Achromatic Color Constancy and Lightness Functions For a Complex Pattern of Luminance

The

JbPanese

Jo"rnal

of

llsychonomic Scr'ence 1982,Vol. 1,No.

].,

51-58

Achromatic

ForColor

Constancy

and

a

Complex

Pattern

ofLightness

Functions

Luminance

Kaoru

NoGucHI

andMasanori

MoToKI

Chiba

Uhaiversity

1izpan

Automobige

Research

institute

Illumination

of a cross-shaped

_pattern

composed of

five

black

to white squares on a white

background

was varied over

2.6

log

units.

The

task

given

to

10Ss

was to make achromatic color namings and

_to

make nurnerical

judgments

of

lightness

for

each of

the

five

squares

ln

the cross as well as

the

background.

Achromatic

color constanc}r was alrnost

_perfect

for

the region ef

the

highest

contrast ratio of surround to

focal

luminance

and

less

perfect

for

the

regions with

lower

contrast ratios.

Lightness

judgments

were

found

to

change as a curvilinear

function

(eoncave

downward)

for

a

log

transformation of

illumination,

Linearly

decreasing

functions

were exceptional.

It

can

be

concluded,

therefore,

that the theoretical claim

for

the

_generality

of negative

functions

for

lightness-illumination

relationships should

be

reconsidered.

Key

words: achromatic color constancy,

brightness-and-lightness

constancy, conttast ratio,

lightness-illumination

relationships,

One

of

controversial

issues

in

the

research area of

bnlgVlrtnessi

contrast and constancy con-cerns

the

_phenomenon

that

is

being

_judged

and

measured,

Some

investigators

explicitly

set

brightness

as

the

_phenomenon.

Others

explicitly set

lightness

as

the

_phenomenon.

Still

others simply

instruct

their

subjects

to

make an equality match

(in

brightnes$

andi'or

lightness).

Most

of

vision

researchers

seem

to

set

brightness

as

the

_phenomenon

and

they

tend

to

make no

distinction

between

brightness

and

lightness.

Phenomenology-oriented

percep-1)

The

term

"brightness"

has

been

used

in

ent senses,

A

detailed

discussion

of

the

different

sens ¢s can

be

seen

in

Beck

(1972).

It

was

fertunate

that `'

brlghtness

"

_has

_been

_too

widely

applied even

to

the

cases where "lightness"

is

more appropriate.

In

the

_present

_paper,

the word "brightness7' _refers

_to

_the

perception of

the

luminous

intensity

of a surface color which

Katz

(1935)

called

Eindringlichleeit,

and the word

`'lightness" _{refers to the}

perception

of

the

black-gray-white

dimension

of a surface color.

When

"

brightness

" _{seems to}

_include

"

lightness

"

or when

it

is

diMcult

to makc a clear

distinction

between

them,

brightness

(with

italic)

will

be

used

below.

tionists

set

lightness

as

the

_phenomenon,

mak-ing

clearer

di$tinctions

between

the

two

per-ceptual

dimensions.

Classical

studies

have

been

mostly carried

out

in

a

simple

situation such as an

arrange-ment composed of a

test-field,

an

inducing-field,

and a

dark

surround.

It

is

not clear,

however,

that

such

a

simple stimulus arrange-ment

is

appropriate

for

studying

the

_problem

of

_perceptual

constancy where

the

distinction

between

brightness

and

lightness

cannot

be

ignored.

As

Flock

and

Noguchi

(1970)

_proposed,

brightness

constancy really

refers

to

the

fact

that

the

achromatic colors of surfaces

sup-posedly

remain

_phenomenally

invariant

over changes

of

illumination

in

a complex environ-ment.

It

is

characteristic

in

a

well-organized visual environment

that

there

are

clearly

dif-ferent

modes of appearance

of

colors.

As

far

as

the

_problem

of constancy

is

concerned,

therefore,

more

research

should

be

required

to

make'clear what

phenomenon

is

being

judged

and measured using

_a

complex

_pattern.

There

have

been

several

attempts

to

inves-tigate

bnLg)ijtness

constancy

in

a

complex

field.

The

first

attempt was made

by

Jameson

and

Hurvich

_(1961).

In

their

experiment

a

52

The

Japanese

Journal

of

grays

was

_presented

against a medium

gray

background

under

three

levels

of

illumination

covering a range of

1.1

log

units.

