99–108 (1982).
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G. E. Legge, G. S. Rubin, D. G. Pelli, M. M. Schleske, “Psychophysics of reading. II. Low vision,” Vision Res. 25, 253–266 (1985).
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E. L. Schwartz, B. Merker, E. Wolfson, A. Shaw, “Applications of computer graphics and image processing to 2D and 3D modeling of the functional architecture of visual cortex,” in Digest of Meeting on Computer Graphics and Applications (Institute of Electrical and Electronics Engineers, New York, 1988), pp. 12–23.

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Shaw, A.

E. L. Schwartz, B. Merker, E. Wolfson, A. Shaw, “Applications of computer graphics and image processing to 2D and 3D modeling of the functional architecture of visual cortex,” in Digest of Meeting on Computer Graphics and Applications (Institute of Electrical and Electronics Engineers, New York, 1988), pp. 12–23.

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Y. Y. Zeevi, N. Peterfreund, E. Shlomot, “Pyramidal image representation in nonuniform systems,” in Visual Communications and Image Processing, ’88,T. R. Hsing, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1001, 563–571 (1988).

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G. S. Rubin, K. Siegel, “Recognition of low-pass filtered faces and letters,” Invest. Ophthalmol. Vis. Sci. Suppl. 25, 71 (1984).

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R. W. Bowen, J. Pokorny, V. C. Smith, “Sawtooth contrast sensitivity: decrements have the edge,” Vision Res. 298, 1501–1509 (1989).

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A. Toet, L. G. van Ruyven, J. M. Valeton, “Merging thermal and visual images by contrast pyramid,” Opt. Eng. 28, 789–792 (1989).
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G. Westheimer, “The oscilloscopic view: retinal illuminance and contrast of point and line targets,” Vision Res. 25, 1097–1103 (1985).
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E. Peli, R. Goldstein, G. Young, L. Arend, “Contrast sensitivity functions for analysis and simulation of visual perception,” in Digest of the Topical Meeting on Noninvasive Assessment of the Visual System (Optical Society of America, Washington, D.C., 1990).

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M. Hubner, I. Rentschler, W. Encke, “Hidden-face recognition: comparing foveal and extrafoveal performance,” Hum. Neurobiol. 4, 1–7 (1985).
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G. S. Rubin, K. Siegel, “Recognition of low-pass filtered faces and letters,” Invest. Ophthalmol. Vis. Sci. Suppl. 25, 71 (1984).

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A. Toet, L. G. van Ruyven, J. M. Valeton, “Merging thermal and visual images by contrast pyramid,” Opt. Eng. 28, 789–792 (1989).
[CrossRef]

E. Peli, T. Peli, “Image enhancement for the visually impaired,” Opt. Eng. 23, 47–51 (1984).
[CrossRef]

Perception (1)

A. Fiorentini, L. Maffei, G. Sandini, “The role of high spatial frequencies in face perception,” Perception 12, 195–201 (1983).
[CrossRef] [PubMed]

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

R. F. Hess, A. Bradley, L. Piotrowski, “Contrast-coding in amblyopia. I. Differences in the neural basis of human amblyopia,” Proc. R. Soc. London Ser. B 217, 309–330 (1983).
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[CrossRef]

Vision Res. (10)

C. F. Stromeyer, S. Klein, “Evidence against narrowband spatial frequency channels in human vision: the detectability of frequency modulated gratings,” Vision Res. 15, 899–910 (1975).
[CrossRef]

R. W. Bowen, J. Pokorny, V. C. Smith, “Sawtooth contrast sensitivity: decrements have the edge,” Vision Res. 298, 1501–1509 (1989).

G. E. Legge, G. S. Rubin, D. G. Pelli, M. M. Schleske, “Psychophysics of reading. II. Low vision,” Vision Res. 25, 253–266 (1985).
[CrossRef]

G. S. Rubin, G. E. Legge, “Psychophysics of reading. VI. The role of contrast in low vision,” Vision Res. 29, 79–91 (1989).
[CrossRef]

M. W. Cannon, S. C. Fullenkamp, “Perceived contrast and stimulus size: experiment and simulation,” Vision Res. 28, 695–709 (1988).
[CrossRef] [PubMed]

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the human visual field with emphasis on the low spatial frequency range,” Vision Res. 29, 1133–1151 (1989).
[CrossRef]

