Post on 07-Mar-2023
Discrimination of Illumination and Reflectance Changes on
Color Constancy
Shigeki Nakauchi, Tatsukiyo Uchida, and Shiro Usui
Department of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Japa n 441-8580
SUMMARY
Human perception of the color of physical surfaces
is practically not affected by changes in illumination. This
phenomenon is called color constancy. Based on results of
previous psychophysical experiments, it has been estab-
lished that there are two types of color perception: apparent
color and surface color. It has also been suggested that
unless there is a complete adaptation to the illuminant, color
constancy can be achieved only with respect to the surface
color. Computational models of color constancy boil down
to problems of estimation of reflectance of the observed
object based on the magnitude of the sensory response, and
duality of color perception has not been adequately ad-
dressed in previous studies. This study was undertaken for
the purpose of making clear the characteristics of the two
types of color perception (apparent color and surface color).
The experimental technique used in this study was based
on the detection of changes of illuminance and reflectance
for the purposes of determination of the effect of the sur -
round stimulus on color perception, rather than on conven-
tional color matching technique. The results of the study
indicate that the surround stimulus exhibits an inhibitive
influence on the color perception of the center stimulus, and
the effect of the size and spatial structure of the surround
stimulus is different with respect to the apparent color and
the surface color. It was also demonstrated that results of
the experiments can be explained by a hypothesis of a
hierarchical structure of the vision system combining two
different types of color perception. © 2000 Scripta Tech-
nica, Electron Comm Jpn Pt 3, 83(11): 43�55, 2000
Key words: Color constancy; apparent color; sur-
face color; surround stimuli; duality of color perception.
1. Introduction
Our color perception is endowed with the ability to
perceive colors almost unchanged under varying illumina-
tion. However, it is necessary to remember that, because of
the color constancy notion, we �understand� rather than
�see� that the color of the object remains the same under
changing illumination conditions. In fact, in previously
performed experiments using the color matching tech-
niques [1�4], the color constancy was investigated as two
types of color perception: the apparent color (color percep-
tion due to the light incident on the retina) and the surface
color (color perception due to surface reflectance of physi-
cal objects). In color matching experiments relating to the
color constancy, the subjects participating in the tests were
usually instructed to match the color of a standard stimulus
with a color patch of the test stimulus illuminated differ-
ently than the standard stimulus. During the experiments,
the subjects were asked to match as close as possible the
hue and saturation of a test stimulus patch to those of the
standard stimulus (so-called hue-saturation match), that is,
the goal of the experiment was to achieve two types of color
matching as if both specimens were cut from the same piece
of paper (paper match). According to the results obtained
by Arend and colleagues [1, 3], almost all individuals
participating in experiments succeeded in matching colors
of test and standard color patches by sensory appearance,
that is, by chromaticity, in the hue matching tests, and by
© 2000 Scripta Technica
Electronics and Communications in Japan, Part 3, Vol. 83, No. 11, 2000Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. J82-A, No. 1, January 1999, pp. 168�178
43
spectral reflectance in the saturation matching tests. There-
fore, we think that it is possible to say that color constancy
exists with respect to both the sensory appearance and the
reflectance of the physical surface (the amount correspond-
ing to the reflectance). Moreover, since the spectral reflec-
tance is illuminance invariant, it can be used to obtain color
constancy if reference could be made accurately for the
spectral reflectance.
On the other hand, several computational and mathe-
matical models have been proposed [5�7] to determine
color constancy by estimating the spectral reflectance of
objects based on the magnitude of sensory response under
changing illumination conditions, but these models were
not satisfactory due to an incorrectly stated problem. In
those studies, the emphasis was placed on the explanations
concerning the surface color, while the apparent color,
which directly depends on color contrast and color adapta-
tion, was completely omitted from the discussion. How-
ever, since the formation of surface color is clearly closely
related to characteristics of the apparent color [8], it is
necessary to develop a new approach to the understanding
of the color constancy that would take into account the
duality of the color perception.
Foster and colleagues [9, 10] have proposed a new
definition of color constancy as �the capacity to determine
whether changes in the apparent color of the surface are due
to changes in illumination or to changes in the spectral
reflectance of the surface.� In conventional color matching
experiments, subjects must correctly assess the magnitude
of the shift in the apparent color of the color chip due to
illumination changes. By contrast, according to the defini-
tion by Foster�s group, it is sufficient to establish whether
the shift of the apparent color is caused by changes of
illumination or by changes of reflectance. In such a case,
their definition of the color constancy is based on the cue
that the changes in the apparent color caused by the illumi-
nation are substantially uniform in the entire field of vision,
while the reflectance changes are spatially localized. In fact,
the experiments in color discrimination performed by Fos-
ter�s group have demonstrated that the reason for color
changes of two visual stimuli presented in succession can
be identified almost immediately.
