Abstract

Individual V1 neurons respond dynamically over only limited ranges of stimulus contrasts, yet we can discriminate contrasts over a wide range. Different V1 neurons cover different parts of the contrast range, and the information they provide must be pooled somehow. We describe a probabilistic pooling model that shows that populations of neurons with contrast responses like those in cat and monkey V1 would most accurately code contrasts in the range actually found in natural scenes. The pooling equation is similar to Bayes’s equation; however, explicit inclusion of prior probabilities in the inference increases coding accuracy only slightly.

© 2003 Optical Society of America

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2002 (5)

D. L. Ringach, “Spatial structure and symmetry of simple-cell receptive fields in macaque primary visual cortex,” J. Neurophysiol. 88, 455–463 (2002).
[PubMed]

L. L. Kontsevich, C. C. Chen, C. W. Tyler, “Separating the effects of response nonlinearity and internal noise psychophysically,” Vision Res. 42, 1771–1784 (2002).
[CrossRef] [PubMed]

A. Gottschalk, “Derivation of the visual contrast response function by maximizing information rate,” Neural Comput. 14, 527–542 (2002).
[CrossRef] [PubMed]

D. L. Ringach, R. Shapley, M. J. Hawken, “Orientation selectivity in macaque V1: diversity and laminar dependence,” J. Neurosci. 22, 5639–5651 (2002).
[PubMed]

W. S. Geisler, R. L. Diehl, “Bayesian natural selection and the evolution of perceptual systems,” Philos. Trans. R. Soc. London, Ser. B 357, 419–448 (2002).

2000 (4)

N. Brady, D. J. Field, “Local contrast in natural images: normalisation and coding efficiency,” Perception 29, 1041–1055 (2000).
[CrossRef]

Y. Tadmor, D. J. Tolhurst, “Calculating the contrasts that retinal ganglion cells and LGN neurons encounter in natural scenes,” Vision Res. 40, 3145–3157 (2000).
[CrossRef]

D. J. Heeger, A. Huk, W. S. Geisler, D. G. Albrecht, “Spikes versus BOLD: What does neuroimaging tell us about neuronal activity?” Nat. Neurosci. 3, 631–633 (2000).
[CrossRef] [PubMed]

W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2000).
[CrossRef]

1999 (1)

G. M. Boynton, J. B. Demb, G. H. Glover, D. J. Heeger, “Neuronal basis of contrast discrimination,” Vision Res. 39, 257–269 (1999).
[CrossRef] [PubMed]

1998 (2)

J. H. van Hateren, A. van der Schaaf, “Independent component filters of natural images compared with simple cells in primary visual cortex,” Proc. R. Soc. London Ser. B 265, 359–366 (1998).
[CrossRef]

F. Sengpiel, R. J. Baddeley, T. C. B. Freeman, R. Harrad, C. Blakemore, “Different mechanisms underlie three inhibitory phenomena in cat area 17,” Vision Res. 38, 2067–2080 (1998).
[CrossRef] [PubMed]

1997 (3)

W. S. Geisler, D. G. Albrecht, “Visual cortex neurons in monkeys and cats: detection, discrimination and identification,” Visual Neurosci. 14, 897–919 (1997).
[CrossRef]

B. A. Olshausen, D. J. Field, “Sparse coding with an overcomplete basis set: a strategy employed by V1?” Vision Res. 37, 3311–3325 (1997).
[CrossRef]

D. L. Ringach, M. J. Hawken, R. Shapley, “Dynamics of orientation tuning in macaque primary visual cortex,” Nature 387, 281–284 (1997).
[CrossRef] [PubMed]

1996 (2)

M. N. Shadlen, K. H. Britten, W. T. Newsome, J. A. Movshon, “A computational analysis of the relationship between neuronal and behavioural responses to visual motion,” J. Neurosci. 16, 1486–1510 (1996).
[PubMed]

D. J. Tolhurst, “The limited contrast-response of single neurons in cat striate cortex and the distribution of contrasts in natural scenes,” J. Physiol. (London) 497, 64P (1996).

1995 (2)

W. S. Geisler, D. G. Albrecht, “Bayesian analysis of identification in monkey visual cortex: nonlinear mechanisms and stimulus certainty,” Vision Res. 35, 2723–2730 (1995).
[CrossRef] [PubMed]

A. Anzai, M. A. Bearse, R. D. Freeman, D. Q. Cai, “Contrast coding by cells in the cat’s striate cortex,” Visual Neurosci. 12, 77–93 (1995).
[CrossRef]

1994 (2)

D. L. Ruderman, “The statistics of natural images,” Network 5, 517–548 (1994).
[CrossRef]

Y. Tadmor, D. J. Tolhurst, “Discrimination of changes in the second-order statistics of natural and synthetic images,” Vision Res. 34, 541–554 (1994).
[CrossRef] [PubMed]

1992 (4)

D. J. Heeger, “Half-squaring in responses of cat striate cortex,” Visual Neurosci. 9, 427–443 (1992).
[CrossRef]

D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–197 (1992).
[CrossRef]

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

G. C. De Angelis, J. G. Robson, I. Ohzawa, R. D. Freeman, “Spatiotemporal organization of simple-cell receptive fields in the cat’s striate cortex,” J. Neurophysiol. 68, 144–163 (1992).

