Perceived Length of Moving Figures : The Effect of Luminance Relationship Between Figure and Background upon Reduction Phenomenon

The 1itPaneselburnatofItsychonomicScience 1982,Vol.1,No. L45-50

PerceivedLength

of

Moving

Figures:

The

Effect

of

Luminance

Relationship

Between

Figure

and

Background

upon

Reduction

Phenomenon

Yoshiaki

Kiznazawa

NAKAJIMA

Uitiversity,

A rectangular figuremoving horizontallyat a constant speed shews a decreasein its

perceived Iength parallelto the directionof movement. This study concerns the effect of

the luminance relationship between figure and backgro"ncl ttpon this _phenomenon. The

perceived lengthina stationary state was also measured fordifferent exposure times cor-responding to the speeds used, in order to obtain the relative differencebetween the per-ceived lengthoi a figureina stationary state and that of the figurein a dynamic state. Three linearfiguresoi 1,5e,3" and 60 were used; all of them had a constant heightof

O.250. The stimulus figure was attqched to a horizontallymeving belt. Speedsof 280/s,

35M!sand 420/swere used. The _pointsof subjective equality of the stimulus figureswere obtained by the method of limits.Eightstudents served as subjects. The same reduction tendencies were shown at the differentspeeds despitethedifferentluminance relation$hips. Key words: rnotion, _perceived length,reduction _penomenon, linear figures,Iuminance

relationships, figureand background.

The

_perceived shape of a rectangular

figure

moving

horizontally

at a constant speed was

investigated.

The

perceivecl length of this

figure

_parallel

to the

direction

of movement

becomes

shorter as the speed increases,up to

a certain speed

(Tanaka,

1943a,1943b,1944;

Tanaka

&

Nakajima,

1970).

Morinaga,

No-guchi and

Ohishi

(1963)

confirmed

this

tendency

and named this decrease in the _perceived

length

of a moving figure"a _reduction

phe-nomenon ".

On

theother hand,Ansbacher

(1944)

reported

thatan illuminatedarc-line

_produced

by

trans-mitted

light

on a

black

disc

appeared shorter when rotated at a constant speed around a central

fixation

point.

Twenty

years

later,

using refiected

light,

Marshal1

and

Stanley

(1964)

reversed the

luminance

relationship

between

arc and

background

and found _a reversed effect :i.e. a

black

arc on a white

background

tended to appear

longer

when rotating than when stationary, although a white arc on a

black

background

tended toappear shorter

in

line

with

Ansbacher's

results.

Although

Ansbacher's

experiment

differed

from

Tanaka's

experiments

in

type of motion

(i.e.

the former used circular motion and the

Iatterusecl rectilinear metion), we rnay guess

that

the shrinkage

_phenomenon

Ansbacher

found in a retating arc is

fundamentally

the

same as the reduction _phenornenon Tanaka

found

in

a

horizentally

moving rectangle. The reason isthatthere are two elements common

to

Ansbacher's

and Tanaka's experiments:

(1)

the stimulus

figure

has

a

longer

actual

length

parallelto the

direction

of movement than the

length _{perpendicular} tothe

direction

of move-ment,

(2)

the_perceived

length

ef the stimulus

figure

appeared shorter _para!leltothe

direction

of rnovement.

When

the results of Tanaka's experlment

(1943a)

are compared with the results of

another of

his

experiments

in

1944,

we see

that the reduction phenomenon can

be

found

in

both

types of

luminance

relationship

be-tweerr

figure

and

background,

i.

e. with a

black

figureon a white

background

or with a

bright

light

figure

on a

dark

background.

Completely･

46 The JapaneseJournalof

different

apparatuses were used in these

ex-periments: the one used in 1943a was

based

on the

_projection

of a

figure

attached to a moving

be!t

upon a _grey sQreen by an opaque

projector exploiting surface refiection; _the

other, used in 1944, was

based

on

light

ire-flected

from a rotating surface mirror which created a moving

light

figure

by

the change of angles of incidenceand refiection. Though

there

is

a

difference

between

these systems, we may assume that the

luminance

relation-ships

between

figureand background of these experiments are the reverse of each other.

