Abstract

Both long-wavelength-sensitive (L) and medium-wavelength-sensitive (M) cones contribute to luminance mechanisms in human vision. This means that luminance and chromatic signals may be confounded. We use power spectra from natural images to estimate the magnitude of the corruption of luminance signals encoded by an array of retinal ganglion cells resembling the primate magnocellular neurons. The magnitude of this corruption is dependent on the cone lattice and is most severe where cones form clumps of a single spectral type. We find that chromatic corruption may equal or exceed the amplitude of other sources of noise and so could impose constraints on visual performance and on eye design.

© 1998 Optical Society of America

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    [CrossRef] [PubMed]
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1996 (4)

S. Marcos, R. Navarro, P. Artal, “Coherent imaging of the cone mosaic in the living human eye,” J. Opt. Soc. Am. A 13, 897–905 (1996).
[CrossRef]

D. T. Miller, D. R. Williams, G. M. Morris, J. Z. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[CrossRef] [PubMed]

A. van der Schaaf, J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
[CrossRef] [PubMed]

O. Packer, D. R. Williams, D. G. Bensinger, “Photopigment transmittance imaging of the primate photoreceptor mosaic,” J. Neurosci. 16, 2251–2260 (1996).
[PubMed]

1994 (1)

D. L. Ruderman, W. Bialek, “Statistics of natural images: scaling in the woods,” Phys. Rev. Lett. 73, 814–817 (1994).
[CrossRef] [PubMed]

1993 (3)

D. R. Williams, N. Sekiguchi, D. Brainard, “Color, contrast sensitivity, and the cone mosaic,” Proc. Natl. Acad. Sci. USA 90, 9770–9777 (1993).
[CrossRef] [PubMed]

B. B. Lee, C. Werhahn, G. Westheimer, J. Kremers, “Macaque ganglion cell responses to stimuli that elicit hyperacuity in man: detection of small displacements,” J. Neurosci. 13, 1001–1009 (1993).
[PubMed]

M. G. Nagle, D. Osorio, “The tuning of human photopigments may minimize red–green chromatic signals in natural conditions,” Proc. R. Soc. London Ser. B 252, 209–213 (1993).
[CrossRef]

1992 (4)

D. Osorio, T. R. J. Bossomaier, “Human cone-pigment sensitivities and the reflectances of natural surfaces,” Biol. Cybern. 67, 217–222 (1992).
[CrossRef]

J. D. Mollon, J. K. Bowmaker, “The spatial arrangement of cones in the primate fovea,” Nature (London) 360, 677–679 (1992).
[CrossRef]

C. A. Curcio, K. R. Sloan, “Packing geometry of human cone photoreceptors—variation with eccentricity and evidence for local anisotropy,” Visual Neurosci. 9, 169–180 (1992).

D. J. Tolhurst, Y. Tadmor, T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229–232 (1992).
[CrossRef] [PubMed]

1991 (1)

M. J. Morgan, “Decoding the retinal colour signal,” Curr. Biol. 1, 215–217 (1991).
[CrossRef] [PubMed]

1990 (2)

P. K. Kaiser, B. B. Lee, P. R. Martin, A. Valberg, “The physiological basis of the minimally distinct border demonstrated in the ganglion cells of the macaque retina,” J. Physiol. (London) 422, 153–183 (1990).

E. Kaplan, B. B. Lee, R. M. Shapley, “New views of primate retinal function,” Prog. Retinal Res. 9, 273–336 (1990).
[CrossRef]

1987 (3)

1986 (1)

A. W. Snyder, T. R. J. Bossomaier, A. Hughes, “Optical image quality and the cone mosaic,” Science 231, 499–501 (1986).
[CrossRef] [PubMed]

1985 (1)

V. H. Perry, A. Cowey, “The ganglion cell and cone distributions in the monkey’s retina: implications for central magnification factors,” Vision Res. 25, 1795–1810 (1985).
[CrossRef]

1984 (1)

A. M. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 219–240 (1984).

1981 (1)

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

1979 (1)

D. H. Kelly, “Motion and vision. II. Stabilized spatio-temporal surface,” J. Opt. Soc. Am. A 69, 1340–1349 (1979).
[CrossRef]

1975 (1)

V. C. Smith, J. Pokorny, “Spectral sensitivities of human foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

Artal, P.