1991 (1)

R. J. Baddeley, P. J. Hancock, “A statistical analysis of natural images matches psychophysically derived orientation tuning curves,” Proc. R. Soc. London Ser. B 246, 219–223 (1991).
[CrossRef]

1990 (2)

G. Sclar, J. H. R. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
[CrossRef] [PubMed]

E. Peli, “Contrast in complex images,” J. Opt. Soc. Am. A 7, 2032–2040 (1990).
[CrossRef] [PubMed]

1989 (3)

A. B. Bonds, “Role of inhibition in the specification of orientation selectivity of cells in the cat striate cortex,” Visual Neurosci. 2, 41–55 (1989).
[CrossRef]

R. Vogels, W. Spileers, G. A. Orban, “The response variability of striate cortical neurons in the behaving monkey,” Exp. Brain Res. 77, 432–436 (1989).
[CrossRef] [PubMed]

D. J. Tolhurst, “The amount of information transmitted about contrast by neurons in the cat’s visual cortex,” Visual Neurosci. 2, 409–413 (1989).
[CrossRef]

1987 (4)

A. Bradley, B. C. Skottun, I. Ohzawa, G. Sclar, R. D. Freeman, “Visual orientation and spatial frequency discrimination: a comparison of single neurons and behavior,” J. Neurophysiol. 57, 755–771 (1987).
[PubMed]

J. P. Jones, A. Stepnowski, L. A. Palmer, “The two-dimensional spectral structure of simple cell receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1212–1232 (1987).
[PubMed]

J. P. Jones, L. A. Palmer, “The two-dimensional spatial structure of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1187–1211 (1987).
[PubMed]

J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).
[PubMed]

1986 (1)

D. J. Field, D. J. Tolhurst, “The structure and symmetry of simple-cell receptive field profiles in the cat’s visual cortex,” Proc. R. Soc. London Ser. B 228, 379–400 (1986).
[CrossRef]

1985 (1)

I. Ohzawa, G. Sclar, R. D. Freeman, “Contrast gain control in the cat’s visual system,” J. Neurophysiol. 54, 651–665 (1985).
[PubMed]

1983 (1)

D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[CrossRef] [PubMed]

1982 (4)

D. G. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,” J. Neurophysiol. 48, 217–237 (1982).
[PubMed]

R. L. De Valois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (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]

M. V. Srinivasan, S. Laughlin, A. Dubs, “Predictive coding: A fresh view of inhibition in the retina,” Proc. R. Soc. London Ser. B 216, 427–459 (1982).
[CrossRef]

1981 (3)

D. J. Tolhurst, I. D. Thompson, “On the variety of spatial frequency selectivities shown by neurons in area 17 of the cat,” Proc. R. Soc. London B213, 183–199 (1981).
[CrossRef]

D. J. Tolhurst, J. A. Movshon, I. D. Thompson, “The dependence of response amplitude and variance of cat visual cortical neuron on stimulus contrast,” Exp. Brain Res. 41, 414–419 (1981).

S. Laughlin, “A Simple Coding Procedure Enhances a Neuron’s Information Capacity,” Z. Naturforsch. Teil C 36, 910–912 (1981).

1980 (1)

S. Marcelja, “Mathematical description of the responses of simple cortical cells,” J. Opt. Soc. Am. A 70, 1297–1300 (1980).
[CrossRef]

1978 (1)

J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurons in areas 17 and 18 of the cat’s visual cortex,” J. Physiol. (London) 283, 101–120 (1978).

1975 (1)

C. Blakemore, R. C. van Sluyters, “Innate and environmental factors in the development of the kitten’s visual cortex,” J. Physiol. (London) 248, 663–716 (1975).

1970 (1)

C. Blakemore, G. F. Cooper, “Development of the brain depends on visual environment,” Nature 228, 477–478 (1970).
[CrossRef] [PubMed]

1966 (1)

K. I. Naka, W. A. H. Rushton, “S-potentials from colour units in the retina of fish (Cyprinidae),” J. Physiol. (London) 185, 536–555 (1966).

1962 (1)

D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex,” J. Physiol. (London) 160, 106–154 (1962).

1959 (1)

D. H. Hubel, T. N. Wiesel, “Receptive fields of single neurones in the cat’s striate cortex,” J. Physiol. (London) 148, 574–591 (1959).

Albrecht, D. G.

D. J. Heeger, A. Huk, W. S. Geisler, D. G. Albrecht, “Spikes versus BOLD: What does neuroimaging tell us about neuronal activity?” Nat. Neurosci. 3, 631–633 (2000).
[CrossRef] [PubMed]

W. S. Geisler, D. G. Albrecht, “Visual cortex neurons in monkeys and cats: detection, discrimination and identification,” Visual Neurosci. 14, 897–919 (1997).
[CrossRef]

W. S. Geisler, D. G. Albrecht, “Bayesian analysis of identification in monkey visual cortex: nonlinear mechanisms and stimulus certainty,” Vision Res. 35, 2723–2730 (1995).
[CrossRef] [PubMed]

D. G. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,” J. Neurophysiol. 48, 217–237 (1982).
[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]

Anzai, A.

