Abstract

Spatial filters that mimic receptive fields of visual cortex neurons provide an efficient representation of achromatic image structure, but the extension of this idea to chromatic information is at an early stage. Relatively few studies have looked at the statistical relationships between the modeled responses to natural scenes of the luminance (LUM), red–green (RG), and blue–yellow (BY) postreceptoral channels of the primate visual system. Here we consider the correlations among these channel responses in terms of pixel, first-order, and second-order information. First-order linear filtering was implemented by convolving the cosine-windowed images with oriented Gabor functions, whose gains were scaled to give equal amplitude response across spatial frequency to random fractal images. Second-order filtering was implemented via a filter–rectify–filter cascade, with Gabor functions for both first- and second-stage filters. Both signed and unsigned filter responses were obtained across a range of filter parameters (spatial frequency, 264  cyclesimage; orientation, 0–135°). The filter responses to the LUM channel images were larger than those for either RG or BY channel images. Cross correlations between the first-order channel responses and between the first- and second-order channel responses were measured. Results showed that the unsigned correlations between first-order channel responses were higher than expected on the basis of previous studies and that first-order channel responses were highly correlated with LUM, but not with RG or BY, second-order responses. These findings imply that course-scale color information correlates well with course-scale changes of fine-scale texture.

© 2005 Optical Society of America

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2005 (2)

F. A.A. Kingdom, S. Rangwala, K. Hamammji, “Chromatic properties of the colour-shading effect,” Vision Res. 45, 1425–1437 (2005).
[CrossRef] [PubMed]

G. D. Horwitz, E. J. Chichilnisky, T. D. Albright, “Blue-yellow signals are enhanced by spatiotemporal luminance contrast in Macaque VI,” J. Neurosci. 93, 2263–2278 (2005).

2004 (4)

F. A.A. Kingdom, C. Beauce, L. Hunter, “Colour vision brings clarity to shadows,” Perception 33, 907–914 (2004).
[CrossRef] [PubMed]

A. P. Johnson, C. J. Baker, “First- and second-order information in natural images: a new view of what second-order sees,” J. Opt. Soc. Am. A 21, 913–925 (2004).
[CrossRef]

A. P. Johnson, C. J. Baker, “Sparse coding in first- and second-order filtered images,” J. Vision 4, 542 (2004).
[CrossRef]

B. A. Olshausen, D. J. Field, “Sparse coding of sensory inputs,” Curr. Opin. Neurobiol. 14, 481–487 (2004).
[CrossRef] [PubMed]

2003 (2)

2002 (3)

J. Golz, D. I.A. MacLeod, “Influence of scene statistics on colour constancy,” Nature 415, 637–640 (2002).
[CrossRef] [PubMed]

N. Prins, F. A.A. Kingdom, “Orientation- and frequency-modulated textures at low depths of modulation are processed by off-orientation and off-frequency texture mechanisms,” Vision Res. 42, 705–713 (2002).
[CrossRef] [PubMed]

C. A. Parraga, T. Troscianko, D. J. Tolhurst, “Spatiochromatic properties of natural images and human vision,” Curr. Biol. 12, 483–487 (2002).
[CrossRef] [PubMed]

2001 (7)

M. G.A. Thomson, “Beats, kurtosis and visual coding,” Network Comput. Neural Syst. 12, 271–287 (2001).
[CrossRef]

H. B. Barlow, “Redundancy reduction revisited,” Network Comput. Neural Syst. 12, 241–253 (2001).
[CrossRef]

E. N. Johnson, M. J. Hawken, Robert Shapley, “The spatial transformation of colour in the primary visual cortex of the macaque monkey,” Nat. Neurosci. 4, 409–416 (2001).
[CrossRef] [PubMed]

N. Graham, S. Wolfson, “A note about preferred orientations at the first and second stages of complex (second-order) texture channels,” J. Opt. Soc. Am. A 18, 2273–2281 (2001).
[CrossRef]

D. Knill, “Contour into texture: information content of surface contours and texture flow,” J. Opt. Soc. Am. A 18, 12–35 (2001).
[CrossRef]