However,

in,

consideration of the results of

Marshall

and Stanley experiment concerning perceived arc-line which showed a reversed

effect

in

reversed

luminance

relationship

be-tween 'figure and

background,''I

wanted to confirm _clearly 'what _{effect the}

IuMinance

re-lationship

betWeen

figure

and

background

has

upon the redugtion' _phenomenon of a

horizon-tally moving

figure,

in _a closely controlled

condition so thata _preci6ecomparison may

be

possiblewith the same apparatus. This

prob-lem isthe firstconcern _{of the present} stUdy.

There

isanother _purpose ofthisstudy.

The

measurement method in the Marshall and

Stanley

experiment is

different

from that

em-ployed

by

Tanaka,

In

hisexperiments, Tanaka used a method of ,reproduction which required the subject to

draw

what he had _seen ona sheet of whit,e _paper. The results repprted

in

h.is

papers were

indicated

with the,index ･a

obtained in the calculation

by

_the following equation :

x:=100+(lt'h)1(L/U>

(1)

where ldenotes,thelength of, the,reproduced

figure,

h

denotes

the height of _the reproduced

figure,

L denotes the length of the original

figureand' ff

denotes

_the

height

_{of the}original

figinre.

As.we

can' see

from

this equation,

Tanaka investigatedthereduction _phenomenon

taking

both

perceived

height

and

_perceived

length intoconsideration.

On

theother hand,

Marshall･and

Stanleyused

a method of/ comparison･in wh'ich _the'subject

was required

to

state whether a straight

line

inthe･center

_(variable

stimulus) 'appeared to

be

longer

or $horter than the arc moving

around

it,･They

calculated the _paint of

sixb-Psychonomic Science Vol. 1,No, 'l

/t

jective

equality of only the length of this arc,

and

did

not

_yefer

tothe change of

height

at

'

all. ' '

We

carinot.directly c6mpare the results

tained by Tanaka and the results obtained by

Marshall

and

Stanley

because

of the

differences

ef measurement method as described above.

So,

I

hope to _provide results that can

be

directly

compared to the results of

Marshall

and

Stanley.

Experiment I

The purpose of this experirp. ent is_to

tigate the

perceived

length

of,linear figures,

, rnoving horizontallyat,constant speeds, and - _the effect of the luminance relationship between

figure and

background

upon this _perceived

length..

' '

Method'and

ProcedUre

The basicarrangement of the appafatus is shgwn

in'Fig.

1:

A

_.white

(or

black)

stimulus

'figure

was attached to the center of a

trans-parent'

belt

which was

dfiven

by

aTi electric

T]-Al.-"(ss B ISCII))

I

i

i

l I'15e]n_{,1 ･}

i

'

l

t

h

Sh SC3 SC2 Ti Fig,

(illS)

1. Basic arrangement of the apparatus. S: subject. Sgi: screen used as a

back-ground. Sc2:$creen with a 20cm

(length)

by I6cm

_(height)

rectangular aperture.

Scs: screen with a viewing hole, B:

transparentbelt. M:'motor. D:,rotating

drum. Tr:Volttransformer.

St:strobo-scope used t6 regulate the,speed: ･Sh: shutter. Ti:timen /.

Y. Nakajima: PerceivedLength ofMoving Figures 47

motor, the speed of which could

be

changed

by

a volt transformer, The $peed was

regu-lated

by

reference to stroboscepe-type system

using a small neon

light

and a

dotted

line

on

the

drive

drum.

A

rnoying stimulus figure was observed

through a rectangular aperture 20cm

<10V)

in

length

by

16cm

(80)

in height which was cut

from a

black

(or

white) screen _placed

just

before the moving

belt.

A black

(or

white)

background

screen was _put

just

behind

the

transpatent belt, The height of a!1the

figures

used was O,5cm

(O.250),

and the

lengths

were

3cm

_(150),

6cm

_(30),

and

12cm

(60).