A. Anzai, M. A. Bearse, R. D. Freeman, D. Q. Cai, “Contrast coding by cells in the cat’s striate cortex,” Visual Neurosci. 12, 77–93 (1995).
[CrossRef]

Baddeley, R. J.

F. Sengpiel, R. J. Baddeley, T. C. B. Freeman, R. Harrad, C. Blakemore, “Different mechanisms underlie three inhibitory phenomena in cat area 17,” Vision Res. 38, 2067–2080 (1998).
[CrossRef] [PubMed]

R. J. Baddeley, P. J. Hancock, “A statistical analysis of natural images matches psychophysically derived orientation tuning curves,” Proc. R. Soc. London Ser. B 246, 219–223 (1991).
[CrossRef]

Bearse, M. A.

A. Anzai, M. A. Bearse, R. D. Freeman, D. Q. Cai, “Contrast coding by cells in the cat’s striate cortex,” Visual Neurosci. 12, 77–93 (1995).
[CrossRef]

Blakemore, C.

F. Sengpiel, R. J. Baddeley, T. C. B. Freeman, R. Harrad, C. Blakemore, “Different mechanisms underlie three inhibitory phenomena in cat area 17,” Vision Res. 38, 2067–2080 (1998).
[CrossRef] [PubMed]

C. Blakemore, R. C. van Sluyters, “Innate and environmental factors in the development of the kitten’s visual cortex,” J. Physiol. (London) 248, 663–716 (1975).

C. Blakemore, G. F. Cooper, “Development of the brain depends on visual environment,” Nature 228, 477–478 (1970).
[CrossRef] [PubMed]

Bonds, A. B.

A. B. Bonds, “Role of inhibition in the specification of orientation selectivity of cells in the cat striate cortex,” Visual Neurosci. 2, 41–55 (1989).
[CrossRef]

Boynton, G. M.

G. M. Boynton, J. B. Demb, G. H. Glover, D. J. Heeger, “Neuronal basis of contrast discrimination,” Vision Res. 39, 257–269 (1999).
[CrossRef] [PubMed]

Bradley, A.

A. Bradley, B. C. Skottun, I. Ohzawa, G. Sclar, R. D. Freeman, “Visual orientation and spatial frequency discrimination: a comparison of single neurons and behavior,” J. Neurophysiol. 57, 755–771 (1987).
[PubMed]

Brady, N.

N. Brady, D. J. Field, “Local contrast in natural images: normalisation and coding efficiency,” Perception 29, 1041–1055 (2000).
[CrossRef]

Britten, K. H.

M. N. Shadlen, K. H. Britten, W. T. Newsome, J. A. Movshon, “A computational analysis of the relationship between neuronal and behavioural responses to visual motion,” J. Neurosci. 16, 1486–1510 (1996).
[PubMed]

Cai, D. Q.

A. Anzai, M. A. Bearse, R. D. Freeman, D. Q. Cai, “Contrast coding by cells in the cat’s striate cortex,” Visual Neurosci. 12, 77–93 (1995).
[CrossRef]

Chao, Tang

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

Chen, C. C.

L. L. Kontsevich, C. C. Chen, C. W. Tyler, “Separating the effects of response nonlinearity and internal noise psychophysically,” Vision Res. 42, 1771–1784 (2002).
[CrossRef] [PubMed]

Chirimuuta, M.

P. L. Clatworthy, M. Chirimuuta, J. S. Lauritzen, D. J. Tolhurst, “Coding of the contrasts in natural images by populations of neurons in striate visual cortex (V1),” Vision Res. (to be published).

Clatworthy, P. L.

P. L. Clatworthy, M. Chirimuuta, J. S. Lauritzen, D. J. Tolhurst, “Coding of the contrasts in natural images by populations of neurons in striate visual cortex (V1),” Vision Res. (to be published).

Cooper, G. F.

C. Blakemore, G. F. Cooper, “Development of the brain depends on visual environment,” Nature 228, 477–478 (1970).
[CrossRef] [PubMed]

De Angelis, G. C.

G. C. De Angelis, J. G. Robson, I. Ohzawa, R. D. Freeman, “Spatiotemporal organization of simple-cell receptive fields in the cat’s striate cortex,” J. Neurophysiol. 68, 144–163 (1992).

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]

R. L. De Valois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef] [PubMed]

Dean, A. F.

D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
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M. V. Srinivasan, S. Laughlin, A. Dubs, “Predictive coding: A fresh view of inhibition in the retina,” Proc. R. Soc. London Ser. B 216, 427–459 (1982).
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D. J. Field, D. J. Tolhurst, “The structure and symmetry of simple-cell receptive field profiles in the cat’s visual cortex,” Proc. R. Soc. London Ser. B 228, 379–400 (1986).
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A. Anzai, M. A. Bearse, R. D. Freeman, D. Q. Cai, “Contrast coding by cells in the cat’s striate cortex,” Visual Neurosci. 12, 77–93 (1995).
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G. C. De Angelis, J. G. Robson, I. Ohzawa, R. D. Freeman, “Spatiotemporal organization of simple-cell receptive fields in the cat’s striate cortex,” J. Neurophysiol. 68, 144–163 (1992).