The

results showed

that

as

illuminance

was

increased,

the

high

reflectance regions

_yielded

_positive

func-tions;

the

low

reflectance region

_yielded

a negative

function

;

and some region

in

between

yielded

a zero

function

(perfect

constancy).

In

order

to

find

a

similar

form

of

brightness

functions,

with

_particular

reference

to

the

oc-currence of negative slopes,

Flock

and

Noguchi

(1970,

1973)

and

Noguchi

and

Masuda

(1971)

have

replicated

the

Jameson

and

Hurvich

study.

Despite

various changes

in

experimental

con-ditions

to

maximize

the

probability

of

getting

negative slopes, none were observed

for

any

S

at

any

treatment

Ievel

in

Flock

and

Noguchi's

two

studies,

and

only

two

negative,

though

slight,

slopes

were

found

in

Noguchi

and

Masuda's

study.

All

of

these

studies

consist-ently showed

that

slopes systematically

decre-ased as

the

reflectance of a

test

region

becarne

lower.

'

Such

confiicting

_results

between

Jameson

and

Hurvich's

study and

its

replications strongly suggest

that

there

should

be

at

least

two

different

_phenomena

or

_perceptual

dimensions,

brightness

and

lightness.

The

stimulu.s ar-rangements and

_procedures

in

replicated

ex-periments

were

engineered

so

that

the

Ss

could

make

judgments

of

brightness

without much

dificulty.

Since

Jameson

and

Hurvich

(1961)

apparently made

no

distinction

between

bright-ness and

lightness,

their

Ss

might

have

made

judgments

of

lightness

rather

than

brightness.

This

would

be

most

_probable

with

the

black-appearing region

having

the

lowest

reflectance.

The

experirnent

described

below,

therefore,

was

designed

to

confirm

_this

inference

using

Table

1.

Luminances

in

log

cd/m2 of

TF

Psychonomic

Science

Vol,

1,

No.

1

procedures

in

which

lightness

was explicitly set as

the

_phenomenon.

Method

Subjects

Ten

Ss,

undergraduates at

Chiba

University,

participated

in

the

experiment,

They

were naive

to

the

_purpose

of

the

experiment,

All

had

normal

vision

in

each eye.

Apparatus

As

shown

in

Figure

1,

a cross-shaped

con-figuration

composed of

five

Munsell

neutral

(N)

grays

was

mounted

on

a

Munsell

N

9,5

(white)

backgreund.

It

was

_presented

frontally

at

a

distance

ef

172cm

and

was viewed under one

of

four

illumination

levels

by

the

right eye

through

a circular aperture,

The

three

grays

in

the

vertical

direction

of

the

cross

irom

top

through

center

to

bottom

were

N5.0,

N9.0,

and

Nl,5

in

Munsell

value.

The

two

_grays

to

the

left

and right of

the

center square were

N

3,O

and

N

7,O

in

Munsell

value, respectively.

Fig.

1,

Six

test-field

(TF)

regions:five squares

in

a cross and

the

background

of

the

cross.

(Munsell

values, contrast ratios, and

Iuminances

are shown

in

Tabre

1.)

regions under

four

levels

of

illuminance.

Location

LogContrastRatio

MunsellValue

Bottom1.501.5 Left1.123.0

Top.735,O

Right.347.0

Center,109.0

Background

o9.5

.S

8i･gca

'ggEA=

2.

59L61

.62o*

L58

.59

-.41-L

05

L95

.96-.03-.66

2.341.36

.38-.28

2,721.

73

,76

,15

2,97L97

.97

,40

3.

042.081.

08

.51

K.

Noguchi

and

M.

Motoki:

AchromaticColor

Constancy

and

Lightness

Functions

53

Each

square of

_gray,

measuring

3cm

on a

side, subtended approximately

1

deg

of

arc

and

the

total

angular

diameter

of

the

display,

includ-ing

the

configuration and visible

_part

of

the

background,

was

7

deg

of

arc,

A

slide

_projector

with an

iodide

halogen

lamp

(24-v,

150-w)

illuminated

the

display.

The

pro-jector

was suitably screened

to

reduce stray

light.

In

order

to

vary

the

illumination

oi

the

display,

four

different

combinations of neutral

density

filters

could

be

_placed

in

a

holder

located

behind

the

eye-piece.