Three

speeds of

56cmis

(28e/s),

70cm!s

(3501s)

and

84cmfs

_(4201s)

were used.

The

luminance

of

the white 'figures

(or.

backgfoiind)

was about

20.lcd/m2'and

that of the

black

figures

(or

background)

was about

1.0cd/m2.

The

view-ing

distance was 115cm.

Monocular

vision

'

was used, ' ''

The

subject sat

in

a

dark

room and was

required tofixupon the center of the

back-ground screen when the shutter

just

behind

the viewing

hole

was opened.

After

the

shut-terwas Qpened, a moving tlgure appeared on

the

background

screen and moved

horizontaliy

to the left.

Immediately

after the meving

figure

disappeared,

a eurtain above the

20

cm

by 16cm regtangular aperture dropped to cover

the aperture and at the same time reveal a comparison figurethat had

been

attached above

the

frame

of thisapperture. This comparison

figure was not visible until this time,

The

comparison figures were stationary linear

figures,

with a fixed height of O,5cm

(O.250)

and variable

len'gth.

The

subject was required

to $tate whether the stationary comparison

figureseemed to

him

to

be

longer

or shorter

than the moving

figure.

The

judgement

of equality was used. The length of the

cem-parisen figure was varied by increments of

O.2cm

_(O.10).

The method of

limits

was used.

Eight

undergraduate students majoring. in

psycho!ogy served as subjects.

All

of them

had normal visual acuity er corrected nermal

acuity. They were trained forthe'observation

and the _proeedure inadvance,

Results

The

_point

of subjective equality of each subject

for

each speed of each figure was calculated

for

both

luminance

relationships of a white

figure

on' a

black

background

and a

black

figure on a white

background.

The

means of those scores were

further

calculated foreach condition and are shown

in

Table''1.

Despite the restricted range of

figures

used,

it

is'possible

te estimate

from

thistabiethat

the _pointsof subjective equality

for

both

types of the

luminance

relationships show the same

tendency of

length

reduction'when the speed

increases,though the amount of reduction

is

not great

in

either case,

These

results

don't

completly coincide with what

Marshall

and

Stanley

found intheir

ex-periment with the rotating arc: that is,a

tendency toward reduction of the _per¢eived

length

of _a white'arc on _a black background, and increaseof the

_perceived

lengthef a black arc on a white

background.

Table 1, Mean perceived lengths

(cm)

two luminanceoE

three moving figuresat

relationships

(n

=8)

three speeds fur

Luminance

relationship Whitet.figureandblackbackground Blackfigureandwhitebackgreund

Speed 156 cmls/1 Figure3cm 6cm 12cm MeanSDMeanSDMeanSD3.01 ,095.70 .2611.11 .79 70cmts 2.88 .2･15.44 .5910.72 .97 84cmfsf:56 cmfs

L

2.80 ,105.00 .64IO,54LOI

l･

t 3.01･ .125.79 .2711,45 ,51 70cmts 2.96 .165.75 ,3011.21 ,72 84crnls i 2.82 .2･45.58 .3411.02 .79

Luminance

relationship Whitefigureandblackbackground Blackfigureandwhitebackground

48 The

Japanese

Journal

of Psychonomic

Experiment

II

There

was a necessity to

investigate

the

perceived

length

of stationary

linear

figures,

when _observed for

different

exposure _times

corresponding to the speeds used

in

Experi-ment

I,

in

order toobtain the relative

differ-ence

between

the _perceived

length

of a

figure

ina stationary state and that of the figurein

a dynamic state.

Method

amd

Procedure

The same three stimulus figuresas used in

ExperimentI

and three exposure times cor-responding to three speeds

in

Experiment

!

were used

in

Experiment

II.

Exposure

times used were .36s, .29s and

.24s.