A. Bradley, B. C. Skottun, I. Ohzawa, G. Sclar, R. D. Freeman, “Visual orientation and spatial frequency discrimination: a comparison of single neurons and behavior,” J. Neurophysiol. 57, 755–771 (1987).
[PubMed]

I. Ohzawa, G. Sclar, R. D. Freeman, “Contrast gain control in the cat’s visual system,” J. Neurophysiol. 54, 651–665 (1985).
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F. Sengpiel, R. J. Baddeley, T. C. B. Freeman, R. Harrad, C. Blakemore, “Different mechanisms underlie three inhibitory phenomena in cat area 17,” Vision Res. 38, 2067–2080 (1998).
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W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2000).
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W. S. Geisler, R. L. Diehl, “Bayesian natural selection and the evolution of perceptual systems,” Philos. Trans. R. Soc. London, Ser. B 357, 419–448 (2002).

W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2000).
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D. J. Heeger, A. Huk, W. S. Geisler, D. G. Albrecht, “Spikes versus BOLD: What does neuroimaging tell us about neuronal activity?” Nat. Neurosci. 3, 631–633 (2000).
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G. M. Boynton, J. B. Demb, G. H. Glover, D. J. Heeger, “Neuronal basis of contrast discrimination,” Vision Res. 39, 257–269 (1999).
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D. G. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,” J. Neurophysiol. 48, 217–237 (1982).
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F. Sengpiel, R. J. Baddeley, T. C. B. Freeman, R. Harrad, C. Blakemore, “Different mechanisms underlie three inhibitory phenomena in cat area 17,” Vision Res. 38, 2067–2080 (1998).
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D. L. Ringach, R. Shapley, M. J. Hawken, “Orientation selectivity in macaque V1: diversity and laminar dependence,” J. Neurosci. 22, 5639–5651 (2002).
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D. L. Ringach, M. J. Hawken, R. Shapley, “Dynamics of orientation tuning in macaque primary visual cortex,” Nature 387, 281–284 (1997).
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D. J. Heeger, A. Huk, W. S. Geisler, D. G. Albrecht, “Spikes versus BOLD: What does neuroimaging tell us about neuronal activity?” Nat. Neurosci. 3, 631–633 (2000).
[CrossRef] [PubMed]

G. M. Boynton, J. B. Demb, G. H. Glover, D. J. Heeger, “Neuronal basis of contrast discrimination,” Vision Res. 39, 257–269 (1999).
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D. J. Heeger, “Half-squaring in responses of cat striate cortex,” Visual Neurosci. 9, 427–443 (1992).
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D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–197 (1992).
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R. L. De Valois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
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Hubel, D. H.

D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex,” J. Physiol. (London) 160, 106–154 (1962).

D. H. Hubel, T. N. Wiesel, “Receptive fields of single neurones in the cat’s striate cortex,” J. Physiol. (London) 148, 574–591 (1959).

Huk, A.

D. J. Heeger, A. Huk, W. S. Geisler, D. G. Albrecht, “Spikes versus BOLD: What does neuroimaging tell us about neuronal activity?” Nat. Neurosci. 3, 631–633 (2000).
[CrossRef] [PubMed]

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J. P. Jones, A. Stepnowski, L. A. Palmer, “The two-dimensional spectral structure of simple cell receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1212–1232 (1987).
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J. P. Jones, L. A. Palmer, “The two-dimensional spatial structure of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1187–1211 (1987).
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J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).
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L. L. Kontsevich, C. C. Chen, C. W. Tyler, “Separating the effects of response nonlinearity and internal noise psychophysically,” Vision Res. 42, 1771–1784 (2002).
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M. V. Srinivasan, S. Laughlin, A. Dubs, “Predictive coding: A fresh view of inhibition in the retina,” Proc. R. Soc. London Ser. B 216, 427–459 (1982).
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P. L. Clatworthy, M. Chirimuuta, J. S. Lauritzen, D. J. Tolhurst, “Coding of the contrasts in natural images by populations of neurons in striate visual cortex (V1),” Vision Res. (to be published).

J. S. Lauritzen, A. Pelah, D. J. Tolhurst, “Perceptual rules for watermarking images: A psychophysical study of the visual basis for digital pattern encryption,” in Human Vision and Electronic Imaging IV, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3644, 392–402 (1999).

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G. Sclar, J. H. R. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
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P. Mamassian, M. Landy, L. T. Maloney, “Bayesian modeling of visual perception,” in Probabilistic Models of the Brain, R. P. N. Rao, B. A. Olshausen, M. S. Lewicki, eds. (MIT Press, Cambridge, Mass., 2002).

Mamassian, P.

P. Mamassian, M. Landy, L. T. Maloney, “Bayesian modeling of visual perception,” in Probabilistic Models of the Brain, R. P. N. Rao, B. A. Olshausen, M. S. Lewicki, eds. (MIT Press, Cambridge, Mass., 2002).

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G. Sclar, J. H. R. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
[CrossRef] [PubMed]

Movshon, J. A.

M. N. Shadlen, K. H. Britten, W. T. Newsome, J. A. Movshon, “A computational analysis of the relationship between neuronal and behavioural responses to visual motion,” J. Neurosci. 16, 1486–1510 (1996).
[PubMed]

D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[CrossRef] [PubMed]

D. J. Tolhurst, J. A. Movshon, I. D. Thompson, “The dependence of response amplitude and variance of cat visual cortical neuron on stimulus contrast,” Exp. Brain Res. 41, 414–419 (1981).