P. Mamassian, M. S. Landy, “Interaction of prior visual constraints,” Vision Res. 41, 2653–2668 (2001).
[CrossRef] [PubMed]

E. N. Johnson, M. J. Hawken, R. Shapley, “The spatial transformation of color in the primary visual cortex of the macaque monkey,” Nat. Neurosci. 4, 409–416 (2001).
[CrossRef] [PubMed]

2000 (1)

A. J. Schofield, “What does second-order vision see in an image?” Perception 29, 1071–1086 (2000).
[CrossRef]

1999 (7)

F. A.A. Kingdom, D. R.T. Keeble, “On the mechanism for scale invariance in orientation-defined textures,” Vision Res. 39, 1477–1489 (1999).
[CrossRef] [PubMed]

C. L. Baker, “Central neural mechanisms for detecting second-order motion” Curr. Opin. Neurobiol. 9, 461–466 (1999).
[CrossRef] [PubMed]

K. T. Mullen, M. J. Sankeralli, “Evidence for the stochastic independence of the blue-yellow, red-green and luminance detection mechanisms revealed by subthreshold summation,” Vision Res. 39, 733–745 (1999).
[CrossRef] [PubMed]

K. T. Mullen, M. A. Losada, “The spatial tuning of color and luminance peripheral vision measured with notch filtered noise masking,” Vision Res. 39, 721–731 (1999).
[CrossRef] [PubMed]

A. J. Schofield, M. A. Georgeson, “Sensitivity to modulations of luminance and contrast in visual white noise: separate mechanisms with similar behaviour,” Vision Res. 39, 2697–2716 (1999).
[CrossRef] [PubMed]

M. G.A. Thomson, “Visual coding and the phase structure of natural scenes,” Network Comput. Neural Syst. 10, 123–132 (1999).
[CrossRef]

M. G.A. Thomson, “Higher-order structure in natural scenes,” J. Opt. Soc. Am. A 16, 1549–1553 (1999).
[CrossRef]

1998 (4)

D. L. Ruderman, T. W. Cronin, C.-C. Chiao, “Statistics of cone responses to natural images: implications for visual coding,” J. Opt. Soc. Am. A 15, 2036–2045 (1998).
[CrossRef]

C. A. Parraga, G. Brelstaf, T. Troscianko, I. R. Moorehead, “Color and luminance information in natural scenes,” J. Opt. Soc. Am. A 15, 563–569 (1998).
[CrossRef]

I. Mareschal, C. L. Baker, “Temporal and spatial response to second-order stimuli in cat A18,” J. Neurophysiol. 80, 2811–2823 (1998).
[PubMed]

N. Graham, A. Sutter, “Spatial summation in simple (Fourier) and complex (non-Fourier) channels in texture segregation,” Vision Res. 38, 231–257 (1998).
[CrossRef] [PubMed]

1997 (6)

A. Chaudhuri, T. D. Albright, “Neuronal responses to edges defined by luminance vs. temporal texture in macaque area V1,” Visual Neurosci. 14, 949–962 (1997).
[CrossRef]

M. A. Webster, J. D. Mollon, “Adaptation and the color statistics of natural images,” Vision Res. 37, 3283–3298 (1997).
[CrossRef]

D. J. Field, N. Brady, “Visual sensitivity, blur and the sources of variability in the amplitude spectra of natural scenes,” Vision Res. 37, 3367–3384 (1997).
[CrossRef]

A. T. Smith, T. Ledgeway, “Separate detection of moving luminance and contrast modulations: fact or artefact?” Vision Res. 37, 45–62 (1997).
[CrossRef] [PubMed]

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]

M. J. Sankeralli, K. T. Mullen, “Postreceptoral chromatic detection mechanisms revealed by noise masking in three-dimensional cone contrast space,” J. Opt. Soc. Am. A 14, 906–915 (1997).
[CrossRef]

1996 (2)

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

Y.-X. Zhou, C. L. Baker, “Spatial properties of envelope responses in area 17 and 18 of the cat,” J. Neurophysiol. 75, 1038–1050 (1996).
[PubMed]

1995 (1)

A. Sutter, G. Sperling, C. Chubb, “Measuring the spatial frequency selectivity of second-order texture mechanisms,” Vision Res. 35, 915–924 (1995).
[CrossRef] [PubMed]