Since the color matching experiments under varying
illumination conditions conducted in the past were unusual
for subjects having no previous experience in such tasks,
the following shortcomings of the experiments are often
pointed out: In many cases it is difficult to obtain consistent
response, color matching takes a long time, and, what is the
most important, there are always doubts that color matching
is performed based on the sensory perception. On the other
hand, we think that the subjects having experience with
visual stimuli that change color perception instantly, will
have a more consistent response. Earlier proposed conten-
tion of immediate color constancy, that is, such a color
constancy that does not require color adaptation, would
manifest itself in reduction of the response time in the case
of color discrimination, thus making it possible to minimize
the overall effect of color adaptation. However, since the
color perception of the subjects is not measured directly, the
experiments by Foster�s group demonstrated only that it is
possible to pinpoint the reasons for perceived color
changes. In order to make details of such a perception clear,
it is necessary to link color perception and color discrimi-
nation characteristics by some kind of a model of color
perception.
This study was undertaken to explain characteristics
of apparent/surface color by means of experiments on color
constancy based on the color discrimination. For this pur-
pose, we attempted to develop a mathematical model of
color perception for color stimuli that could be used for the
explanation of characteristics of the apparent/surface color
discrimination, especially the effect provided by the sur-
round stimulus. Below, we present principles of measure-
ments of the color perception characteristics based on color
discrimination and discuss psychological and physical ex-
periments related to the effect of the magnitude of chro-
maticity changes and the area of the peripheral stimulus.
We also present comparison of results of various experi-
ments and predictions given by the model.
2. Measurements of Threshold Magnitude
Based on Color Discrimination and
Principles of Experiments
2.1. Principles of experiments
Consider a case in which two stimuli (each consisting
of multiple color patches) are presented in succession to
subjects for viewing. Stimulus located in the main field of
vision is called the central stimulus, and remaining stimuli
are called surround stimuli. Let the color perception of the
first stimulus be P1 and the color perception of the second
stimulus be P2. If the color perception of the central stimu-
lus is denoted P, and assuming that it depends on both the
central stimulus Cc and the surround stimulus Cs, then we
can write
Under these conditions, the subjects of the experiment
notice the difference between perceptions with respect to
two successive stimuli ('P) when it exceeds a certain
threshold value (Pthreshold):
(1)
(2)
44
The discrimination threshold is the amount of chromaticity
difference 'Cc Cc2 � Cc1 that satisfies this condition.
Considering that the surround stimulus influences the color
perception of the central stimulus, we must assume that the
discrimination threshold 'Cc also changes depending on
the surround stimulus. In this study, we, using the method
described below, performed measurements of the effect of
the surround stimulus on the color perception of the
central stimulus by investigating the changes in the dis-
crimination threshold 'Cc of the central stimulus in re-
sponse to variations of such parameters of the surround
stimulus as the chromaticity magnitude and the area of the
surround stimulus.
2.2. Experimental methods
2.2.1. Goal of the experiments
The discrimination threshold of the center stimulus
was measured by presenting two stimuli to subjects taking
part in the experiments for 1 second each. Perceived color
of the stimulus was quantified by measuring only the
CIELUV chromaticity coordinates (ug) that could change
in the red direction (+uc) or in the green direction (�uc).
Therefore, the discrimination threshold was measured as
r'uc while simultaneously changing the color of the sur-
round stimulus. The cases when chromaticity magnitudes
of the center and surround stimuli changed in the same
degree were considered as simulation of only illumina-
tion changes, and cases when changes of both parameters
were substantially different were considered as simulation
of the changes in reflectance (for details, see Sections 3 and
4). Subjects of experiments were instructed to declare after
viewing these two stimuli whether they noticed no
changes in stimuli color (�unchanged�), or if it looked
like the color shifted toward red (�red�) or toward green
(�green�) directions.
