Color constancy in natural scenes with and without an explicit illuminant cue

Abstract

Observers can generally make reliable judgments of surface color in natural scenes despite changes in an illuminant that is out of view. This ability has sometimes been attributed to observers' estimating the spectral properties of the illuminant in order to compensate for its effects. To test this hypothesis, two surface-color-matching experiments were performed with images of natural scenes obtained from high-resolution hyperspectral images. In the first experiment, the sky illuminating the scene was directly visible to the observer, and its color was manipulated. In the second experiment, a large gray sphere was introduced into the scene so that its illumination by the sun and sky was also directly visible to the observer, and the color of that illumination was manipulated. Although the degree of color constancy varied across this and other variations of the images, there was no reliable effect of illuminant color. Even when the sky was eliminated from view, color constancy did not worsen. Judging surface color in natural scenes seems to be independent of an explicit illuminant cue.

Full text

Color constancy in natural scenes with and without
an explicit illuminant cue
KINJIRO AMANO,
1
DAVID H. FOSTER,
1
and SÉRGIO M.C. NASCIMENTO
2
1Sensing, Imaging, and Signal Processing Group, School of Electrical and Electronic Engineering, University of Manchester,
Manchester, United Kingdom
2Department of Physics, Gualtar Campus, University of Minho, Braga, Portugal
(Received March 8, 2006; Accepted March 8, 2006!
Abstract
Observers can generally make reliable judgments of surface color in natural scenes despite changes in an illuminant
that is out of view. This ability has sometimes been attributed to observers’ estimating the spectral properties of the
illuminant in order to compensate for its effects. To test this hypothesis, two surface-color-matching experiments
were performed with images of natural scenes obtained from high-resolution hyperspectral images. In the first
experiment, the sky illuminating the scene was directly visible to the observer, and its color was manipulated. In the
second experiment, a large gray sphere was introduced into the scene so that its illumination by the sun and sky
was also directly visible to the observer, and the color of that illumination was manipulated. Although the degree
of color constancy varied across this and other variations of the images, there was no reliable effect of illuminant
color. Even when the sky was eliminated from view, color constancy did not worsen. Judging surface color in
natural scenes seems to be independent of an explicit illuminant cue.
Keywords: Color constancy, Sky, Natural scenes, Illuminant estimate, Spatial cone-excitation ratios, Specular
highlights
Introduction
The spectrum of the light reaching the eye from a scene depends
both on the reflecting properties of surfaces within it and on the
spectrum of the light illuminating it. Consequently, to make an
accurate judgment of the color of a particular surface, an observer
must somehow discount the effects of the illuminant ~von Helm-
holtz, 1867!, even when the illuminant itself is not directly visible.
To a variable extent, human observers are successful in this task,
that is, color constancy holds, and there is a large literature,
partially summarized elsewhere ~Foster, 2003; Smithson, 2005!,
reporting estimates of the degree of color constancy with geomet-
ric stimuli, both planar ~e.g. Arend & Reeves, 1986!and three-
dimensional ~e.g. Kraft & Brainard, 1999; de Almeida et al., 2004!.
Some theories of color constancy assume that the observer
estimates the spectral properties of the illuminant in order to
compensate for its effects, an estimation that is theoretically pos-
sible in some circumstances ~D’Zmura & Iverson, 1993a, 1993b,
1994; Maloney, 1999!. Yet just because observers can estimate the
illuminant spectrum does not necessarily imply that they do.
Certainly, for matching colored papers in Mondrian-like patterns,
it appears to be unnecessary ~Amano et al., 2005!. But is it pos-
sible that explicit information about an illuminant, rather than
indirect inference, might influence judgments, particularly in those
natural scenes where the illuminant forms part of the normal field
of view?
To test this hypothesis, two surface-color-matching experi-
ments were performed with images of natural scenes obtained
from high-resolution hyperspectral images ~Foster et al., 2004!.
The cues to the illuminant in the scenes were manipulated using an
approach that was similar to the cue-perturbation method adopted
by Yang and Maloney ~2001!~see also Linnell & Foster, 1997!.