Bensinger, D. G.

O. Packer, D. R. Williams, D. G. Bensinger, “Photopigment transmittance imaging of the primate photoreceptor mosaic,” J. Neurosci. 16, 2251–2260 (1996).
[PubMed]

Bialek, W.

D. L. Ruderman, W. Bialek, “Statistics of natural images: scaling in the woods,” Phys. Rev. Lett. 73, 814–817 (1994).
[CrossRef] [PubMed]

Bossomaier, T. R. J.

D. Osorio, T. R. J. Bossomaier, “Human cone-pigment sensitivities and the reflectances of natural surfaces,” Biol. Cybern. 67, 217–222 (1992).
[CrossRef]

A. W. Snyder, T. R. J. Bossomaier, A. Hughes, “Optical image quality and the cone mosaic,” Science 231, 499–501 (1986).
[CrossRef] [PubMed]

Bowmaker, J. K.

J. D. Mollon, J. K. Bowmaker, “The spatial arrangement of cones in the primate fovea,” Nature (London) 360, 677–679 (1992).
[CrossRef]

Brainard, D.

D. R. Williams, N. Sekiguchi, D. Brainard, “Color, contrast sensitivity, and the cone mosaic,” Proc. Natl. Acad. Sci. USA 90, 9770–9777 (1993).
[CrossRef] [PubMed]

D. R. Williams, N. Sekiguchi, W. Haake, D. Brainard, O. Packer, “The cost of trichromacy for spatial vision,” in From Pigments to Perception, A. Valberg, B. B. Lee, eds. (Plenum, New York, 1991), pp. 11–22.

Burton, G. R.

Chao, T.

D. J. Tolhurst, Y. Tadmor, T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229–232 (1992).
[CrossRef] [PubMed]

Cowey, A.

V. H. Perry, A. Cowey, “The ganglion cell and cone distributions in the monkey’s retina: implications for central magnification factors,” Vision Res. 25, 1795–1810 (1985).
[CrossRef]

Curcio, C. A.

C. A. Curcio, K. R. Sloan, “Packing geometry of human cone photoreceptors—variation with eccentricity and evidence for local anisotropy,” Visual Neurosci. 9, 169–180 (1992).

Derrington, A. M.

A. M. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 219–240 (1984).

Field, D. J.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Haake, W.

D. R. Williams, N. Sekiguchi, W. Haake, D. Brainard, O. Packer, “The cost of trichromacy for spatial vision,” in From Pigments to Perception, A. Valberg, B. B. Lee, eds. (Plenum, New York, 1991), pp. 11–22.

Hubel, D. H.

M. S. Livingstone, D. H. Hubel, “Psychophysical evidence for separate channels for the perception of form, color, movement, and depth,” J. Neurosci. 7, 3416–3468 (1987).
[PubMed]

Hughes, A.

A. W. Snyder, T. R. J. Bossomaier, A. Hughes, “Optical image quality and the cone mosaic,” Science 231, 499–501 (1986).
[CrossRef] [PubMed]

Kaiser, P. K.

P. K. Kaiser, B. B. Lee, P. R. Martin, A. Valberg, “The physiological basis of the minimally distinct border demonstrated in the ganglion cells of the macaque retina,” J. Physiol. (London) 422, 153–183 (1990).

Kaplan, E.

E. Kaplan, B. B. Lee, R. M. Shapley, “New views of primate retinal function,” Prog. Retinal Res. 9, 273–336 (1990).
[CrossRef]

Kelly, D. H.