J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurons in areas 17 and 18 of the cat’s visual cortex,” J. Physiol. (London) 283, 101–120 (1978).

Naka, K. I.

K. I. Naka, W. A. H. Rushton, “S-potentials from colour units in the retina of fish (Cyprinidae),” J. Physiol. (London) 185, 536–555 (1966).

Newsome, W. T.

M. N. Shadlen, K. H. Britten, W. T. Newsome, J. A. Movshon, “A computational analysis of the relationship between neuronal and behavioural responses to visual motion,” J. Neurosci. 16, 1486–1510 (1996).
[PubMed]

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G. C. De Angelis, J. G. Robson, I. Ohzawa, R. D. Freeman, “Spatiotemporal organization of simple-cell receptive fields in the cat’s striate cortex,” J. Neurophysiol. 68, 144–163 (1992).

A. Bradley, B. C. Skottun, I. Ohzawa, G. Sclar, R. D. Freeman, “Visual orientation and spatial frequency discrimination: a comparison of single neurons and behavior,” J. Neurophysiol. 57, 755–771 (1987).
[PubMed]

I. Ohzawa, G. Sclar, R. D. Freeman, “Contrast gain control in the cat’s visual system,” J. Neurophysiol. 54, 651–665 (1985).
[PubMed]

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B. A. Olshausen, D. J. Field, “Sparse coding with an overcomplete basis set: a strategy employed by V1?” Vision Res. 37, 3311–3325 (1997).
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R. Vogels, W. Spileers, G. A. Orban, “The response variability of striate cortical neurons in the behaving monkey,” Exp. Brain Res. 77, 432–436 (1989).
[CrossRef] [PubMed]

Palmer, L. A.

J. P. Jones, L. A. Palmer, “The two-dimensional spatial structure of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1187–1211 (1987).
[PubMed]

J. P. Jones, A. Stepnowski, L. A. Palmer, “The two-dimensional spectral structure of simple cell receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1212–1232 (1987).
[PubMed]

J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).
[PubMed]

Pelah, A.

J. S. Lauritzen, A. Pelah, D. J. Tolhurst, “Perceptual rules for watermarking images: A psychophysical study of the visual basis for digital pattern encryption,” in Human Vision and Electronic Imaging IV, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3644, 392–402 (1999).

Peli, E.

Perry, J. S.

W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2000).
[CrossRef]

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D. L. Ringach, “Spatial structure and symmetry of simple-cell receptive fields in macaque primary visual cortex,” J. Neurophysiol. 88, 455–463 (2002).
[PubMed]

D. L. Ringach, R. Shapley, M. J. Hawken, “Orientation selectivity in macaque V1: diversity and laminar dependence,” J. Neurosci. 22, 5639–5651 (2002).
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D. L. Ringach, M. J. Hawken, R. Shapley, “Dynamics of orientation tuning in macaque primary visual cortex,” Nature 387, 281–284 (1997).
[CrossRef] [PubMed]

D. L. Ringach, Departments of Neurobiology and Psychology, Franz Hall, Room 8441B, University of California, LosAngeles, Los Angeles, California 90095-1563 (personal communication, 2002).

Robson, J. G.

G. C. De Angelis, J. G. Robson, I. Ohzawa, R. D. Freeman, “Spatiotemporal organization of simple-cell receptive fields in the cat’s striate cortex,” J. Neurophysiol. 68, 144–163 (1992).

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D. L. Ruderman, “The statistics of natural images,” Network 5, 517–548 (1994).
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K. I. Naka, W. A. H. Rushton, “S-potentials from colour units in the retina of fish (Cyprinidae),” J. Physiol. (London) 185, 536–555 (1966).

Sclar, G.

G. Sclar, J. H. R. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
[CrossRef] [PubMed]

A. Bradley, B. C. Skottun, I. Ohzawa, G. Sclar, R. D. Freeman, “Visual orientation and spatial frequency discrimination: a comparison of single neurons and behavior,” J. Neurophysiol. 57, 755–771 (1987).
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I. Ohzawa, G. Sclar, R. D. Freeman, “Contrast gain control in the cat’s visual system,” J. Neurophysiol. 54, 651–665 (1985).
[PubMed]

Sengpiel, F.

F. Sengpiel, R. J. Baddeley, T. C. B. Freeman, R. Harrad, C. Blakemore, “Different mechanisms underlie three inhibitory phenomena in cat area 17,” Vision Res. 38, 2067–2080 (1998).
[CrossRef] [PubMed]

Shadlen, M. N.

M. N. Shadlen, K. H. Britten, W. T. Newsome, J. A. Movshon, “A computational analysis of the relationship between neuronal and behavioural responses to visual motion,” J. Neurosci. 16, 1486–1510 (1996).
[PubMed]

Shapley, R.

D. L. Ringach, R. Shapley, M. J. Hawken, “Orientation selectivity in macaque V1: diversity and laminar dependence,” J. Neurosci. 22, 5639–5651 (2002).
[PubMed]

D. L. Ringach, M. J. Hawken, R. Shapley, “Dynamics of orientation tuning in macaque primary visual cortex,” Nature 387, 281–284 (1997).
[CrossRef] [PubMed]

Skottun, B. C.