The

four

log

relative

illuminances

were

O,

0.62,

1.61,

and

2.59.

The

luminances

of

the

five

square

and

their

background

expressed

in

log

cd/m2 are

shown

in

Table

1.

Procedure

Before

being

presented

the

display,

each

S

was

trained

to

establish a subjective

scale

of

lightness,

using a

Munsell

N

scale.

The

E

presented

nine

Munsell

_patches

(3cmx3cm),

ranging

from

N1.0

to

N9.0

in

steps

of

1.0

in

Munsell

value, at random on a

black

back-groud.

The

Swas

asked

to

rank

these

nine

patches

in

order

to

make

the

Munsell

N

scale.

The

S

a!so was

told

to

remember

them

and

to

sort

into

five

achromatic color categories:

black,

dark

_gray,

medium

_gray,

light

_gray,

and

white.

Then

the

E

presented

the

five

Munsell

patches,

N1.0,

3.0,

5.0,

7.0,

and

9.0,

one

at

a

time,

and

asked

the

S

to

say whether

it

was

black,

dark

_gray,

medium

gray,

light

gray,

or

white, and

thereafter

to

assign

it

the

Munsell

value.

Again,

the

E

showed

the

nine

Munsell

patches

one at a

time

in

a random order and asked

the

S

tQ

number

them

correctly.

After

this

task

was completed,

the

fellowing

instruc-tions

were

_given:

"In

the

experiment

you

are

_going

to

_participate,

a

black

which

is

blacker

than

N1,O

or a white which

is

whiter

than

N9.0

might

appear.

In

this

case

_you

can use a nurnber such as

O

or

10.

That

is,

_you

can use any number within a

O-10

lightness

scale."

After

this

training

period,

S

was

taken

to

the

observation

booth

where

he

received

in-strctions

about

his

task

and

left

in

the

dark

for

10

min,

The

instructions

_given

to

the

S

were:

"Your

_task

_is

_to

_make

judgments

_about

blackness,

grayness,

and

whiteness.

A

cross

composed of

five

squares will

be

_presented

to

the

right

eye.

Each

square

in

the

cross

will

be

designated

by

the

lecation,

`top', `center',

`bottom', `right',

and

`left',

and

the

circular

field

surrounding

the

cross will

be

called

`background'.

_You

_{are asked}

_to

_look

_{at a}

square

(or

background)

designated

by

its

loca-tion

and

to

say at once whether

it

is

`black', `dark

gray',

`medium

gray',

`light

gray',

or

`white',

and

then

to

assign a number

to

it,

using

the

_previously

learned

Munsell

scale.

For

example, say `black,

_1.0',

`medium

gray,

5.0',

`light

gray,

7.0'

and

so

on.

Also,

_you

can use

fractions

such as `black,

1,5',

`medium

gray,

5.5',

or `white,

_9.5'."

In

short,

in

_the

_present

_experiment,

_two

classes

of

judgments

were made:

(1)

First

the

S

was asked

to

look

at one of

the

six

test

field

(TF)

regions

designated

by

its

location

_and

_to

say at once

its

achromatic color

(category

judgment);

and

then

(2)

he

was required

to

assign

a

number

to

it,

indicating

its

degree

of

lightness

_(numerical

_judgment).

The

E

specified

the

TF

region

after

the

display

had

appeared

for

le

sec.

The

SS

were

instructed

not

to

look

at any

_particular

area

until

the

E]

specified

the

TF

region.

Each

S

was

tested

for

each

of

the

six

TF

regions

₍₅

squares and

1

background)

at each of

the

four

illumination

levels.

The

total

of

24

treatment-combinations was

_presented

in

a random

order

with a

20-sec

dark

interval

between

trials.

This

_procedure

was

replicated

four

_times

_with

different

random sequences.

Therefore,

each

S

made a

total

of

96

judments

each

for

the

two

classes of

tasks.

Resultsand

Discussion

Achrornatic

Color

Naming

First

look

at

the

results

as

to

hew

the

Ss

assigned

the

five

categories of achromatic colors･

to

each of

the

six

TF

regiens under

the

four

levels

of

illuminance.