Measurements of the discrimination threshold were
based on the �staircase� method [11] in which stimuli are
successively presented to individuals while chromaticity
values of the center stimulus are varied. Then, if the subjects
were able to see the difference between the stimuli, differ-
ence in chromaticity values of the stimuli was reduced, and
if no distinction was observed, the difference was increased
and the stimuli were presented to the subjects again. The
process was repeated until a stable change of chromaticity
value was finally achieved, which was considered the dis-
crimination threshold. Average value obtained from results
of five experiments was considered the measured magni-
tude of the discrimination threshold. Before the experi-
ments, the individuals were shown for 3 minutes a gray
color patch illuminated by a D65 illuminant (30 cd/m2) for
the purpose of adaptation. The two stimuli were presented
for 2 seconds, after which the subjects underwent the adap-
tation procedure again. Time for response was not limited.
2.2.2. Criteria for the color judgment
In this study, the subjects were instructed to use two
different types of judgment criteria: for the apparent color
and for the surface color to be applied to measurements of
the discrimination threshold. In this paper, they are called,
respectively, �apparent color discrimination� and �surface
color discrimination.� It can be said that the apparent color
represents the changes of light entering the eyes of the
individuals from the center stimulus, and the surface color
discrimination criterion is the reflectance spectrum of the
center stimulus.
The instructions given to the individual with respect
to these parameters were as follows.
Apparent color discrimination: A stimulus imi-
tating an illuminated color patch is displayed on a CRT. At
times, in the process of testing, the illuminant color will be
changed and sometimes the color of the center color patch
will be changed simultaneously. If at such a time, you sense
that the color of the center color patch changed (for what-
ever reason, whether change of the illuminant color or
change of the color patch), indicate in what direction the
color shifted (toward red or green color).
Surface color discrimination: A stimulus imitat-
ing an illuminated color patch is displayed on a CRT. At
times, in the process of testing, the illuminant color will be
changed and sometimes the color of the center color patch
will be changed simultaneously. If, at such a time, you sense
that not only the illuminant color but also the color of the
color patch have changed, indicate in what direction the
color shifted (toward red or green color).
In both cases, the stimulus color is changed from the
first stimulus to the second stimulus, but for the apparent
color discrimination, it is important only to notice if the
color of the center stimulus changed, regardless of whether
it was caused by changes in the illuminant or in reflectance.
But for the surface color discrimination, it is necessary to
distinguish whether it was a global color change caused
only by the illuminant change, or if it was caused by
unbalance between the center and surround stimuli due to
a change in reflectance [9, 10]. In such a case, the phrase
�the color patch is replaced with a color patch of a different
color� means that the color changes of the center and
surround stimuli are substantially different.
2.2.3. Experimental setup and equipment
The experiments were conducted in a dark room. The
distance at which the subjects viewed the stimuli was fixed
at 80 cm, and the stimuli were displayed on a CRT allowing
45
for the color adjustments and J compensation. The stimuli
were controlled using a workstation. The CRT was placed
in a black box, and the subjects could observe the stimuli
through a window made in the box front panel. Responses
of the subjects after the presentation of stimuli were regis-
tered by selecting appropriate entries from pull-down
menus displayed on the CRT. For the CRT, we used a
GDM-2000TC monitor (made by Sony), and for the stimu-
lus control, a Kubota Titan 2 600 ZLX-M1 workstation.
3. Experiment 1: Effect of Magnitude of
the Color Change in the Surround Stimulus
Measurements of the discrimination threshold
changes of the center stimulus relative to the surround
stimulus were performed using judgment criteria for the
apparent and surface colors, respectively.
3.1. Experimental conditions
3.1.1. Visual stimuli
Visual stimuli used in these experiments (see Fig. 1)
were prepared in the form of randomly selected color
patches (1 u 1 degrees) arranged in a 7 u 7 array over a gray
background (10 u 10 degrees). The color patch appearing
in the center of the array was used as the center stimulus,
and the remaining patches formed the surround stimulus.
Numerical values inside the patches shown in Fig. 1 are the
Yucvc parameters of the first stimulus, where Y is brightness,
and ucvc are colorimetric coordinates of the patch color.
Colors of the second stimulus were changed com-
pared to the first stimulus, and the discrimination threshold
for the center stimulus was determined by means of the
above-mentioned staircase method. In the process of ex-
periments, colors were changed not only in the center
stimulus but also in the surround stimulus. Namely, the
color changes of the surround stimuli were made in the
following five increments of uc: 0.0, 0.008, 0.016, 0.024,
0.032, and the discrimination thresholds with respect to the
center stimulus was measured for all of these increments.