D. H. Kelly, “Motion and vision. II. Stabilized spatio-temporal surface,” J. Opt. Soc. Am. A 69, 1340–1349 (1979).
[CrossRef]

Kremers, J.

B. B. Lee, C. Werhahn, G. Westheimer, J. Kremers, “Macaque ganglion cell responses to stimuli that elicit hyperacuity in man: detection of small displacements,” J. Neurosci. 13, 1001–1009 (1993).
[PubMed]

Lee, B. B.

B. B. Lee, C. Werhahn, G. Westheimer, J. Kremers, “Macaque ganglion cell responses to stimuli that elicit hyperacuity in man: detection of small displacements,” J. Neurosci. 13, 1001–1009 (1993).
[PubMed]

E. Kaplan, B. B. Lee, R. M. Shapley, “New views of primate retinal function,” Prog. Retinal Res. 9, 273–336 (1990).
[CrossRef]

P. K. Kaiser, B. B. Lee, P. R. Martin, A. Valberg, “The physiological basis of the minimally distinct border demonstrated in the ganglion cells of the macaque retina,” J. Physiol. (London) 422, 153–183 (1990).

Lennie, P.

A. M. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 219–240 (1984).

Liang, J. Z.

D. T. Miller, D. R. Williams, G. M. Morris, J. Z. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[CrossRef] [PubMed]

Lim, J. S.

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Livingstone, M. S.

M. S. Livingstone, D. H. Hubel, “Psychophysical evidence for separate channels for the perception of form, color, movement, and depth,” J. Neurosci. 7, 3416–3468 (1987).
[PubMed]

Marcos, S.

Marks, R. J.

R. J. Marks, Introduction to Shannon Sampling and Interpolation Theory (Springer-Verlag, New York, 1991).

Martin, P. R.

P. K. Kaiser, B. B. Lee, P. R. Martin, A. Valberg, “The physiological basis of the minimally distinct border demonstrated in the ganglion cells of the macaque retina,” J. Physiol. (London) 422, 153–183 (1990).

Miller, D. T.

D. T. Miller, D. R. Williams, G. M. Morris, J. Z. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[CrossRef] [PubMed]

Mollon, J. D.

J. D. Mollon, J. K. Bowmaker, “The spatial arrangement of cones in the primate fovea,” Nature (London) 360, 677–679 (1992).
[CrossRef]

Moorhead, I. R.

Morgan, M. J.

M. J. Morgan, “Decoding the retinal colour signal,” Curr. Biol. 1, 215–217 (1991).
[CrossRef] [PubMed]

Morris, G. M.

D. T. Miller, D. R. Williams, G. M. Morris, J. Z. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[CrossRef] [PubMed]

Nagle, M. G.

M. G. Nagle, D. Osorio, “The tuning of human photopigments may minimize red–green chromatic signals in natural conditions,” Proc. R. Soc. London Ser. B 252, 209–213 (1993).
[CrossRef]

Navarro, R.

Oppenheim, A. V.

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Osorio, D.

M. G. Nagle, D. Osorio, “The tuning of human photopigments may minimize red–green chromatic signals in natural conditions,” Proc. R. Soc. London Ser. B 252, 209–213 (1993).
[CrossRef]

D. Osorio, T. R. J. Bossomaier, “Human cone-pigment sensitivities and the reflectances of natural surfaces,” Biol. Cybern. 67, 217–222 (1992).
[CrossRef]

Packer, O.

O. Packer, D. R. Williams, D. G. Bensinger, “Photopigment transmittance imaging of the primate photoreceptor mosaic,” J. Neurosci. 16, 2251–2260 (1996).
[PubMed]

D. R. Williams, N. Sekiguchi, W. Haake, D. Brainard, O. Packer, “The cost of trichromacy for spatial vision,” in From Pigments to Perception, A. Valberg, B. B. Lee, eds. (Plenum, New York, 1991), pp. 11–22.

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw-Hill, New York, 1991).