Figure

2

shows sche-matically

the

distribution

of

the

total

of

960

category

judgments

(6

TF

regions ×

4

illumi-nances ×

4

replications x10

SS).

The

TF

region with

the

highest

contrast ratio

(CR=1.50)

of surround

to

focal

luminance

(or

lowest

reflect-ance,

N1.5)

was almost always reported

to

be

`black', _{regardless of changes}

_in

_illuminance.

54

;y5g-rgs8

The

Japanese

Journalof

PsychonomicScience

Vol.

1,

No,

1

LogCentrastRatielCR)1,51.1211O.73o,34o,101'oi MunsellV21ue 1.5 13.0i5,O7.09.09.51Total

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₁

'1

e

L,R,L: Log Rela;ive ttturninanee

Fig,

2.

Schematic

representation of

this

TF

rergion was named `dark

gray'.

Achromatic

color namings

for

the

other

TF

regions with

lower

CRs

(or

higher

refiectances) were

less

constant:

As

illuminance

was

incre-ased

over approximately

2.6

log

units, some

TF

regions

shifted

from

black

to

gray

(mostly

`,dark

gray')

and sorne

from

_gray

(mostly

`light

gray')

to

white.

Such

shifts

of

color names were

largely

restricted within

two

adjacent

region

categories :

for

example, a

S

who named a

TF

`dark

gray'

under

one

level

of

illuminance

tended

to

name

the

same

TF

region `medium

gray'

under

the

higher

level

of

illuminance,

but

he

continued

to

use

that

same co!or name with

further

increases

in

illuminanee.

The

total

of each category

distribution

over changes

in

illuminance

(with

the

category responses

totaled

across

the

different

TF

regions) clearly

demonstrates

that

`black'

was

virtually

invariant

and

`white' _{was very susceptible}

_to

_changes

in

illuminance

(See

the

rightest column

of

Figure

2).

It

may

be

useful

to

introduce

the

concept of achromatic color constancy

for

describing

ap-pearances

of

achromatic colors with changing

illumination.

It

can

be

defined

like

this:

the

achromatic colors of surfaces

like

the

Munsell

gray

series remain relatively constant

over

a

reasonable

range

of

the

_photopic

vision.

That

is,

a

TF

region as named `black'

(or

`gray' or

`white') _{under one}

level

_of

i!lumination

con-tinues

to

appear

to

be

`black'

(or

`gray' _or

distribution

ofachromatic color namings.

`white')

under all other

levels

ef

iliumination.

In

fact,

Flock

₍₁₉₇₄₎

demonstrated

that

this

class

of

achromatic

constancy was

_almost

perfect

over changes

in

illumination

of

2.8

log

units.

His

Ss

reported

that,

regardless of changes

in

illumination,

the

TF

square with

the

highest

CR

was

black;

the

TF

squares with

lower

CRs

were white; and

the

TF

squares with

intermediate

CRs

were

_gray.

In

FIock's

experiment

there

were

virtually

_perfect

constancies

for

all

tl]e

seven

TF

squares arrayed

in

a cross-shape on a white

background,

In

the

_present

experiment,

however,

the

degree

of

achromatic

constancy changed with

different

TF

regions.

As

stated

earlier,

perfect

constancy occurred

only

for

the

TF

region

of

the

highest

CR

that

was reported

to

be

black,

As

the

CR

of

the

TF

region was made

lower,

achromatic constancy

became

less

perfect.

Such

difference

may

be

due

to

the

mode

of

adaptation:

Flock's

Ss

were

light-adapted

for

42

seconds

to

the

level

near

the

background

luminance

on

each

trial

without any

dark-adaptation

between

trials,

whereas

the

Ss

in

this

experiment were

light-adapted

only

for

10

seconds with

_a

20

second

dark-adaptation

between

trials.

In

addition

to

this,

Flock's

Ss

were required

to

employ only

three

judgment

categories,

black,

_gray,

_and

white,

in$tead

of

five

categories which

were

used

in

the

_present

experiment.

Lightness

Functions

judg-1QO

K.

_Noguchi

and

M.Motoki

:Achrornatic

-=oEmz:"

no=-=en:

Background

-:

N

9.S

! .i;=:/･

'lle9A?er

Color

Constancy

and

Lightness

Functions

90

8.0

zo

6.0

5.0

4P

3.0

2.0

1.0

o

./.T

(--

--.//

"---/

ig

/

---･

v.x--NZOR;ght

N

5.0

Top

N3.0Left

N1.5Bottom

O

1.0

2.0

3.0

Leg

Re{at;ve

:llum;nance

Fig.