The judgment criterion for the apparent color was estab-
lished based on the appearance of the color of the center
stimulus regardless of the color changes of the surround
stimulus. As for the criterion for the surface color, the
individuals were instructed to respond that the color did not
change if they had the impression that only the illuminant
changed, and that the color changed when they saw that the
color patch of the center stimulus has changed to a different
color.
Hues of the visual stimulus shown in Fig. 1 are
calculated based on the spectral reflectance of randomly
selected Munsell color chips and on spectral distribution of
the standard illuminant D65. To simulate changes of the
illuminant or the surface color, it is necessary to change the
function of the spectral distribution of the illuminant and
the reflectance spectrum generating the visual stimulus, but
in these experiments the magnitudes of color variations of
the center and surround stimuli were made independently,
and if the variation in the color of the center and surround
stimuli is of the same order, then it is perceived as the
change in the illumination, but if the color difference be-
tween the center and surround stimuli is considerable, it
corresponds to a change in reflectance. In fact, in the case
of variations of the illuminant, the hue values are shifted
almost uniformly, and it was confirmed that the subjects can
perceive these changes as the illuminant change.
3.1.2. Subjects participating in the experiments
The experiments were conducted with participation
of four adult male subjects (SH, HS, HI, SF), all of whom
had normal color vision. Subjects were not informed about
the purpose of the experiment (naive test). SH and SF wore
corrective glasses, and HS used contact lenses.
3.2. Model predictions
It is well known that the color perception of the center
visual stimulus not only depends on the stimulus color
itself, but is also influenced by the surround stimulus due
to such phenomena as simultaneous color contrast. It is also
suggested that even if color constancy refers to the surfaceFig. 1. Visual stimulus used in Expt. 1.
46
color, the color information is encoded in a certain relation-
ship with the surrounding color. Based on such an approach,
Kawamura and Inui [12] proposed a model of perception
of lightness and brightness of color and attempted to ex-
plain results of psychophysical experiments relating to the
constancy of color brightness. They expressed lightness
perception as a function of the center stimulus and the
center�surround contrast, and perception of color bright-
ness as a function of contrast.
Based on this information, in this study, we represent
the color perception of the center visual stimulus as a
function of the center visual stimulus and the center�sur-
round contrast (difference) expressed by the following
formula:
Here, * stands for either a and s to distinguish between the
apparent or surface color. Terms k1 and k2 are weight
coefficients for the center visual stimulus and the contrast,
with the values of these coefficients in this model being
different for the apparent and surface color. That is, the
difference of these coefficients expresses duality of the
color perception.
In many cases, changes of color of the visual stimu-
lus due to the illuminant changes occur in a spatially
uniform manner within the entire field of vision. Unlike
relatively small variations of center�surround contrast in
response to the illuminant changes, variations of spectral
reflectance of physical surface are localized, and contrast
shows stronger trends for changes. Hence, in cases when
the color of the center stimulus changes while the cen-
ter�surround contrast remains the same, it will be per-
ceived as if the spectral reflectance of the center stimulus
did not change.
In such a case, behavior of coefficients k1, k2 with
respect to the two types of judgment criteria, that is, to
apparent and surface color, can be explained as follows.
Since for the estimation of the apparent color, only the
information about the color of the center stimulus is
important, magnitude of the weight coefficient k1 of the
data only on the color of the center stimulus is made
large, while magnitude of the weight coefficient k2 of the
difference between Cc and Cs is small. On the other hand,
since for the estimation of the surface color, the center�
surround relation is important, magnitude of k2 is taken
large and that of k1 is small.
In such a case, the change of the discrimination
threshold for the magnitude of the color change of the
surround stimuli can be represented as follows. When the
difference, 'P*, in the color perception between the first
and second visual stimuli is equal to the threshold, the
following holds:
Here, Cc1, Cc2 are chromaticity values of the center stimulus
for the first and the second test pattern, and Cs1 and Cs2 are
chromaticity values of the surround stimulus. Expressions
'Cc Cc2 � Cc1 and 'Cs Cs2 � Cs1 represent values of
chromaticity changes in the center and surround stimuli,
respectively. If magnitudes of changes in the color for the
surround stimuli ('Cs) and for the center stimulus ('Cc) are
determined from the above equations, then, for the change
of the center stimulus in the positive direction, we have
and for the change in the negative direction, we have
Therefore, in a plane formed by 'Cs as the horizontal axis
and 'Cc as the vertical axis, values of the discrimination
threshold at which subjects can notice color changes in the
positive direction (red shift) and in the negative direction
(green shift), appear as parallel lines differing only by
intercept symbols. The model also predicts that gradients
of the lines, k2 / �k1 � k2�, for the surface color will be greater
than that for the apparent color.