Perry, V. H.

V. H. Perry, A. Cowey, “The ganglion cell and cone distributions in the monkey’s retina: implications for central magnification factors,” Vision Res. 25, 1795–1810 (1985).
[CrossRef]

Pokorny, J.

V. C. Smith, J. Pokorny, “Spectral sensitivities of human foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Ruderman, D. L.

D. L. Ruderman, W. Bialek, “Statistics of natural images: scaling in the woods,” Phys. Rev. Lett. 73, 814–817 (1994).
[CrossRef] [PubMed]

Sekiguchi, N.

D. R. Williams, N. Sekiguchi, D. Brainard, “Color, contrast sensitivity, and the cone mosaic,” Proc. Natl. Acad. Sci. USA 90, 9770–9777 (1993).
[CrossRef] [PubMed]

D. R. Williams, N. Sekiguchi, W. Haake, D. Brainard, O. Packer, “The cost of trichromacy for spatial vision,” in From Pigments to Perception, A. Valberg, B. B. Lee, eds. (Plenum, New York, 1991), pp. 11–22.

Shapley, R. M.

E. Kaplan, B. B. Lee, R. M. Shapley, “New views of primate retinal function,” Prog. Retinal Res. 9, 273–336 (1990).
[CrossRef]

Sloan, K. R.

C. A. Curcio, K. R. Sloan, “Packing geometry of human cone photoreceptors—variation with eccentricity and evidence for local anisotropy,” Visual Neurosci. 9, 169–180 (1992).

Smith, V. C.

V. C. Smith, J. Pokorny, “Spectral sensitivities of human foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

Snyder, A. W.

A. W. Snyder, T. R. J. Bossomaier, A. Hughes, “Optical image quality and the cone mosaic,” Science 231, 499–501 (1986).
[CrossRef] [PubMed]

Tadmor, Y.

D. J. Tolhurst, Y. Tadmor, T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229–232 (1992).
[CrossRef] [PubMed]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Tolhurst, D. J.

D. J. Tolhurst, Y. Tadmor, T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229–232 (1992).
[CrossRef] [PubMed]

Valberg, A.

P. K. Kaiser, B. B. Lee, P. R. Martin, A. Valberg, “The physiological basis of the minimally distinct border demonstrated in the ganglion cells of the macaque retina,” J. Physiol. (London) 422, 153–183 (1990).

van der Schaaf, A.

A. van der Schaaf, J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
[CrossRef] [PubMed]

van Hateren, J. H.

A. van der Schaaf, J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
[CrossRef] [PubMed]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Werhahn, C.

B. B. Lee, C. Werhahn, G. Westheimer, J. Kremers, “Macaque ganglion cell responses to stimuli that elicit hyperacuity in man: detection of small displacements,” J. Neurosci. 13, 1001–1009 (1993).
[PubMed]

Westheimer, G.

B. B. Lee, C. Werhahn, G. Westheimer, J. Kremers, “Macaque ganglion cell responses to stimuli that elicit hyperacuity in man: detection of small displacements,” J. Neurosci. 13, 1001–1009 (1993).
[PubMed]

Williams, D. R.

O. Packer, D. R. Williams, D. G. Bensinger, “Photopigment transmittance imaging of the primate photoreceptor mosaic,” J. Neurosci. 16, 2251–2260 (1996).
[PubMed]

D. T. Miller, D. R. Williams, G. M. Morris, J. Z. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[CrossRef] [PubMed]

D. R. Williams, N. Sekiguchi, D. Brainard, “Color, contrast sensitivity, and the cone mosaic,” Proc. Natl. Acad. Sci. USA 90, 9770–9777 (1993).
[CrossRef] [PubMed]

D. R. Williams, N. Sekiguchi, W. Haake, D. Brainard, O. Packer, “The cost of trichromacy for spatial vision,” in From Pigments to Perception, A. Valberg, B. B. Lee, eds. (Plenum, New York, 1991), pp. 11–22.