A. Bradley, B. C. Skottun, I. Ohzawa, G. Sclar, R. D. Freeman, “Visual orientation and spatial frequency discrimination: a comparison of single neurons and behavior,” J. Neurophysiol. 57, 755–771 (1987).
[PubMed]

Spileers, W.

R. Vogels, W. Spileers, G. A. Orban, “The response variability of striate cortical neurons in the behaving monkey,” Exp. Brain Res. 77, 432–436 (1989).
[CrossRef] [PubMed]

Srinivasan, M. V.

M. V. Srinivasan, S. Laughlin, A. Dubs, “Predictive coding: A fresh view of inhibition in the retina,” Proc. R. Soc. London Ser. B 216, 427–459 (1982).
[CrossRef]

Stepnowski, A.

J. P. Jones, A. Stepnowski, L. A. Palmer, “The two-dimensional spectral structure of simple cell receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1212–1232 (1987).
[PubMed]

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W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2000).
[CrossRef]

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Y. Tadmor, D. J. Tolhurst, “Calculating the contrasts that retinal ganglion cells and LGN neurons encounter in natural scenes,” Vision Res. 40, 3145–3157 (2000).
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Y. Tadmor, D. J. Tolhurst, “Discrimination of changes in the second-order statistics of natural and synthetic images,” Vision Res. 34, 541–554 (1994).
[CrossRef] [PubMed]

D. J. Tolhurst, Y. Tadmor, Tang Chao, “The amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229–232 (1992).
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Thompson, I. D.

D. J. Tolhurst, I. D. Thompson, “On the variety of spatial frequency selectivities shown by neurons in area 17 of the cat,” Proc. R. Soc. London B213, 183–199 (1981).
[CrossRef]

D. J. Tolhurst, J. A. Movshon, I. D. Thompson, “The dependence of response amplitude and variance of cat visual cortical neuron on stimulus contrast,” Exp. Brain Res. 41, 414–419 (1981).

J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurons in areas 17 and 18 of the cat’s visual cortex,” J. Physiol. (London) 283, 101–120 (1978).

Thorell, L. 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).
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Tolhurst, D. J.

Y. Tadmor, D. J. Tolhurst, “Calculating the contrasts that retinal ganglion cells and LGN neurons encounter in natural scenes,” Vision Res. 40, 3145–3157 (2000).
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D. J. Tolhurst, “The limited contrast-response of single neurons in cat striate cortex and the distribution of contrasts in natural scenes,” J. Physiol. (London) 497, 64P (1996).

Y. Tadmor, D. J. Tolhurst, “Discrimination of changes in the second-order statistics of natural and synthetic images,” Vision Res. 34, 541–554 (1994).
[CrossRef] [PubMed]

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

D. J. Tolhurst, “The amount of information transmitted about contrast by neurons in the cat’s visual cortex,” Visual Neurosci. 2, 409–413 (1989).
[CrossRef]

D. J. Field, D. J. Tolhurst, “The structure and symmetry of simple-cell receptive field profiles in the cat’s visual cortex,” Proc. R. Soc. London Ser. B 228, 379–400 (1986).
[CrossRef]

D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[CrossRef] [PubMed]

D. J. Tolhurst, J. A. Movshon, I. D. Thompson, “The dependence of response amplitude and variance of cat visual cortical neuron on stimulus contrast,” Exp. Brain Res. 41, 414–419 (1981).

D. J. Tolhurst, I. D. Thompson, “On the variety of spatial frequency selectivities shown by neurons in area 17 of the cat,” Proc. R. Soc. London B213, 183–199 (1981).
[CrossRef]

J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurons in areas 17 and 18 of the cat’s visual cortex,” J. Physiol. (London) 283, 101–120 (1978).

J. S. Lauritzen, A. Pelah, D. J. Tolhurst, “Perceptual rules for watermarking images: A psychophysical study of the visual basis for digital pattern encryption,” in Human Vision and Electronic Imaging IV, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3644, 392–402 (1999).

P. L. Clatworthy, M. Chirimuuta, J. S. Lauritzen, D. J. Tolhurst, “Coding of the contrasts in natural images by populations of neurons in striate visual cortex (V1),” Vision Res. (to be published).

Tyler, C. W.

L. L. Kontsevich, C. C. Chen, C. W. Tyler, “Separating the effects of response nonlinearity and internal noise psychophysically,” Vision Res. 42, 1771–1784 (2002).
[CrossRef] [PubMed]

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J. H. van Hateren, A. van der Schaaf, “Independent component filters of natural images compared with simple cells in primary visual cortex,” Proc. R. Soc. London Ser. B 265, 359–366 (1998).
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J. H. van Hateren, A. van der Schaaf, “Independent component filters of natural images compared with simple cells in primary visual cortex,” Proc. R. Soc. London Ser. B 265, 359–366 (1998).
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van Sluyters, R. C.

C. Blakemore, R. C. van Sluyters, “Innate and environmental factors in the development of the kitten’s visual cortex,” J. Physiol. (London) 248, 663–716 (1975).

Vogels, R.

R. Vogels, W. Spileers, G. A. Orban, “The response variability of striate cortical neurons in the behaving monkey,” Exp. Brain Res. 77, 432–436 (1989).
[CrossRef] [PubMed]

Wiesel, T. N.