Values of parameters were assumed for each subject
by applying this model to the experimental results obtained
by them for apparent and surface colors. In this case, the
parameters included k2 / �k1 � k2� and P threshold. Magnitudes
of the discrimination threshold computed using these pa-
rameters are referred to below as the model predictions.
3.3. Experimental results
Figure 2 shows measured values of the discrimination
threshold 'Cc of the center stimulus as a function of values
of the color change 'Cs of the surround stimulus based on
judgment criteria for the apparent and surface color as
perceived by subjects SH and HI. In addition to the experi-
mental data, standard deviations are also plotted. It can be
seen that the model predictions show a good approximation
to the results of both subjects.
The meaning of the region between straight lines is
that subjects do not notice changes of the center stimulus
color. In the case of the apparent color, the attention is
drawn only to the changes of the center stimulus color, and
(4)
(3)(5)
(6)
47
if the color of the surround stimulus is changed to a consid-
erable degree, subjects perceive it as a change of the center
stimulus color even if in fact it was not changed ('Cc 0),
that is, we deal with an apparent shift of the discrimination
threshold. On the other hand, in the case of the surface color,
it is evident that when changes of the color of the center
stimulus are of the same order as those of the surround
stimulus, the subject�s response was �unchanged,� and the
surface color was distinguished by virtue of the color con-
trast between the center and surround stimuli. These condi-
tions are not limited to the examples mentioned here; two
other subjects also perceived the shift in the discrimination
threshold as dependent on the amount of color change in
the surround stimuli.
Gradient of straight lines, that is, the influence (in-
hibitive) of the surround stimulus on the color perception
when the effect of the center stimulus is taken as 1, can be
expressed as
The influence Rcs calculated from results of the experiment
is shown in Fig. 3. It can be seen that all subjects indicated
that the surround stimulus also influences the apparent
color, but its effect on the surface color is much stronger.
4. Experiment 2: Measurements of Spatial
Characteristics of Sensitivity with Respect to
Surround Stimuli
Based on results of Experiment 1, the contrast be-
tween the center and surround stimuli is important for the
discrimination of the surface color. We think that, depend-
ing on the contrast detection, vision mechanisms can be
divided into two types. One of them is the local mechanism
that brings about simultaneous color contrast. The assump-
tion is that this mechanism works by inhibiting the color
perception in a certain portion of the stimulus by its sur-
rounding portion. Another mechanism consists in detecting
(by some means) the color deviation of the stimulus occu-
pying the entire field of vision and in extracting it from the
entire field of vision (global mechanism). For the estab-
lishment of color constancy, it is necessary to eliminate the
luminance-induced color deviation by one of these mechanisms.
Experiment 2 was performed to investigate the spatial
structure of an inhibitive field for the perception of apparent
and surface colors. The experiment was performed simi-
larly to Experiment 1 by measuring the discrimination
threshold of the center stimulus by changing the area of the
surround stimuli.
Fig. 2. Results and model predictions for Expt. 1.
(7)
Fig. 3. Influence of surround stimuli on color
perception calculated from the results of Expt. 1.
48
4.1. Experimental conditions
4.1.1. Stimuli
Visual stimulus used in Experiment 2 (see Fig. 4)
consisted of a round background having a 10.0° diameter
on which the center stimulus and surround stimuli were
arranged. The center stimulus was different from the center
stimulus used in Experiment 1 in that it was round and that
it could display a whole color patch or a part of it. The
colorimetric scheme was the same as in Experiment 1.
However, unlike in Experiment 1 where the magnitude of
color change in the surround stimuli was varied, in Experi-
ment 2 the magnitude of the color change was fixed at
'Cs 0.032 and the center stimulus was surrounded by a
black mask having radius Rm. The mask radius Rm was
varied from 0.5° (no mask) to 1, 2, 3, and 4°, thus changing
the area of the surround stimulus. In addition, in Experi-
ment 1, we measured the discrimination threshold in two
directions (shifts in red and green directions), while in
Experiment 2, only changes of the discrimination threshold
in the green direction were measured as a function of the
mask radius.
4.1.2. Subjects
Subjects of the experiment were three adult males
(SH, HI, SF). None of the subjects had previously partici-
pated in such experiments (naive), all of them had normal
color vision, and SH and SF wore eyeglasses.