D. R. Badcock, “Spatial phase or luminance profile discrimination?” Vision Res. 24, 613–623 (1984).
[CrossRef] [PubMed]

R. F. Hess, J. S. Pointer, “Evidence for spatially local computations underlying discrimination of periodic patterns in fovea and periphery,” Vision Res. 27, 1343–1360 (1987).
[CrossRef] [PubMed]

G. Westheimer, “The oscilloscopic view: retinal illuminance and contrast of point and line targets,” Vision Res. 25, 1097–1103 (1985).
[CrossRef] [PubMed]

Other (13)

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E. Peli, R. B. Goldstein, “Contrast in images,” in Visual Communication and Image Processing ’88, T. R. Hsing, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1001, 521–528 (1988).

W. K. Pratt, Digital Image Processing, (Wiley, New York, 1978), pp. 307–344.

P. S. Schenker, D. R. Urangst, T. F. Knaak, D. T. Huntley, W. R. Patterson, “Pyramidal normalization filter: visual model with application to image understanding,” in Real Time Signal Processing V, J. Trimble, ed., Proc. Soc. Photo-Opt. Instrum. Eng.341, 99–108 (1982).
[CrossRef]

R. Shapley, C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” in Progress in Retinal Research, N. N. Osborne, ed. (Pergamon, Oxford, 1984), Vol. 3, pp. 263–343.
[CrossRef]

E. Peli, R. Goldstein, G. Young, L. Arend, “Contrast sensitivity functions for analysis and simulation of visual perception,” in Digest of the Topical Meeting on Noninvasive Assessment of the Visual System (Optical Society of America, Washington, D.C., 1990).

E. L. Schwartz, B. Merker, E. Wolfson, A. Shaw, “Applications of computer graphics and image processing to 2D and 3D modeling of the functional architecture of visual cortex,” in Digest of Meeting on Computer Graphics and Applications (Institute of Electrical and Electronics Engineers, New York, 1988), pp. 12–23.

E. L. Schwartz, B. Merker, “Computer-aided neuroanatomy differential geometry of cortical surfaces and on optimal flattening algorithm,” in Digest of Meeting on Computer Graphics and Applications (Institute of Electrical and Electronics Engineers, New York, 1986), pp. 36–49.
[CrossRef]

Y. Y. Zeevi, N. Peterfreund, E. Shlomot, “Pyramidal image representation in nonuniform systems,” in Visual Communications and Image Processing, ’88,T. R. Hsing, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1001, 563–571 (1988).

D. G. Pelli, “Reading and contrast adaptation,” in Digest of Topical Meeting on Applied Vision (Optical Society of America, Washington, D.C., 1989), pp. 102–103.

O. A. Hilsenrath, Y. Y. Zeevi, “Adaptive two-dimensional neighborhood sensitivity control by a one-dimensional process,” in Visual Communication and Image Processing ’88, T. R. Hsing, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1001, 717–723 (1988).

The pyramidal image transform used here is conceptually identical to any of the commonly used pyramids of bandpass-filtered images. Since for our application images of equal size are used at all bands, we avoided the common approach of subsampling the images recursively, filtering, and then unsampling the reduced size images, instead; all filtering was done in the frequency domain. Thus the content of our final images in the pyramid of image scales was identical to the images that would be calculated by upsampling images obtained on a pyramid of image resolution.

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Figures (8)

Fig. 1
Fig. 1

Compound grating image as described in Eq. (10). The apparent contrast of the high-frequency component changes across the image although the amplitude is fixed.

Fig. 2
Fig. 2

Comparison between bandpass amplitude image (left) and local band-limited contrast image (right) for two spatial frequencies, 16 (top) and 32 (bottom) cycles per picture. Note the relative increase of contrast around the eyes and over dark areas in the original image (at left in Fig. 3 below).

Fig. 3
Fig. 3

Simulation of the perceived contrast image. This image was reconstructed by adding the local band-limited contrast images (right) instead of the original bandpass-filtered images (left).

Fig. 4
Fig. 4

Illustration of the different effects of linear rescaling on patterns of different spatial frequency composition. The compound gratings at the right were linearly scaled equally (2×), resulting in their respective gratings on the left. The amplitudes of the two sinusoidal components in each image pair are equal, and the high-frequency component is of the same period in all images. Note the relative increase in contrast of this component in the lower-left-hand image compared with the upper-left-hand image.