3.

Mean

scalar

judgments

oi

lightness

for

six

TF

regions plotted against

Iog

relative

illuminance.

55

ments as a

funqtion

ef

log

_relative

illuminance

is

shown

in

Figure

3.

The

data

_points

in

Figure

3

are mean

lightness

judgment

averaged over

the

10Ss.

A

treatmentsxSs

ANOVA

was

_performed

to

determine

the

effects of

illumination

and

TF

region on

lightness

judg-ments.

There

_were

significant main effects:

for

illumination,

P<3,27)==69.21,

_P<,O05;

for

TFregion,F<5,45)==294,29,P<.O05,

Theinter-action

term

of

illuminance

×

TF

region was

also significant,

IJ<15,135)==5.10,

_p<,O05.

Treated

,as

linear

functions,

the

fiuctuations

Qf

lightness

judgments

over

the

four

levels

of

illuminance

were

fitted

by

least-squares

straight

lines.

In

Table

2

is

listed

individual

and

mean regression coeffcients.

Table

2

indicates

_that

individual

S's

coethcients

distributed

widely

between

different

TF

regions and

between

Ss.

The

total

range was

between

-.23

and

.99.

A

t-test

was

_performed

to

determine

whether each coethcient

differs

significantly

from

zero.

As

shown

in

Table

2,

22

of

the

60

coeMcients were

found

to

be

significantly

different

from

zero.

Except

for

one negative slope

(-.18),

these

significant slopes were all

_positive.

It

would seem,

therefore,

that

it

is

a rare

occurrence

to

find

slepes

that

are

negative.

From

the

test

for

significance of

linear

regression coeMcients,

the

total

of

the

60

lightness

functions

can

be

classified

into

_three

_groups:

(1)

1

negative

function

that

was observed

for

the

black-Table

2,Individualandmeanlinear

regressien coefieients.

LonContrast

Ratio

L50

1.12

.73

.34

,10

o

#1

#2

#3

#4

#5

Ss

#6

#7

#8

#9

#le

l8*1108030508091732*41

,07n

23-.Ol

04

71**

35

eo

.46

29

75*

.43*-.03

.21

.11

.46*

.14

.30

.51

.57

.16**

.52

.23

a39"

.52*

.31

.29-.08

.26

.33

.28*

.49.48.55**.13.30**.39.80**.40.48.37**

.44*.90**.63*.27.30*.38**.97*.99**.53.41*

Mean

r2

.07.82 ..2475 .29.81 .31.80

.45*.96

.51**.98

*p<.05 *\<.Ol

56

The

Japanese

Journal

of appearing

TF

region

_;

(2)

21

_posiLive

functions

that

were mostly observed

for

the

light

gray-and

white-appearing

TF

regions; and

(3)

38

functions

with zero slopes

or

_possibly

nonlinear

components which will

be

discussed

later.

Mean

linear

regression

coethcients are also

given

in

Table

2

(one

up

from

the

bottom),

ANOVA

was

run

to

determine

whether

these

coeMcients

changed

with

different

TF

regions.

There

was a significant main

effect,

liK5,45)=

5.73,

_P<.Ol.

It

seemed

that

the

slopes

tended

to

become

increasingly

steeper as

the

CR

of

TF

region

was

decreased,

However,

the

stopes

were not significantly

different

from

zero

ex-cept

for

the

two

steepest ones obtained

for

the

TF

regions

having

the

CRs

of

O

and

.10

(N

9.5

and

N

9.0).

It

should

be

_pointed

out

_that

the

use of

linear

regressiQn coeMcients

omitted

any

reference

to

_possibly

nonlinear

fiuctuations

in

lightness

judgments

over

changes

in

illuminance.

The

values of r2

in

Table

2

suggest

the

existence

of

nonlinear

flttctuations

at

least

for

the

TF

regions of

higher

CRs.

As

a rough measure

of

the

degree

of such nonlinear effects,

there-fore,

the

reversals

in

each

S's

scalar

judgments

for

the

four

successively

increasing

levels

of

illurninance

were counted.