4.2. Structure of the field inhibiting the
apparent color
4.2.1. Model of inhibiting field with local
mechanism
One of the phenomena related to the dependence of
the apparent color on the surround stimuli is the simultane-
ous color contrast. In simultaneous color contrast, the color
perception of the object stimulus depends on the color of
the scene surrounding the object. From previous studies, it
is known that effect of the surround stimuli on color per-
ception is of an inhibitive nature and that it exponentially
diminishes with distance from the center stimulus [13].
In this paper, we express spatial distribution of sensi-
tivity to the apparent color, Ga�r� by
where r is the distance from the center stimulus having point
? symmetry independent of direction. Rc is the radius of the
center stimulus; Rs is the radius of the entire stimulus; and
ka1, ka2 are constants representing the peak sensitivity and
the decay rate, respectively. Therefore, the spatial distribu-
tion of the sensitivity to the apparent color has the charac-
teristics of the receptive field of the configuration shown in
Fig. 5, where it is seen that the apparent color is positively
affected by the center stimulus and negatively by the sur-
round stimuli.
Perceived magnitude of apparent color PA is denoted
as an integral of the product of the stimuli S�r; Rm� and
Ga�r� over the entire stimulus area:
Fig. 4. Visual stimulus used in Expt. 2.
(8)
(9)Fig. 5. Sensitivity of apparent color receptive field.
49
Expressing the discrimination threshold 'Cc as a function
of the mask radius Rm, we have
where
4.2.2. Experimental results and model
predictions
Figure 6 depicts changes of the discrimination thresh-
old of the center stimulus as a function of the mask radius.
Symbols represent the experimental results, and the solid
line shows the model predictions based on spatial charac-
teristics of sensitivity inferred from the experimental data.
Values of the mask radius Rm are plotted along the X-axis,
and values of the discrimination threshold 'Cc are plotted
along the Y-axis. Parameters estimated by the model pre-
dictions from the experimental data are ka1, ka2, and
Pa�threshold. According to the data not limited only to the
subjects referred to herein, in the region of the mask radius
values greater than 2.5°, the discrimination threshold re-
mains unchanged. In other words, the data indicate that the
inhibitory field of the apparent color is caused by the local
mechanism acting within relatively narrow margins, thus
suggesting that the model predictions are compatible with
the experimental results.
4.3. Structure of the inhibitory field of the
surface color
4.3.1. Local model of inhibitory field
Above, it was shown that color constancy can be
attributed to the surface color, but so far no conclusion has
been made as to whether the color constancy is caused by
the global or local mechanism. Therefore, in this subsection
we attempt to explain results of experiments by assuming
that the surface color, similarly to the apparent color, is
based on the local mechanism. That is, we assume that the
spatial distribution of sensitivity for the surface color
Gs�r� can be expressed by the following equation similar to
those for the spatial distribution of sensitivity for the appar-
ent color Ga�r�:
In this case, it can be expected that, similarly to Experiment
1, the inhibitory field of the surface color will be greater
than that of the apparent color (deep and/or wide). Let us
compare the effect of the surround stimuli with the case of
the apparent color by estimating parameters from the ex-
perimental results. The discrimination threshold for the
surface color, similarly to the case of the apparent color, can
be expressed as follows:
(10)
Fig. 6. Results and model predictions for Expt. 2
(apparent color).
(11)
(12)
50
4.3.2. Experimental results and local field
model predictions
Figure 7 shows experimental results for subjects SH
and HI and the local mechanism model predictions. The
gray lines represent results relating to the apparent color
shown in Fig. 6. Since, according to all subjects, the model
predictions are in good agreement with the experimental
results, the hypothesis that the surface color is produced by
the local vision field mechanism cannot be dismissed based
solely on the interpretation of the results of Experiment 2.
Next, based on the spatial sensitivity distribution of
the apparent and surface colors inferred from the experi-
mental results, we calculated the magnitude of the effect of
the surround stimuli Rcs similarly to Experiment 1. In this
case, the value Rcs was determined as a ratio of integrals of
spatial sensitivity distribution:
Results of calculations are shown in Fig. 8. In Experiment
1, effect of the surround stimuli was determined by chang-
ing the value of its color change, but in this case, it was
evident that the effect of the surround stimuli was greater
on the surface color than on the apparent color. However,
when effect of the area changes of the surround stimuli on
color perception is to be determined as in Experiment 2,
then, according to results obtained for subjects SH and HI,
the effect of surround stimuli is greater on the apparent
color than on the surface color, which contradicts the results
of Experiment 1 shown in Fig. 3. Moreover, according to
subject HI, the influence of the surround stimuli is excita-
tory rather than inhibitory. Therefore, attempts to explain
perception of the surface color similarly to that of the
apparent color by local vision mechanism lead to discrep-
ancy between results of experiments on the quantitative
effect of the surround stimuli and on the spatial structure.