The images used here were of an urban and a rural scene, as shown
in Fig. 1. In the first experiment, the sky ~but not the sun!
illuminating the scene was made clearly visible to the observer,
and its color was varied. The rationale was that including the sky
in the scene may or may not improve performance, since its
spectrum was consistent with the radiance spectrum of the scene,
but changing its spectrum, so that it was inconsistent with the
radiance spectrum of the scene, ought to have a biasing effect. In
fact, although the degree of color constancy varied across this and
other changes to the images, there was no reliable effect of the
color of the sky. When the sky was eliminated from view, perfor-
mance was neither better nor worse. Despite the absence of any
reliable effect of a visible sky, it might be argued that observers
were able to separate the effects of the ambient illumination it
provided from the direct illumination by the sun, and ignore the
Address correspondence and reprint requests to: Kinjiro Amano, Sens-
ing, Imaging, and Signal Processing Group, School of Electrical and
Electronic Engineering, University of Manchester, Manchester M60 1QD,
UK. E-mail: k.amano@manchester.ac.uk
Visual Neuroscience ~2006!,23, 351–356. Printed in the USA.
Copyright © 2006 Cambridge University Press 0952-5238006 $16.00
DOI: 10.10170S0952523806233285
351

former. Since there are practical problems in imaging a scene with
a visible sun, in the second experiment, a large gray sphere was
introduced into the scene so that its illumination by the sun ~and
sky!could be reliably inferred from its diffuse highlight, and the
color of the illumination on the sphere varied. Again, there was no
reliable effect of illuminant color.
Judging surface color in natural scenes seems to be indepen-
dent of explicit knowledge of the color of the illumination.
Materials and methods
Stimuli
Two natural scenes were selected from a hyperspectral image
database ~Foster et al., 2004; Foster et al., 2006a!. Hyperspec-
tral data were used to enable the accurate and independent
control of illuminant and reflectance spectra. The data were
obtained with a high-resolution hyperspectral imaging system,
based on a digital camera with a spatial resolution of 1344 ⫻
1024 pixels ~Hamamatsu, model C4742-95-12ER, Hamamatsu
Photonics K.K., Japan!with a fast tuneable liquid-crystal filter
~VariSpec, model VS-VIS2-10-HC-35-SQ, Cambridge Research
& Instrumentation, Inc., MA!mounted in front of the lens,
together with an infrared blocking filter. Peak-transmission wave-
length of the filter was varied in 10-nm steps over 400–720 nm.
Further details of the system and its calibration are given in
Foster et al. ~2004!and Foster et al. ~2006a!.
An urban scene was used for the first experiment and a rural
scene for the second experiment, as shown in Fig. 1. The urban
scene, from Porto, Portugal, consisted of a group of sixteenth–
eighteenth-century buildings and sky. The test surface was one of
the roofs in the middle of the image, which was illuminated by the
sky. The rural scene, from the Brufe region, Portugal, consisted of
fields and trees, some low farm buildings, distant mountains, and
sky. A large ~30-cm diam.!gray sphere ~painted with Munsell N7
matt emulsion paint @VeriVide Ltd., Leicester, UK#! was intro-
duced into the scene so that it reflected light from the sun, which
was to the right of the observer. The sphere was the brightest object
in the scene ~the intensity of its image was clipped in the printed
figure!, and the diffuse highlight on it gave a reliable cue to the
color of the direct illumination ~Yang & Maloney, 2001!. The test
surface was the roof of one of the farm buildings in the lower
center of the scene. In both scenes the sky occupied about a quarter
of the image and was clearly visible to observers.
Display system and calibration
Stimuli were produced on the screen of a 21-inch RGB color
monitor ~Trinitron Color Graphic Display, model GDM-F500R,
Sony Corp., Tokyo, Japan!, with spatial resolution 1600 ⫻1200
pixels, controlled by a color-graphics workstation ~Fuel V12,
Silicon Graphics, Inc., Mountain View, CA!whose 10-bit digital-
to-analog converters provided an intensity resolution of 1024
levels on each of the red, green, and blue guns. Each image was
limited to 80–85% of the displayable area of the screen. The
images of the two scenes subtended 1339 ⫻972 and 1339 ⫻1018
pixels. A calibrated telespectroradiometer ~SpectraColorimeter,
PR-650, Photo Research Inc., Chatsworth, CA!and photometer
~LMT, L1003, Lichtmesstechnik GmbH, Berlin, Germany!were
used to monitor and calibrate the display system. Calibration data
included the phosphor coordinates and voltage-intensity look-up
tables for the three guns. The monitor was allowed1htowarmup
before use.
Routine monitoring of the display system tested whether errors
in the displayed CIE ~x,y,Y!coordinates of a white test patch
were ⬍0.005 in ~x,y!and ⬍5% in Y~⬍10% at low light levels!.