Appl. Opt. (1)

Biol. Cybern. (1)

D. Osorio, T. R. J. Bossomaier, “Human cone-pigment sensitivities and the reflectances of natural surfaces,” Biol. Cybern. 67, 217–222 (1992).
[CrossRef]

Curr. Biol. (1)

M. J. Morgan, “Decoding the retinal colour signal,” Curr. Biol. 1, 215–217 (1991).
[CrossRef] [PubMed]

J. Neurosci. (3)

M. S. Livingstone, D. H. Hubel, “Psychophysical evidence for separate channels for the perception of form, color, movement, and depth,” J. Neurosci. 7, 3416–3468 (1987).
[PubMed]

B. B. Lee, C. Werhahn, G. Westheimer, J. Kremers, “Macaque ganglion cell responses to stimuli that elicit hyperacuity in man: detection of small displacements,” J. Neurosci. 13, 1001–1009 (1993).
[PubMed]

O. Packer, D. R. Williams, D. G. Bensinger, “Photopigment transmittance imaging of the primate photoreceptor mosaic,” J. Neurosci. 16, 2251–2260 (1996).
[PubMed]

J. Opt. Soc. Am. A (3)

J. Physiol. (London) (2)

P. K. Kaiser, B. B. Lee, P. R. Martin, A. Valberg, “The physiological basis of the minimally distinct border demonstrated in the ganglion cells of the macaque retina,” J. Physiol. (London) 422, 153–183 (1990).

A. M. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 219–240 (1984).

Nature (London) (1)

J. D. Mollon, J. K. Bowmaker, “The spatial arrangement of cones in the primate fovea,” Nature (London) 360, 677–679 (1992).
[CrossRef]

Ophthalmic Physiol. Opt. (1)

D. J. Tolhurst, Y. Tadmor, T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229–232 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

D. L. Ruderman, W. Bialek, “Statistics of natural images: scaling in the woods,” Phys. Rev. Lett. 73, 814–817 (1994).
[CrossRef] [PubMed]

Proc. IEEE (1)

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

D. R. Williams, N. Sekiguchi, D. Brainard, “Color, contrast sensitivity, and the cone mosaic,” Proc. Natl. Acad. Sci. USA 90, 9770–9777 (1993).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. B (1)

M. G. Nagle, D. Osorio, “The tuning of human photopigments may minimize red–green chromatic signals in natural conditions,” Proc. R. Soc. London Ser. B 252, 209–213 (1993).
[CrossRef]

Prog. Retinal Res. (1)

E. Kaplan, B. B. Lee, R. M. Shapley, “New views of primate retinal function,” Prog. Retinal Res. 9, 273–336 (1990).
[CrossRef]

Science (1)

A. W. Snyder, T. R. J. Bossomaier, A. Hughes, “Optical image quality and the cone mosaic,” Science 231, 499–501 (1986).
[CrossRef] [PubMed]

Vision Res. (4)

V. H. Perry, A. Cowey, “The ganglion cell and cone distributions in the monkey’s retina: implications for central magnification factors,” Vision Res. 25, 1795–1810 (1985).
[CrossRef]

A. van der Schaaf, J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
[CrossRef] [PubMed]

V. C. Smith, J. Pokorny, “Spectral sensitivities of human foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

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Figures (9)

Fig. 1
Fig. 1

A: Measured spectra, Sϕ¯(f) (upper) and Sδϕ(f) (lower), orientationally averaged. Power-law fits are as in Eq. (8). B: Scatterplot of L and M values from within the images, showing that they are highly correlated along a 45-deg axis. This implies that (L+M)/2 and (L-M)/2 signals are decorrelated from one another, so that it is not possible to make a linear estimate of luminance information from the chromatic signal, a conclusion confirmed by more detailed analysis of these data.