4.3.3. Global vision field model
The discrimination threshold was perceived by
subject HI as almost independent of the area of the
surround stimuli. This probably can be explained as
follows. In order to discriminate changes of the surface
color, it is necessary to assume existence of a module
acquiring the information related to the illuminance of
the entire field of vision. By subtracting the output of that
module from the receptor output, it is possible to infer
characteristics of the physical surface. At this time, the
clue relating to the illuminant does not depend on the
stimulus area. For example, in a visual system in which
Fig. 7. Results and predictions by a local mechanism
model for Expt. 2 (surface color).
(13)
Fig. 8. Influence of surround stimuli on color
perception calculated from the results of Expt. 2.
51
the average chromaticity of the stimulus is gray, such as in
the gray world hypothesis [5], the discrimination
threshold of the surface color does not change depend-
ing on the area of the surround stimulus. However, ac-
cording to other subjects, threshold of surface color
discrimination clearly depends on the area of the sur-
round stimuli. Therefore, such results cannot be ex-
plained simply by introducing only an illuminance-
detecting module that does not depend on the surface of
the surround stimuli.
Then, it is possible to propose a hypothesis of a
hierarchical structure determining the surface color by
detecting the illuminant color from the apparent color of
the surround stimuli and subtracting it from the apparent
color of the center stimulus. This model is called a global
mechanism model for the surface color. Figure 9 is a
conceptual diagram of this model. Its performance is
expressed by the following equation:
Here, I�Cs� is the illuminant chromaticity determined from
the surround stimuli that is calculated from the apparent
color of the surround stimuli. It is assumed that this function
does not depend on the location and the area of the surround
stimuli, and it is computed as the average chromaticity of
the surround stimuli. The constant ks is determined indi-
vidually for each subject to account for the effect of the
surround stimuli on the apparent/surface color estimated
based on results of Experiment 1. Specifically, from Fig. 3,
one can see that influence of the surround stimuli is stronger
for the surface color than for the apparent color. Therefore,
in the case of the apparent color of the center stimulus, the
output of the apparent color module is referred to as the
apparent color, and in the case of the surface color, the value
obtained by subtracting the output of the illuminant color
detector from the output of the apparent color module, so
that the effect of the surround stimuli matches the results of
Experiment 1, is referred to as the surface color. For the
parameters of the apparent color module ka1, ka2, values
obtained in Experiment 2 for each subject were used.
Assuming this model, the discrimination threshold
can be given by the following equation:
where
Comparison of this equation with Eq. (10) shows that their
first members are the same; the second members are also
the same, except for the term Ps�threshold; and the third term
appears due to the introduction of the module of the illumi-
nant color detector. In addition, the term 'I�'Cs, Rm� is
obtained by multiplying the spatial distribution of the ap-
parent color by the stimuli actually used in the experiments
and integrating its numerical values with subsequent aver-
aging of these values over the area.
4.3.4. Experimental results and predictions by
the global mechanism model
Figure 10 shows results of Experiment 2 and predic-
tions concerning the surface color based on the global
mechanism model. In this figure, the parameters obtained
by each subject are only threshold values, Ps�threshold, of Ps.
Since in the case of the global mechanism model, the output
value of the illuminant color detector module does not
change depending on the radius of the mask while output
of the apparent color module changes, the result is that the
discrimination threshold of the surface color changes.
Changes of the discrimination threshold predicted by such
a model to some degree adequately explain the experimen-
tal data on the global scale. Advantages of the global model
(as can be seen from Table 1) compared to the local mecha-
nism model are: fewer free parameters and, most important,
the fact that the influence of the surround stimuli dem-
onstrated in Experiment 1 can be explained without
contradictions, as well as the fact that the duality of color
perception (apparent color and surface color) can be
represented in the form of a hierarchical model of color
perception.
(14)
Fig. 9. Global mechanism model for surface color.