If

S's

judgments

for

some

TF

region under

the

four

levels

of

illuminance,

for

exarnple, were

2.0,

2,5,

2.4,

and

2,3,

respectively,

there

would

be

twe

reversals.

Had

his

judgments

been

2.9,

3,8,

3.8,

and

2.9,

there

would

be

1

reversal and

1

tie.

Correspondingly,

for

each

TF

region with

10

Ss,

30

reversals

would

be

possible.

For

the

6

TF

regions,

Bottom

(Nl.5),

Left

(N3,5),

Top

(N

5.0),

Right

_(N

7.0),

Center

_(N

9.0),

and

Back-ground

(N9.5),

the

reversals were

10

(with3

ties),

9,

9

_(with

2

ties),

9

_(with

2

ties),

2

_(with

1

tie),

and

2,

respectively.

It

seemed,

therefore,

that

the

reversals were suMciently rare

to

warrant

the

use

of

linear

regression coethcients

for

Center

and

Background

which were

lowest

Psychonomic

Science

Vol.

1,

No,

1

in

CR.

Fer

the

other

TF

regions

of

higher

CRs,

however,

there

did

exist nonlinear effects,

Closer

inspection

of

the

data

configuration

in

Figure

3

also reveals

that

there

would

be

nonlinear

fluctuations

of

lightness

judgments

over

the

change

in

illuminance.

Namely,

there

seemed

to

exist

two

components

to

the

lightness

functions:

in

the

case of

focal

TF

regions

(squares),

there

was

an

initial,

_pronounced

in-crease

in

lightness

for

the

lower

levels

of

illu-minance and

then

slight

decrease

ior

the

highest

level

of

illuminance;and

when

the

background

served

as

a

TF

region,

this

relation was

re-versed.

Now

it

is

clear

that

the

fit

of

the

linear

relationship will not

be

satisfactory.

There-iore,

the

fiuctuations

of

lightness

judgments

for

each

TF

region

over

the

four

illuminances

were

fitted

by

least-squares

curves

(second-degree).

The

_quadratic

equations and

their

coethcients of

determination

(R2)

are

listed

in

Table

3,

Table

3,

Curvilinear

regression

(second-degree)

equations

(y=

Be+Bix+BzxZ)

and ceeMcients of

determination

(R2),

TF

Region

BottomLeftTopRightCenterBackground

Po

,8411.9813.4515.1027.1037.275

fi1.183.754.701.853.747.284

P2r.043-.196-.158--.210-.113

.108

R2

1Ili

.974.998.937.998.998.998

2)

B2

was

_positive

only when the

background

served

as

TE

This

suggests

that

it

would

have

been

dithcult

or

impossible

for

the

Ss

to

separate

between

lightness

and

brightness

due

to

the

appearance of

the

background

which

tended

to

be

seen as a

film

color rather than as a surface

color.

So.

it

may

be

that

the

Ss

might

have

responded to

brightness

instead

of

lightness,

The

values of

R2

_prove

that

the

match

between

the

observed

data-points

and

the

values

predicted

from

these

equations

is

rather clese and,

therefore,

that

lightness

functions

are curvilinear

for

a

semilog

transformation,

Furthermore,

it

can

be

seen

from

the

sign of

the

B22)

coethcients

that

the

lightness

functions

for

the

TF

regions which are

five

squares

forming

a

cross would

be

regarded

_as

_pesitively

decelerating

curves

(concave

downward)

and

the

function

for

the

TF

region which

isa

background

surrounding

the

cross

is

negatively accelerating curve

(concave

upward).

General

Discussion

and

Conclusions

Several

theories

of

brig)lltness

_perception

under contrast

(Bartelson

&

Breneman,

1967;

K.

Noguchi

and

M,

Motoki:

Achrornatic

Jameson

&

Hurvich,

1964,

1970;

Marimont,

1962;

Stevens

&

Stevens,

1960)

predict

that

brightness

_judgments

decrease

rather

than

increase

for

certain conditions

when

illuminance

is

increased.

These

_predicted

negative

func-tions

seem

to

occur

when

the

CR

of surround

to

focal

luminance

is

relatively

large

and

i,s

held

constant over

the

increases

in

illuminance,

As

the

magnitude of

the

CR

is

decreased,

functions

correspondingly

become

less

negative,

become

flat,

and

then

become

increasingly

positive.