D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex,” J. Physiol. (London) 160, 106–154 (1962).

D. H. Hubel, T. N. Wiesel, “Receptive fields of single neurones in the cat’s striate cortex,” J. Physiol. (London) 148, 574–591 (1959).

Yund, E. W.

R. L. De Valois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef] [PubMed]

Exp. Brain Res. (2)

D. J. Tolhurst, J. A. Movshon, I. D. Thompson, “The dependence of response amplitude and variance of cat visual cortical neuron on stimulus contrast,” Exp. Brain Res. 41, 414–419 (1981).

R. Vogels, W. Spileers, G. A. Orban, “The response variability of striate cortical neurons in the behaving monkey,” Exp. Brain Res. 77, 432–436 (1989).
[CrossRef] [PubMed]

J. Neurophysiol. (8)

D. G. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,” J. Neurophysiol. 48, 217–237 (1982).
[PubMed]

A. Bradley, B. C. Skottun, I. Ohzawa, G. Sclar, R. D. Freeman, “Visual orientation and spatial frequency discrimination: a comparison of single neurons and behavior,” J. Neurophysiol. 57, 755–771 (1987).
[PubMed]

J. P. Jones, A. Stepnowski, L. A. Palmer, “The two-dimensional spectral structure of simple cell receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1212–1232 (1987).
[PubMed]

J. P. Jones, L. A. Palmer, “The two-dimensional spatial structure of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1187–1211 (1987).
[PubMed]

G. C. De Angelis, J. G. Robson, I. Ohzawa, R. D. Freeman, “Spatiotemporal organization of simple-cell receptive fields in the cat’s striate cortex,” J. Neurophysiol. 68, 144–163 (1992).

D. L. Ringach, “Spatial structure and symmetry of simple-cell receptive fields in macaque primary visual cortex,” J. Neurophysiol. 88, 455–463 (2002).
[PubMed]

J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).
[PubMed]

I. Ohzawa, G. Sclar, R. D. Freeman, “Contrast gain control in the cat’s visual system,” J. Neurophysiol. 54, 651–665 (1985).
[PubMed]

J. Neurosci. (2)

D. L. Ringach, R. Shapley, M. J. Hawken, “Orientation selectivity in macaque V1: diversity and laminar dependence,” J. Neurosci. 22, 5639–5651 (2002).
[PubMed]

M. N. Shadlen, K. H. Britten, W. T. Newsome, J. A. Movshon, “A computational analysis of the relationship between neuronal and behavioural responses to visual motion,” J. Neurosci. 16, 1486–1510 (1996).
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J. Opt. Soc. Am. A (2)

E. Peli, “Contrast in complex images,” J. Opt. Soc. Am. A 7, 2032–2040 (1990).
[CrossRef] [PubMed]

S. Marcelja, “Mathematical description of the responses of simple cortical cells,” J. Opt. Soc. Am. A 70, 1297–1300 (1980).
[CrossRef]

J. Physiol. (London) (6)

C. Blakemore, R. C. van Sluyters, “Innate and environmental factors in the development of the kitten’s visual cortex,” J. Physiol. (London) 248, 663–716 (1975).

D. H. Hubel, T. N. Wiesel, “Receptive fields of single neurones in the cat’s striate cortex,” J. Physiol. (London) 148, 574–591 (1959).

D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex,” J. Physiol. (London) 160, 106–154 (1962).

J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurons in areas 17 and 18 of the cat’s visual cortex,” J. Physiol. (London) 283, 101–120 (1978).

K. I. Naka, W. A. H. Rushton, “S-potentials from colour units in the retina of fish (Cyprinidae),” J. Physiol. (London) 185, 536–555 (1966).

D. J. Tolhurst, “The limited contrast-response of single neurons in cat striate cortex and the distribution of contrasts in natural scenes,” J. Physiol. (London) 497, 64P (1996).

Nat. Neurosci. (1)

D. J. Heeger, A. Huk, W. S. Geisler, D. G. Albrecht, “Spikes versus BOLD: What does neuroimaging tell us about neuronal activity?” Nat. Neurosci. 3, 631–633 (2000).
[CrossRef] [PubMed]

Nature (2)

D. L. Ringach, M. J. Hawken, R. Shapley, “Dynamics of orientation tuning in macaque primary visual cortex,” Nature 387, 281–284 (1997).
[CrossRef] [PubMed]

C. Blakemore, G. F. Cooper, “Development of the brain depends on visual environment,” Nature 228, 477–478 (1970).
[CrossRef] [PubMed]

Network (1)

D. L. Ruderman, “The statistics of natural images,” Network 5, 517–548 (1994).
[CrossRef]

Neural Comput. (1)

A. Gottschalk, “Derivation of the visual contrast response function by maximizing information rate,” Neural Comput. 14, 527–542 (2002).
[CrossRef] [PubMed]

Ophthalmic Physiol. Opt. (1)

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

Perception (1)

N. Brady, D. J. Field, “Local contrast in natural images: normalisation and coding efficiency,” Perception 29, 1041–1055 (2000).
[CrossRef]

Philos. Trans. R. Soc. London, Ser. B (1)

W. S. Geisler, R. L. Diehl, “Bayesian natural selection and the evolution of perceptual systems,” Philos. Trans. R. Soc. London, Ser. B 357, 419–448 (2002).