1994 (2)

T. Ledgeway, A. T. Smith, “Evidence for separate motion-detecting mechanisms for first- and second-order motion in human vision,” Vision Res. 34, 2727–2740 (1994).
[CrossRef] [PubMed]

D. J. Field, “What is the goal of sensory coding,” Neural Comput. 6, 559–601 (1994).
[CrossRef]

1993 (5)

R. A. Humanski, H. R. Wilson, “Spatial-frequency adaptation: evidence for a multiple channel model of short-wavelength-sensitive cone spatial vision,” Vision Res. 33, 665–675 (1993).
[CrossRef] [PubMed]

N. Graham, A. Sutter, C. Venkatesan, “Spatial-frequency- and orientation-selectivity of simple and complex channels in region segregation,” Vision Res. 33, 1893–1911 (1993).
[CrossRef] [PubMed]

G. R. Cole, T. Hine, W. McIlhagga, “Detection mechanisms in L-, M-, and S-cone contrast space,” J. Opt. Soc. Am. A 10, 38–51 (1993).
[CrossRef] [PubMed]

N. Sekiguchi, D. R. Williams, D. H. Brainard, “Aberration-free measurements of the visibility of isoluminant gratings,” J. Opt. Soc. Am. A 10, 2105–2117 (1993).
[CrossRef]

A. B. Poirson, B. A. Wandell, “The appearance of colored patterns: pattern-color separability,” J. Opt. Soc. Am. A 12, 2458–2471 (1993).
[CrossRef]

1992 (4)

H. R. Wilson, V. P. Ferrera, C. Y. O, “A psychophysically motivated model for two-dimensional motion perception,” Visual Neurosci. 9, 79–97 (1992).
[CrossRef]

K. R. Gegenfurtner, D. C. Kiper, “Contrast detection in luminance and chromatic noise,” J. Opt. Soc. Am. A 9, 1880–1888 (1992).
[CrossRef] [PubMed]

T. D. Albright, “Form-cue invariant motion processing in primate visual cortex,” Science 255, 1141–1143 (1992).
[CrossRef] [PubMed]

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

1988 (2)

C. Chubb, G. Sperling, “Drift-balanced random stimuli: a general basis for studying non-Fourier motion perception,” J. Opt. Soc. Am. A 5, 1986–2007 (1988).
[CrossRef] [PubMed]

A. Bradley, E. Switkes, K. DeValois, “Orientation and spatial frequency selectivity of adaptation to color and luminance gratings,” Vision Res. 28, 841–856 (1988).
[CrossRef] [PubMed]

1987 (2)

1985 (3)

J. G. Daugman, “Uncertainty relations for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,” J. Opt. Soc. Am. A 2, 1160–1169 (1985).
[CrossRef] [PubMed]

K. Mullen, “The contrast sensitivity of human colour vision to red-green and blue-yellow chromatic gratings,” J. Physiol. (London) 359, 381–400 (1985).

C. F. Stromeyer, G. R. Cole, R. E. Kronauer, “Second-site adaptation in the red-green chromatic pathways,” Vision Res. 25, 219–237 (1985).
[CrossRef] [PubMed]

1984 (1)

M. Livingstone, D. H. Hubel, “Anatomy and physiology of a color system in the primate visual cortex,” J. Neurosci. 4, 309–356 (1984).
[PubMed]

1983 (2)

G. Buchsbaum, A. Gottschalk, “Trichromacy, opponent colour coding and optimum colour information transmission in the retina,” Proc. R. Soc. London, Ser. B 220, 89–113 (1983).
[CrossRef]

C. Norlander, J. J. Koenderink, “Spatial and temporal discrimination ellipsoids in color space,” J. Opt. Soc. Am. 73, 1533–1543 (1983).
[CrossRef]

1982 (2)

J. Krauskopf, D. H. Williams, D. W. Heeley, “Cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982).
[CrossRef] [PubMed]

J. M. Rubin, W. A. Richards, “Color vision and image intensities: When are changes material?” Biol. Cybern. 45, 215–226 (1982).
[CrossRef] [PubMed]

1975 (1)

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

1972 (1)

H. B. Barlow, “Single units and sensation: a neuron doctrine for perceptual psychology?” Perception 1, 371–394 (1972).
[CrossRef] [PubMed]

Adelson, E. H.