It

is

not clear,

however,

whether

these

theories

really

refer

to

the

_phenomenon

of

brightness.

It

seerns

probable

that

the

data

supporting

some

theories

have

riothing

to

do

with

brightness

a'nd

instead

would

have

been

obtained

under conditions

in

which only

light-ness

judgments

could

be

made.

The

opponent-process

theory

(Flock,

1970;

Jameson

&

Hurvich,

1964,

1970)

can

be

inter-preted

to

tie

together

brightness

and

lightness

judgments:

As

illuminance

is

increased,

all

light

_grays

and

whites will

become

increasingly

t`brighter" _and "whiter'' _at

the

_same rate,

all

dark

grays

and

blacks

will

become

incre-asingly "less

bright"

_and "blacker" _at

the

same rate, and some mid-gray will not change either

in

brightness

or

in

lightness.

This

type

of

theory

unfortunately

blurs

any

distinction

between

these

two

perceptual

dimensions.

It

is

not

clear

from

Jameson

and

Hurvich's

(1961)

use

of

the

terms

brightness

and

lightness

if

they

made

a

distinction.

Later

studies

(Flock

&

Noguchl,

1970,

1973;

Noguchi

&

Masuda,

1971)

where

the

S's

task

was explicitly

to

judge

brightness

have

all

failed

to

find

significant negative

or

zero

functions,

In

the

present

experiment,

therefore,

it

was

questioned

whether negative

or

zero

functions

could

be

observed when

the

Ss

were required

to

make

lightness

judgments

instead

of

bright-ness

judgments,

In

order

to

facilitate

lightness

responses,

the

task

of achromatic color naming was

_given

to

the

S

before

making

lightness

judgments

in

terms

of

the

Munsel!

neutral

scale.

Although

most of

the

lightness

functions

were

positive

or approximately zero, negative

functions,

though

very exceptional, were also observed

for

some

Ss

when

the

TF

regions

had

the

Iargest

CR.

In

his

lightness

match

experiment,

Helson

(1943)

also

found

approxi-Color

Constancy

and

Lightness

Functions

57

mate zero

(.05)

and

negative

(-.12)

functions

for

the

TF

regions of

the

largest

CR.

These

findings

suggest

that

the

possibility

of

finding

negative and zero slopes seems

to

be

higher

for

lightness

than

for

brightness

_judments.

It

should

be

_pointed

out,

however,

that

the

sign-ificant

negative slope was contributed

by

only

one of

the

10

Ss

in

the

present

experiment and

was much

less

steep

than

that

of

Jameson

and

Hurvich's

(1961).

Furthermore,

mean

lightness

judgments

averaged

over

all

the

Ss

showed

no negative slopes even

for

the

TF

region

of

the

highest

CR

which

_gave

an almost zero slope.

The

_previous

studies

(Fiock,

Noguchi,

&

Muter,

1974;

Kozaki

&

Noguchi,

1976)

on

lightness

judgments

also

demonstrated

that

the

occurren ¢e

of

negative

slopes

was

very rare.

The

negative

slopes

obtained

in

Helson

₍₁₉₄₃₎

and

Jameson

and

Hurvich

(1961)

would

_probab!y

be

due

to

thls:

in

both

ex-periments,

there

was an

anomalous

asymmetry

betwgen

preadaptation

and

TF

luminances;

their

Ss

were

allowed

to

look

back

and

forth

from

the

brightly

illuminated

comparison region

to

the

very

dimly

illuminated

TF

region.

In

other

words,

the

S's

eyes were always

adapted

to

a relatively

high

level

of

illumination

when

the

S

observed

the

darkest

TF

region under

a very

low

level

of

illumination.

It

would seem reasonable

that

the

negative slopes obtained under such anomalous conditions

are

rather exceptional,

It

can

be

concluded,

therefore,

that

the

theoretical

claim

for

the

_generality

of negative

functlons

for

both

lightness

and

brightness

domains

should

be

rejected.

The

results

from

lightness

and

brightness

experiments

(for

iightness,

Flock

et al.,

1974;

KQzaki

&

Noguchi,

1976

_;

this

study, and

for

brightness,

Flock

&

Noguchi,

1970,

1974;

Noguchi

&

Masuda,

1971)

seem

to

indicatea

similar

data

configuration when

_plotted

against

log

relative

illuminance

:

there

would

be

a

high

positive

correlation

between

a

_group

of

lightness

functions

and

those

of

brightness

functions.