Proc. R. Soc. London (1)

D. J. Tolhurst, I. D. Thompson, “On the variety of spatial frequency selectivities shown by neurons in area 17 of the cat,” Proc. R. Soc. London B213, 183–199 (1981).
[CrossRef]

Proc. R. Soc. London Ser. B (4)

D. J. Field, D. J. Tolhurst, “The structure and symmetry of simple-cell receptive field profiles in the cat’s visual cortex,” Proc. R. Soc. London Ser. B 228, 379–400 (1986).
[CrossRef]

M. V. Srinivasan, S. Laughlin, A. Dubs, “Predictive coding: A fresh view of inhibition in the retina,” Proc. R. Soc. London Ser. B 216, 427–459 (1982).
[CrossRef]

J. H. van Hateren, A. van der Schaaf, “Independent component filters of natural images compared with simple cells in primary visual cortex,” Proc. R. Soc. London Ser. B 265, 359–366 (1998).
[CrossRef]

R. J. Baddeley, P. J. Hancock, “A statistical analysis of natural images matches psychophysically derived orientation tuning curves,” Proc. R. Soc. London Ser. B 246, 219–223 (1991).
[CrossRef]

Vision Res. (12)

G. M. Boynton, J. B. Demb, G. H. Glover, D. J. Heeger, “Neuronal basis of contrast discrimination,” Vision Res. 39, 257–269 (1999).
[CrossRef] [PubMed]

L. L. Kontsevich, C. C. Chen, C. W. Tyler, “Separating the effects of response nonlinearity and internal noise psychophysically,” Vision Res. 42, 1771–1784 (2002).
[CrossRef] [PubMed]

D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[CrossRef] [PubMed]

W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2000).
[CrossRef]

B. A. Olshausen, D. J. Field, “Sparse coding with an overcomplete basis set: a strategy employed by V1?” Vision Res. 37, 3311–3325 (1997).
[CrossRef]

R. L. De Valois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (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]

Y. Tadmor, D. J. Tolhurst, “Calculating the contrasts that retinal ganglion cells and LGN neurons encounter in natural scenes,” Vision Res. 40, 3145–3157 (2000).
[CrossRef]

G. Sclar, J. H. R. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
[CrossRef] [PubMed]

F. Sengpiel, R. J. Baddeley, T. C. B. Freeman, R. Harrad, C. Blakemore, “Different mechanisms underlie three inhibitory phenomena in cat area 17,” Vision Res. 38, 2067–2080 (1998).
[CrossRef] [PubMed]

W. S. Geisler, D. G. Albrecht, “Bayesian analysis of identification in monkey visual cortex: nonlinear mechanisms and stimulus certainty,” Vision Res. 35, 2723–2730 (1995).
[CrossRef] [PubMed]

Y. Tadmor, D. J. Tolhurst, “Discrimination of changes in the second-order statistics of natural and synthetic images,” Vision Res. 34, 541–554 (1994).
[CrossRef] [PubMed]

Visual Neurosci. (6)

A. B. Bonds, “Role of inhibition in the specification of orientation selectivity of cells in the cat striate cortex,” Visual Neurosci. 2, 41–55 (1989).
[CrossRef]

W. S. Geisler, D. G. Albrecht, “Visual cortex neurons in monkeys and cats: detection, discrimination and identification,” Visual Neurosci. 14, 897–919 (1997).
[CrossRef]

D. J. Tolhurst, “The amount of information transmitted about contrast by neurons in the cat’s visual cortex,” Visual Neurosci. 2, 409–413 (1989).
[CrossRef]

A. Anzai, M. A. Bearse, R. D. Freeman, D. Q. Cai, “Contrast coding by cells in the cat’s striate cortex,” Visual Neurosci. 12, 77–93 (1995).
[CrossRef]

D. J. Heeger, “Half-squaring in responses of cat striate cortex,” Visual Neurosci. 9, 427–443 (1992).
[CrossRef]

D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–197 (1992).
[CrossRef]

Z. Naturforsch. Teil C (1)

S. Laughlin, “A Simple Coding Procedure Enhances a Neuron’s Information Capacity,” Z. Naturforsch. Teil C 36, 910–912 (1981).

Other (5)

P. Mamassian, M. Landy, L. T. Maloney, “Bayesian modeling of visual perception,” in Probabilistic Models of the Brain, R. P. N. Rao, B. A. Olshausen, M. S. Lewicki, eds. (MIT Press, Cambridge, Mass., 2002).

D. Marr, Vision (Freeman, San Francisco, Calif., 1982).

J. S. Lauritzen, A. Pelah, D. J. Tolhurst, “Perceptual rules for watermarking images: A psychophysical study of the visual basis for digital pattern encryption,” in Human Vision and Electronic Imaging IV, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3644, 392–402 (1999).

D. L. Ringach, Departments of Neurobiology and Psychology, Franz Hall, Room 8441B, University of California, LosAngeles, Los Angeles, California 90095-1563 (personal communication, 2002).

P. L. Clatworthy, M. Chirimuuta, J. S. Lauritzen, D. J. Tolhurst, “Coding of the contrasts in natural images by populations of neurons in striate visual cortex (V1),” Vision Res. (to be published).

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