Tests of image fidelity used images from the experiments, as
described in Foster et al. ~2006b!. Errors for patches of width ⬎20
pixels were ⱕ0.002 in ~u
'
,v
'
!coordinates, less than 15% of the
0.015 grid spacing in the ~u
'
,v
'
!plane used to sample observers’
responses. Since images were presented sequentially in the same
position on the screen, position-dependent chromatic errors in each
pair of images were the same. Other details of stimulus generation
and display are given in Foster et al. ~2006a!.
Stimulus variation
Images were prepared off-line. From the hyperspectral acquisition,
the color signal for each scene, that is, the original radiance image
C
0
~l;x,y!as a function of wavelength land position ~x,y!, was
recovered, along with the spectrum E
0
~l! of the global illumina-
tion on the scene, recorded at a particular reference point ~scenes
were recorded in direct sunlight under a cloudless sky or under a
sky with uniform cloud; Foster et al., 2004!. A new radiance image
C~l;x,y!was generated for a new global illuminant E~l! by
putting C~l;x,y!⫽C
0
~l;x,y!E~l!0E
0
~l!. In effect, for each
surface in the scene, the new radiance at each point ~x,y!is the
same as that obtained by multiplying a spectral reflectance R~l;x,y!
at that point by the new global illuminant E~l!, where, by defi-
Fig. 1. Sample images of the ~a!urban and ~b!rural natural scenes used in Experiments 1 and 2. The test surface in each scene is
indicated by an arrow.
352 K. Amano, D.H. Foster, and S.M.C. Nascimento

nition, R~l;x,y!⫽C
0
~l;x,y!0E
0
~l! ~an analysis of effective
reflectances with surfaces under direct and indirect illumination in
terms of bidirectional reflectance functions is given in Foster et al.
2006b!. For luminous and non-spectrally selective reflecting areas
in the scene, such as the sky or specular highlights, this global
illuminant change from C
0
~l;x,y!to C~l;x,y!has the critical
property that it preserves the spectral relationships between these
areas and the surfaces of the scene; for example, if the illumination
on the scene becomes more blue, then the sky and specular
highlights also become more blue.
In Experiment 1, the global illuminant E~l! was first a daylight
with correlated color temperature 25,000 K and then 6700 K; in
Experiment 2, the global illuminant was first 15,000 K and then
5700 K. This difference between the pairs of illuminants was due
to limits on the displayable color gamuts of the scenes, but the
color difference in 1976 CIE ~u
'
,v
'
!space between the members of
each pair of illuminants was the same.
The reflectance of the test surface in the first image was
manipulated independently of the global illuminant: five different
initial test-surface colors ~“yellowish,” “greenish,” etc.!were tested
in five separate blocks. In each block, the spectral reflectance of
the test surface in the second image varied randomly, from trial to
trial, in one of 65 ways ~all randomization was without replace-
ment!. This variation was achieved by a computational device, as
follows. Suppose that the initial spectral reflectance was R~l;x,y!
at each point ~x,y!of the surface and the global illuminant
spectrum was E~l!, so that the color signal was R~l;x,y!E~l!.
With a change in spectral reflectance to R
'
~l;x,y!, say, the color
signal becomes R
'
~l;x,y!E~l!. But the same color signal can be
achieved with the original R~l;x,y!by replacing E~l! locally by
a different daylight E
'
~l! such that R
'
~l;x,y!E~l! ⫽R~l;x,y!
E
'
~l!; the change in reflectance k~l! is given by k~l!⫽R
'
~l;x,y!0
R~l;x,y!⫽E
'
~l!0E~l!. Varying the chromaticity of this local
illuminant E
'
~l! is closely related to varying the chromaticity of
the test surface, but the representation of changes in spectral
reflectances R
'
~l;x,y!0R~l;x,y!in terms of changes in local
illuminants E
'
~l!0E~l! has the advantage of a natural colorimetric
parameterization and of a quantification that is independent of the
initial spectral reflectance of the test surface, so that averages may
be calculated over stimuli ~see Foster et al., 2001a!.
These local illuminants were constructed from a linear combi-
nation of the daylight spectral basis functions ~Judd et al., 1964!
whose corresponding chromaticities were drawn from the gamut in
the ~u
'
,v
'
!diagram consisting of 65 locations, with spacing 0.015
in the u
'
and v
'
directions, shown by the small solid points in the
graphs of Fig. 2. The same technique was used to produce the five
different initial test-surface spectra, whose corresponding chroma-
ticities were shifted from the original or Munsell N5 or N7 by
~0.015, 0!,~0, 0.015!,~⫺0.015, 0!,~0, ⫺0.015!, and ~0, 0!.