(15)
52
However, the prediction given by this model that, at
small radii of the mask, the discrimination threshold will
experience abrupt changes could not be confirmed by the
experimental data. Such abrupt changes occur because the
apparent color of the center stimulus surrounded by the
mask changes exponentially, while the apparent color of the
surround stimuli changes at a slower rate. In such a case,
apparent color of the surround stimuli is computed using
the same module as for the center stimulus, but according
to introspective reports by the subjects, the apparent color
of the surround stimuli is clearly perceived differently in
the case when no mask is used, that is, when the center
stimulus and surround stimuli are next to each other, and in
the case when the center stimulus and surround stimuli are
separated by a mask that is 1° wide. In order to explain the
change of the discrimination threshold observed in the data
obtained from the experiments, it is necessary to improve
the model to account for the differences of characteristics
of the center and surround stimuli. In addition, in this study,
sensitivity of the receptive field to the apparent color was
expressed by a discontinuous function shown in Fig. 5;
however, as mentioned in Section 4.2.1, as distinct from a
good match for the data of previous experiments based on
simultaneous color contrast, in the experiments described
in this paper, the stimuli were structured using not only
color patches, thus creating a problem of inconsistency with
more conventional stimuli. We also think that it is better to
use such well-known continuous functions as Laplacian,
Gaussian, and Difference of Gaussian (DOG) as the func-
tions for the physiological receptive field, which can better
represent local mechanism. In the future, we plan to under-
take investigations in this direction.
5. Conclusions
In this study, we investigated, based on psychophysi-
cal experiments, the effect of the surround stimuli on the
color discrimination characteristics using two judgment
criteria: apparent color and surface color. In addition, we
proposed a mathematical model describing the effect of the
surround stimuli on color perception that makes it possible
to predict changes in the discrimination threshold depend-
ing on changes in color and area of the surround stimuli.
The following conclusions have been obtained from the
study.
(1) The vision system first computes the apparent
color by the local vision field mechanism, after which the
surface color is computed by applying the global mecha-
nism to the apparent color.
(2) If there is a module gathering the information
relating to the illuminance from the entire field of vision, it
is not substantially influenced by the dimensions and loca-
tion of the stimuli.
The objects of this study were results of experiments
concerning color discrimination; however, characteristics
of the illuminant detector assumed in this study are based
only on the difference of output values of two stimuli.
Similarly to previously performed experiments using color
Table 1. Errors of the model predictions for the results
of Expt. 2 (surface color)
Subject Local mechanism Global mechanism
SH 0.001105 0.001673
HI 0.001159 0.002076
SF 0.001398 0.002735
Fig. 10. Results and predictions by global mechanism
model for Expt. 2 (surface color).
53
matching, for the explanations concerning results of direct
measurements of the surface color it is necessary to refer to
a specific computation algorithm of the illuminant detect-
ing module. In the future, it is necessary to investigate these
aspects in more details along with computational theory
related to the color constancy.
Acknowledgment. This study was supported in
part by a research grant (B) (2) (No. 09555125) from the
Ministry of Education Fund for Support of Science and
Research.
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AUTHORS (from left to right)
Shigeki Nakauchi (member) completed his doctorate course at Toyohashi University of Technology in 1993 and then
joined the Department of Information and Computer Sciences as an assistant. His research interests include computing theory
and psychological aspects of color perception, and color recovery in color media. In 1989, he received the IEICE Shinohara
Award for Science Encouragement, and in 1997, the Award of the Japan Neural Circuit Society. He is a member of the Japan
Neural Circuit Society, the Japan Neuroscience Society, and IS&T. He holds a D.Eng. degree.
Tatsukiyo Uchida received his M.A. degree from Toyohashi University of Technology in 1998 and then joined Matsushita
Electric Works, Ltd. His research interests are focused on color constancy.
54
AUTHORS (continued)
Shiro Usui (member) completed his doctorate course at the University of California (Department of Electrical Engineering
and Computer Sciences) in 1974 and joined the Engineering Department of Nagoya University as an assistant. In 1979, he
joined Toyohashi University of Technology as a lecturer, then an assistant professor, and since 1986, as a professor. His research
interests are focused on bio-information engineering and physiological engineering. He is the author of Mathematical Models
of Brain and Neural System and other books. He is a member of IEE Japan, the Society of Instrument and Control Engineers,
the Information Processing Society of Japan, the Japanese ME Society, the Physiological Society of Japan, the Japan
Neuroscience Society, the Japan Neural Circuit Society, IEEE (Fellow), INNS, and other societies. He holds a Ph.D. degree.
55