Fig. 2
Fig. 2

Spatial frequency plane. Frequencies are marked in cycles per degree (cpd). The square delimits the Nyquist zone of frequencies, which will not alias when sampled by a square lattice of spacing 1/25 deg. The circle bounds the region of frequencies that are admitted by the optics.

Fig. 3
Fig. 3

Convolution with aliasing. One spectrum (zero frequency at center) is repeated (A: only a 3×3 block is shown), and the other (B) is convolved with these repeats. This yields a convolution spectrum (C: 3×3 block shown), which is then band limited (D) to frequencies within the Nyquist region (|fx| <1/2a, |fy|<1/2a).

Fig. 4
Fig. 4

Examples of lattice spectra types, their correlation functions, and spectra. A–C, alternating lattice: A, example; B, correlation function; C, spectrum, which has power only at the highest diagonal spatial frequencies. D–F, random lattice: D, example; E, correlation function, which is nonzero only at the origin; F, spectrum, which is uniform. G–I, clustered lattice: G, example; H, correlation function (zero correlation corresponds to gray near the edges); I, spectrum, with power concentrated in a narrow annulus. Dark pixels in lattice images correspond to L cones, white pixels to M cones. The center of correlation images corresponds to zero displacement, and darker pixels correspond to higher correlation. The center of spectrum images corresponds to dc, with darker pixels being higher power.

Fig. 5
Fig. 5

Example of noise spectrum when sampled by an alternating cone lattice. The original noise power spectrum is displaced so that the region of maximum power has moved to where there is no signal to corrupt. Low frequencies escape corruption altogether, and higher frequencies experience increasing noise levels. See the text for details.

Fig. 6
Fig. 6

Power spectra of luminance signal (dotted–dashed curve) and chromatic noise when sampled with an alternating lattice (dotted curve), a random lattice (solid curve), and a clustered lattice (dashed curve).

Fig. 7
Fig. 7

Signal-to-noise ratios (SNR’s) for the spectra shown in Fig. 4. Curves correspond to an alternating lattice (dotted), a random lattice (solid), and a clustered lattice (dashed).

Fig. 8
Fig. 8

Receptive field profile of (A) a difference-of-Gaussian ganglion cell as in Eq. (13) and (B) its power gain as given by the square of its Fourier transform, Eq. (14).

Fig. 9
Fig. 9

Signal and noise spectra of ganglion cell responses. The signal spectrum (dotted–dashed curve) shows a peak near 10 cpd. Noise spectra for different lattice types show varying degrees of signal corruption. The alternating lattice (dotted curve) shows minimal noise, which is present only at the highest frequencies. The random lattice (solid curve) displays fairly broadband noise. The clustered lattice (dashed curve), which was designed to maximally corrupt this channel, shows a marked peak near the peak frequency of the model magnocellular channel.

Tables (2)

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Table 1 Signal-to-Noise Ratios in Luminance Signalsa

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Table 2 Equivalent Contrast of Chromatic Noisea

Equations (15)

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ϕ¯(x)=12[L(x)+M(x)].
δϕ(x)=12[L(x)-M(x)].
ϕ(x)=ϕ¯(x)+(x)δϕ(x).
Cϕ(x)=ϕ(0)ϕ(x).
Sϕ(f)=a2xCϕ(x)exp(-2πifx),
Cϕ(x)=d2f Sϕ(f)exp(2πifx),
σ2=d2f S(f),
Sϕ¯(f)=2.7×10-3f-1.95,Sδϕ(f)=4.2×10-6f-1.75.
σϕ¯2=2π012.5df fSϕ¯(f);
σϕ¯=0.62,σδϕ=0.014.
CN(x)=C(x)Cδϕ(x).
SN(f)=qd2fS(f+f+q)Sδϕ(f),
g(r)=exp(-r2/2σ2)-1α2exp(-r2/2α2σ2).
G(f)=exp[-(2πf/25)2σ2/2]-exp[-(2πf/25)2α2σ2/2].
Σ=A2G(2.6).

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