Changes to the spectrum of the sky in Experiment 1 and to
the spectrum of the illumination on the gray reflecting sphere in
Experiment 2 were made in the same way; that is, the radiance
spectrum C~l;x,y!at each point ~x,y!of the sky or sphere was
replaced by the spectrum C~l;x,y!k~l!, making the sky or
sphere appear, for example, more blue or more red, depending
on k~l!. This illuminant change k~l! was the same for the first
and second images, for making inconsistent changes across the
two images is known to worsen color-constancy judgments ~Foster
et al., 2006a!.
Procedure
In each trial, two images of a particular scene were presented in
sequence on the screen of the color monitor, each for 1 s, with no
interval. The images differed in their global illuminants.As already
mentioned, during the global illuminant change, the spectral re-
flectance of the test surface in the second image also changed, by
a random amount. The observer’s task was to decide whether the
test surface in the successive images was the same or different, that
is, whether an illuminant change or an illuminant change accom-
panied by a change in the spectral reflectance of the test surface
had occurred ~Craven & Foster, 1992!. Responses were made with
mouse buttons connected to a computer. Observers were allowed
to move their eyes freely. At the beginning of the session, the
experimenter indicated the identity of the test surface to the
observer verbally and by pointing and gave a demonstration of
illuminant and varying sizes of reflectance changes.
In each experimental session, there was just one color change
to the sky or sphere and just one test-surface color. In all, 20
conditions were tested in Experiment 1 and 15 in Experiment 2. A
further control condition was introduced in Experiment 2, in which
the scene was cropped to remove both the sphere and sky.
The images on the screen of the monitor were viewed binoc-
ularly at 100 cm and subtended approximately 18 deg ⫻13 deg
visual angle. The test surfaces subtended approximately 1 deg ⫻
0.5 deg and 3 deg ⫻1 deg for Experiments 1 and 2, respectively.
The reflecting sphere of Experiment 2 subtended approximately 1
deg. Images were presented in a dark surround, and the luminance
at each pixel varied from 0 to 33 cd m
⫺2
. Room luminance was
approximately 0.5 cd m
⫺2
. Observers each performed at least 1300
trials in all.
Observers
Twelve observers, aged 23–34 years, took part in the experiments:
two male and four female for Experiment 1 and the same for
Experiment 2. All observers had normal color vision verified with
the Farnsworth-Munsell 100-Hue test; Ishihara pseudoisochro-
matic plates ~24-plates edition, 1964!; Rayleigh and Moreland
anomaloscopy; and luminance matching ~Interzeag Color Vision
meter 712, Schlieren, Switzerland!. All had normal or corrected-
to-normal visual acuity. The experiments were conducted in ac-
Fig. 2. Contour plots showing the relative frequency of “illuminant-
change” responses by observers in the CIE 1976 ~u',v'!chromaticity
diagram as a function of the chromaticity of the reflectance change of the
test surface. The square symbols show the first illuminant, a daylight with
correlated color temperature, 25,000 K in ~a!and 15,000 K in ~b!; the
circles the second illuminant, 6700 K in ~a!and 5700 K in ~b!; and the
triangles the mode, from which the color-constancy index was derived.
The line marked Lis the daylight locus.
Color constancy and a visible illuminant 353

cordance with principles embodied in the Declaration of Helsinki
~Code of Ethics of the World Medical Association!and were
approved by the Research Ethics Committee of the University of
Manchester. All observers were unaware of the purpose of the
experiment.
Analysis
Only one out of the 65 changes in the spectral reflectance of the
test surface was a null change, that is, corresponded to a pure
illuminant change on the scene. An observer with perfect color
constancy would therefore give “illuminant-change” responses
only to this stimulus combination and “reflectance-change” re-
sponses to all the others. The frequency of “illuminant-change”
responses in each condition was therefore plotted as a function of
the chromaticity of the local illuminant in the CIE 1976 ~u
'
,v
'
!
chromaticity diagram. This frequency plot was then smoothed by
a two-dimensional nonparametric locally weighted quadratic re-
gression ~“loess”; Cleveland & Devlin, 1988!and contour plots
derived as shown in Fig. 2 ~cf. Bramwell & Hurlbert, 1996, who
used a two-dimensional Gaussian model!. Each contour represents
a constant relative frequency, with differences between contours of
approximately 0.10–0.15. The position of the maximum of each
distribution was obtained numerically from the loess analysis
~shown by the triangles in Fig. 2!. If the observer had perfect color
constancy, that position would coincide with the position of the
second illuminant ~circles!.