M. F. Tappen, W. T. Freeman, E. H. Adelson, “Recovering intrinsic images from a single image,” in Advances in Neural Information Processing Systems, (NIPS, MIT Press, 2003), Vol. 15, pp. 1343-1350.

Albright, T. D.

G. D. Horwitz, E. J. Chichilnisky, T. D. Albright, “Blue-yellow signals are enhanced by spatiotemporal luminance contrast in Macaque VI,” J. Neurosci. 93, 2263–2278 (2005).

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Appl. Opt. (1)

Biol. Cybern. (1)

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Curr. Biol. (1)

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Curr. Opin. Neurobiol. (2)

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J. Neurophysiol. (2)

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J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (15)

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Figures (5)

Fig. 1
Fig. 1

Channel image representations. A typical RGB database image is first converted into L-, M-, and S-cone-sampled images, which are then combined to produce LUM, chromatic RG, and chromatic BY channel images. Note that channel values have been scaled to maximize available range. We also include the edge maps of each channel image to show the relationships among structural features.

Fig. 2
Fig. 2

Example of first-order model (top) and FRF cascade (bottom). The first-order model convolves each channel image with a single Gabor filter to detect luminance/chromatic variations. The FRF (second-order) model convolves each channel image with a high-spatial-frequency Gabor filter (F1) whose square rectified response is then convolved with a second Gabor (F2) having a lower spatial frequency to detect luminance/chromatic texture variations. In this example, the first-order (F0) and second-order (F2) filters (shown at magnified scale) have the same orientation, phase, and spatial frequency.

Fig. 3
Fig. 3

Correlation between signed first-order channel responses as a function of spatial frequency (cycles per image), averaged over filter orientation and even/odd phase from an ensemble of natural scenes ( n = 80 ) . (a) Circles correspond to correlations between LUM-with-RG channels, squares to LUM-with-BY, and triangles to RG-with-BY. For comparison, the solid symbols show the corresponding correlations for the raw pixels. Error bars denote the standard error across images and filter responses. (b) Sample of LUM, RG, and BY filter responses from a typical image ranging from low spatial frequency (left) to high spatial frequency (right), with the filter orientation of 0° (i.e., vertical) and odd-symmetric phase (90°).

Fig. 4
Fig. 4

Correlations between unsigned first-order channel responses as a function of spatial frequency (cycles per image), averaged over filter orientation and phase for the ensemble of images ( n = 80 ) . Responses were full-wave rectified to remove the directionality of response. Circles correspond to correlations between LUM and RG channels, squares to LUM and BY, and triangles to RG and BY. Error bars denote the standard error across images and filter responses.

Fig. 5
Fig. 5

Correlation between first-order (F0) and second-order (F2) responses as a function of spatial frequency ratio, averaged across the ensemble of natural scenes ( n = 80 ) and averaged across other filter parameters satisfying the constraint that the early-stage (F1) to late-stage (F2) of the FRF ratio equals 8:1 or 4:1 (optimal ratios of FRF[49] with similar response): (a) signed correlation of all three first-order channels (LUM, RG, BY) with second-order LUM; (b) unsigned correlation for all three channels with second-order LUM; (c) unsigned correlation with second-order RG; (d) unsigned correlation with second-order BY. Note that first-order chromatic channels correlate more strongly with second-order luminance channel than with either of the second-order chromatic channels.

Equations (8)

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

LUM = L + M ,
RG = ( L M ) ( L + M ) ,
BY = S LUM S + LUM .
g λ θ ϕ σ ( x , y ) = A exp [ ( x 2 + y 2 ) 2 σ 2 ] cos [ 2 π ( x λ ) + Φ ] ,
x = x cos θ + y sin θ ,
y = x sin θ + y cos θ ,
[ Input of F 2 ] = [ Output of F 1 ] 2 .
R = ( a x y b x y ) [ ( a x y 2 ) × ( b x y 2 ) ] 0.5 ,

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