As

pointed

out

by

Flock

(1974),

however,

the

presence

of a correlation

between

lightness

and

brightness

should

not

be

allowed

to

blur

the

difference

between

these

two

dimensions.

It

is

suggested

that

_given

a

log

transformation

of

illuminance,

lightness

functions

are

concave

58

The

Japanese

Journal

of upward: as

illuminance

is

increased,

_there

is

a small amount

_of

change

in

the

lightness

of

a

TF

region and

the

decelerating

use of number

in

judging

its

_grayness,

whereas

_there

is

_an

accelerating use

of

number

in

speciiying

the

brightness

of

that

TF

region,

References

Bartleson,

C.

R.,

&

Breneman,

E,

_J.

1967

Brightness

perception

in

cornp]ex

fields.

Iburnal

of

the

QPtical

Sociely

of

America,

57,

953-957.

Beck,

_J.

1972

Sut:face

color

percoption.

Ithaca,

N.

Y.:

Cornel!

Universitv

Press.

Flock,

H.R,

1971

Toward

a

thelory

of

brightness

contrast.

In

M.H.

Appley

(Ed.),

level

theor.v,

A

symposium,

New

York

and

London:

Acadernic

Press.

Flock,

H.R.

1974

Stimttlus

structure

in

lightness

and

brightness

experiments.

In

R.

B.

McLeod,

&

H.L.

Pick,

Jr.

{Eds.),

Plarcqption.

fdssays

in

honor

of

Jdmes

f.

Gibson.

Ithaca,

N.

Y.

:

Cornell

University

Press.

Flock,

H.L.,

&

NoguchL

K.

1970

An

experirnental

test

of

Jameson

and

Hurvich's

_theory

of

brightness

contrast.

Percaption

&

lvchoPdysics,

8,

129-136,

F'lock.

H.R,,

&

Noguchi,

K,

1973

Brightness

tions

for

a complex

field

with changing

mination and

background.

CZxnadian

lb"rnal

of

)PSychology,

27,

16-38.

Flock,

H.R.,

Noguchi,

K,,

&

Muter,

RM,

1974

Lightness

changes

in

a complex

field

with

Psychonomic

_Science

_Vol,

1,

No.

1

changing

illumination

and

background,

dian

lburnal

of

Rsycholag),,

28,

446-467.

Helsonr

II.

1943

Some

factQrs

and

implications

of

color constancy,

lburnel

of

the

QPtical

Sociely

of

America,

33,

555-567.

Jameson,

D.,

&

Hurvich,

L.M.

1961

Complexities

of

_perceived

brightness.

Science,

133,

174-179.

Jameson,

D.

&

Hurvich,

LM.

1964

Theory

of

brightness

and color contrast

in

human

vision,

Vision

Research,

4,

135-l54,

Jameson,

D.,

&

I'Iurvich,

L,M,

1970

Improvable,

yes;

insoluble,

no : a reply to

Flock,

1lercaption

&

Rsychqpdysics,

8,

125-128.

Katz,

D.

1935

The

world

ofeoJour.

(Translated

from

the

2nd

German

edition

by

R,B,

MacLeod

and

C.W.

Fox).

London:

Kegan

PauL

Kozaki,

A.,

&

Noguchi,

K.

1976

The

relationship

between

perceived

surface-lightness and

ceived

illumination.

A

manifestation of

ceptual scission.

lvcholagical

Research,

39,

1-16.

Marimont,

R.B,

1962

Model

forvisual

respense

to

contrast.

Jburnal

of

the

(iptical

Sociely

_of

America,

52,

800-806.

Noguchi,

K.,

&

Masuda,

N.

197i

Brightness

changes

in

a complex

field

with changing

illumination

:

A

re-examination of

Jamesen

and

Hurvich's

study of

brightness

constancy.

knanese

lisy

cholagical

Research,

13,

60-69,

Stevens,

S.

S.,

&

Stevens,

J.C.

1960

Brightness

functions:

Pararnetric

effects of adaptation

and contrast,

fournal

of

the

Ciptical

Sociely

_of

America,

50,

1139.