Fig. 5
Fig. 5

Simulation of the appearance of a face image (spanning 4 deg of visual angle) to a low-vision patient whose contrast sensitivity function is illustrated in Fig. 6. Top left, the original image; top right, the simulated appearance of the same image to the patient. The three rows of four images represent processing at different spatial frequencies on the pyramid. The far-left-hand image in each row is the bandpass-filtered image obtained from the original image. The second column shows the corresponding low-pass-filtered version for the same scale, i.e., all the energy below the band represented in the first column, or the local luminance mean. The third column represents the contrast images. Contrast arrays are bipolar, and a DC level of 128 has been added arbitrarily to present those arrays as images. Images in the fourth column on the far-right-hand side represent the thresholded, bandpass-filtered images. For each image in the third column, each point was tested against the threshold value illustrated in Fig. 6 for the corresponding spatial frequency. If the contrast of the image at that point is above threshold, the corresponding point from the far-left image is reproduced in the far-right column. If the contrast at a certain point is below threshold, the corresponding point is set to zero (gray) in the far-right image. The simulated appearance image (top right) is generated by summing all the images in the far-right column. Actual processing included two more rows at 2 and 32 cycles per picture (not shown).

Fig. 6
Fig. 6

Contrast detection thresholds (dotted curve) of a low-vision patient with central scotoma owing to age-related maculopathy used in the simulation of Fig. 5. Contrast detection thresholds of 15 normal observers are illustrated by the thick curve. The thin curve represents mean, radially averaged contrast spectra of five different faces.

Fig. 7
Fig. 7

Simulation of the appearance of an image to a normal observer including the nonuniform characteristic of the visual system. Simulation is carried out with the assumption of fixation at the center of the image. The technique applied is similar to the one used for Fig. 5, except that for every point in the contrast image the distance from the center of fixation in degrees of visual angle was calculated, and the contrast detection threshold corresponding to spatial frequency and retinal eccentricity was used in thresholding the images. The image at the left represents processing when the scene was considered to span 32 deg of visual angle. The image at the right represents the same image processed as if it spanned only 2 deg of visual angle. The most striking effect is the small variability across the visual field in both cases. Note that more heterogeneity is expressed over the image at the right (2 deg of visual angle).

Fig. 8
Fig. 8

Comparison of Gaussian (Gabor filters) with the cosine log filters used here, (a) Filter bank of 1-octave-wide Gaussian filters and the sum of all filters, (b) Filter bank of 1-octave-wide cosine log filters. Here the summation of all the filters adds to the unity. Note also the symmetry of the cosine log filters on a logarithmic scale.

Equations (20)

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

C = L max L min L max + L min ,
C = Δ L L ,
C = Δ L L + Δ L ,
rms = [ 1 n 1 i = 1 n ( x i x ¯ ) 2 ] 1 / 2 ,
x ¯ = 1 n i = 1 n x i .
C ( u , υ ) = 2 A ( u , υ ) DC ,
I ( x , y ) = I 0 [ 1 + C ( x , y ) ] ,
A ( u , υ ) A ( r , θ ) = F ( r , θ ) G ( r ) ,
a ( x , y ) = f ( x , y ) * g ( x , y ) ,
c ( x , y ) = a ( x , y ) l ( x , y ) ,
f ( x , y ) = I 0 ( 1 + a 1 cos w x + a 2 cos 8 w x ) ,
a 2 1 + a 1 c 8 a 2 1 a 1 .
k a 2 1 + k a 1 c 8 k a 2 1 k a 1 .
r i ( x , y ) = l i ( x , y ) l i 1 ( x , y ) = c i ( x , y ) + 1.
I 0 ( x , y ) = ln l i ( x , y ) l i 1 ( x , y ) .
F ( u , υ ) = F ( r , θ ) = L 0 ( r , θ ) + i = 1 n 1 A i ( r , θ ) + H n ( r , θ ) ,
G i ( r ) = 1 2 [ 1 + cos ( π log 2 r π i ) ] .
f ( x , y ) = l 0 ( x , y ) + i = 1 n 1 a i ( x , y ) + h n ( x , y ) .
l i ( x , y ) = l 0 ( x , y ) + j = 1 i 1 a j ( x , y ) ,
c i ( x , y ) = a i ( x , y ) l i ( x , y ) .

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