To summarize the error in the surface-color judgment, that is,
the bias, a standard color-constancy index ~Arend et al., 1991!was
then derived. Thus, if ais the distance between the positions of the
maximum ~triangle!and the 6700-K, or 5700-K illuminant ~circle!
~the bias in observers’ responses!and bthe distance between the
positions of the 25,000-K or 15,000-K illuminant ~square!and
6700-K or 5700-K, respectively, illuminant, then the constancy
index is 1 ⫺a0b. The standard error ~SE!of this index was
estimated with a bootstrap procedure, based on 1000 replications,
with resampling over observers ~Efron & Tibshirani, 1993!. Per-
fect constancy corresponds to an index of unity. Perfect incon-
stancy corresponds to an index of 0, which occurs when the
response peak coincides with the first global illuminant.
Results
Recall that these experiments were designed to test for a system-
atic effect on surface-color judgments of initial shifts in color of a
visible sky or of the color of illumination on a visible sphere. The
distributions of observers’ responses without these color shifts are
shown in Figs. 2a and b. Fig. 3 shows mean color constancy
indices for the six observers of Experiment 1 in which the color of
the sky was shifted in increments along the daylight locus. Data are
grouped according to the shift in sky color. Within groups, each
data point corresponds to a different initial color of the test surface.
Vertical bars show 61 SE of the mean. The control condition is
discussed later.
Color constancy indices ranged from 0.56 to 0.88, with an
overall mean of 0.71. Neither the initial shift in sky color nor the
initial test-surface color seemed to affect performance. This was
confirmed by a repeated-measures analysis of variance ~ANOVA!.
Thus, sky-color shift had no significant effect ~F~3,15!⫽1.3, P⫽
0.3!; nor did test-surface color ~F~4, 20!⫽0.8, P⫽0.5!; nor was
there an interaction between the two ~F~12,60!⫽1.0, P⫽0.4!.
Since data from the same scene location were also available
from a separate experiment in which the same kinds of surface-
color judgments were made without a visible illuminant ~Foster
et al., 2006a!, the mean level of color constancy is also included
in Fig. 3 for comparison ~labeled “control”!. Despite the absence
of the sky, and a different group of observers, performance was
similar. An ANOVA showed formally that the visible sky had no
significant effect ~F~4,135!⫽1.1, P⫽0.4!and neither did the
initial test-surface color ~F~4, 135!⫽0.5, P⫽0.8!.
Fig. 4 shows mean color constancy indices for the six observers
of Experiment 2, in which the color of the light illuminating the
sphere in the scene was shifted in increments along the daylight
locus. As in Fig. 3, data are grouped according to the shift of the
sphere illuminant color. Within groups, each data point corre-
Fig. 3. Color-constancy indices from Experiment 1 in which the color of
the sky in the scene ~Fig. 1a!was shifted in increments along the daylight
locus. Data are grouped according to the shift in initial sky color; within
groups, each data point corresponds to a different shift in initial color of
the test surface. Data are averaged over six observers. Vertical bars show
61 SE of the mean.
Fig. 4. Color-constancy indices from Experiment 2 in which the color of
the light from the sun and sky illuminating the sphere in the scene ~Fig. 1b!
was shifted in increments along the daylight locus. Other details as for
Fig. 3.
354 K. Amano, D.H. Foster, and S.M.C. Nascimento

sponds to a different initial color of the test surface. Vertical bars
show 61 SE of the mean.
Color constancy indices ranged from 0.60 to 0.81, with an
overall mean of 0.70. As with the main experiment, neither the
initial shift in illuminant color nor the initial test-surface color
seemed to affect performance. This was confirmed by a repeated-
measures ANOVA. Thus, sphere-illuminant color shift had no
significant effect ~F~2,10!⫽0.6, P⫽0.5!; nor did test-surface
color ~F~4,20!⫽1.7, P⫽0.2!; nor was there an interaction
between the two ~F~8,40!⫽1.0, P⫽0.4!.
Results for the control condition, in which the scene was
cropped to remove both the sphere and sky, were similar. A
repeated-measures ANOVA showed formally that the presence of
the sphere had no significant effect ~F~1,5!⫽0.3, P⬎0.5!and
neither did the initial test-surface color ~F~4, 20!⫽1.0, P⫽0.4!.
