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