Discussion
If the gamut of surfaces in a scene is sufficiently large, then, in
theory, it is possible to make a reliable estimate of the color of the
illumination, for example, by assuming that it coincides with a
spatial average color of the scene ~Buchsbaum, 1980!, or with the
color of the highest-luminance surface ~Land & McCann, 1971!,
or by appealing to other statistical properties of the image ~Fin-
layson et al., 2001; Golz & MacLeod, 2002!. In experiments with
Mondrian-like patterns, observers are able to estimate the color of
an illuminant on a scene ~Linnell & Foster, 2002!, and, as ex-
pected, the accuracy of estimation improves as the number of
surfaces in the patterns increases. Space-average scene color may
also be used as the cue in some surface-color matching experi-
ments in which both the illuminant and test-surface position vary
~Amano & Foster, 2004!. Even so, there are clearly conditions
where space-average scene color gives an unreliable cue to the
illuminant, most notably where the color gamut is limited. Making
information about the illuminant on a scene explicit, rather than
inferential, ought therefore to influence judgments, particularly in
natural scenes.
As was shown here, however, shifting the color of a directly
visible sky along the daylight locus so that it differed from the true
illuminant spectrum on the scene had no reliable effect on the ac-
curacy of surface-color judgments, nor did removing the sky from
the field of view. Shifting the color of the light from the sun and sky
illuminating a clearly visible sphere in the scene so that it, too,
differed from the true illuminant spectrum on the scene also had no
reliable effect. It might be argued that in the images of Experiment
2~Fig. 1b!, the right-hand side of the house whose roof was the test
surface could also have been used to infer the color of the direct
illumination, but it was less bright than the sphere and had no dif-
fuse highlight that allowed the illuminant color to be inferred.
These shifts in color of the sky and the light on the sphere were
substantial, in the 1976 CIE ~u
'
,v
'
!color diagram of the same
order as the color difference between the two global illuminants.
Moreover, performance was no worse when both the sky and the
sphere were eliminated from the field of view. The mean levels of
color constancy of 0.71 and 0.70 found here were compatible with
those reported for a much larger population of rural and urban
scenes ~Foster et al., 2006a!.
The simplest conclusion is that judging surface color in natural
scenes does not depend on explicit knowledge of the color of the
illumination ~cf. Yang & Maloney, 2001!. This conclusion is
consistent with another experiment ~Amano et al., 2005!in which
observers made asymmetric color matches between pairs of simul-
taneously presented Mondrian-like patterns of colored papers un-
der different daylights. The patterns had either 49 surfaces or a
minimal 2 surfaces, too few for an accurate estimate of the
illuminant to be formed. Yet color-constancy indices were almost
identical ~0.73 and 0.72 for 1 deg paper squares and closely similar
to the mean values reported here!.
As has been argued elsewhere ~Foster, 2003!, a possible expla-
nation for the insensitivity of surface-color judgments to informa-
tion about the illuminant on a scene is observers’ use of “relational
color constancy” ~Foster & Nascimento, 1994!. This refers to the
constancy of perceived color relations between surfaces under
different illuminants, as distinct from color constancy, which refers
to the constancy of perceived colors of surfaces. Thus, when
discriminating between illuminant and material changes in scenes,
observers simply compare how the color of the test surface relates
to the color of one or more other surfaces in the scene or, indeed,
to the scene as a whole, first under the one illuminant and then
under the other.
There is a ready physiological substrate for these comparisons:
the ratios of cone-photoreceptor excitations generated in response
to light reflected from pairs of surfaces or groups of surfaces. Such
ratios, which can also be calculated across postreceptoral combi-
nations and spatial averages of cone signals, have the remarkable
property of being almost exactly invariant under changes in illu-
minant both with natural surfaces ~Nascimento et al., 2002!and
with colored papers ~Foster & Nascimento, 1994!.
More generally, when surface-color judgments were measured
with a much larger group of scenes ~Foster et al., 2006a!, the
variation in color-constancy indices across the scenes, from 0.69 to
0.97, was best explained by spatial ratios of cone excitations being
calculated globally for each scene, that is, over all possible pairs of
points, rather than just between the test surface and one or more
other surfaces in the scene.
In everyday viewing, we are able to make rapid and relatively
accurate judgments about the colors of things, an ability that seems
not to require attentional effort ~Foster et al., 2001b!. Yet the
illuminant is often not visible, and our percepts are much the same
as when the illuminant is visible, an intuition that seems confirmed
by the present experiments.
Acknowledgments
This research was supported by the EPSRC ~grant nos. GR0R39412001
and EP0B00025701!.
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