The

calculation of these times was

based

upon

dividing

the

length

(20cm)

of the rectangular aperture in which the

figures

rnoved

by

their speeds. The exposure

time

was varied

by

a timer-controlledshutter

be-hind

the viewing hole. The subject viewed a stationary

figure

within the aperture frame

until the timed shutter closed.

Immediately

after the shutter closed and the curtain above

the 20cm

by

16cm

rectangular aperture was

lowered,

revealing the variable comparison

figure,

theshutter was reopened.

The

subject was then required tostate whether the

com-parison figurewas longer or shorter than the

figure

which was

_presented

for

a restricted

time.

Other

condition were the same as in

Experiment

I.

The

sarne eight students served as subjects inExperiment II.

Table 2. Mean perceived lengths

(cm)

of three corresponding to three speeds for two

.24 Exposure timet .36s .29s Figure Mean 3cm SD Mean 6cm SD Mean 12cm SD 3,05 .115.91 .3111.77 .42 3.02 .095.93 .2311.85 .43

Science Vol. 1,No. 1

Results

The

results obtained are shown

in

Table

2.

This

table obviously shows thatthe _pointof

subjective equality of _the length of each

sta-tionary figure _presented for each exposure

time

is

almost

equal to the original

length

in

both

luminance relationships

between

figure

and

background.

Discussion

Though

results obtained

from

Experiment

II

do

not appear to

indicate

a clear change in

perceived

length

of a stationary

figure

pre-sented

for

a short exposure time, itseemed

better

to use an

index

_ip

which expresses the relative

difference

between

the

perceived

length of a figurein a stationary state and that of

this figure in a dynamic state. Therefore,

from

both

results of Experiment Iand

Experi-ment II,the index _¢ was calculated by the

followingequation :

ip-(A-B)fA

(2)

where

A

denotes

the _perceived length of a

figure

in

a stationary state and

B

denotes

the

perceived

length

of this figureina

dynamic

state.

The

re$ults of thiscalculation foreach

speed are shown

in

Fig. 2. The statistical

P-values

of each figure

for

each luminance

relationship fortesting the hypothesisof

_di=O

(i.

e.

A=:B)

were calculated foreach speed and

those for testingthe

difference

between

the

two luminance relationships were also

calcu-lated.

The results obtained are shown

in

stationary figuresfor three exposure times

luminance relationships

(n=8)

s .36s .29s .24s 3 5 11 .03.11.91.17.79.42 3.06 .09 6.02 .1311.78 .51 3.03 .10 6.05 .0711.88 .40 3.06 .09 6.05 .0911.86 .38

t

The calculation of exposure times was based

aperture inwhich the figr2resmoved by theirupon

dividingthe speeds.

Y.Nakajima: Perceived Length of Moving Figures 49

('PX

IIi

O).--I i'

{

gL

/

iileh.tsii

ifillts

] ,,:.;l,,,,,ild '5X

illi

`')Fi""]'`''ti`'-M ,/ " (`'`'X

:/l

,iF O) Figurc:i2cm

:'

H{Rlr,fl,C

::ttl:r()und

ii

/

il

' t .n

10 1'O

/

lo,n p.-..f'i 9 g / [) J .

:･,

..,･/

lili

_,/

"

l

ily _.tiX' ,,/ 5 JJt n ' f xt

L-

/,,.

.4 _,,:- ･ 4

i･l

,･"'

.･'

;,

;

de

Ugt ₇₀

_",l

g56

_t

_tt

84 056 7C)84

Speecl(cm,,'s) Speed

(cmi's)

Speed(cm!s)

Fig.2. The disof three figuresat three speeds for two luminancerelationships. The

di

expresses the relative differencebetween A, i.e.the perceived length of a figureina

stationary state, and B, i,e,that of this figure ina dynamic state:

e=(A-B)IA.

Table

3

and

Table

4.

From

the

p-values

in

the question arises as _to why the reduction

Table

4,

we may say that the clear effects of _phenomenon

is

found

without reference

to

the

luminance

relationship

between

figureand

luminance

relationship

between

figure

and

background do not exist,

but

as is obvious

background

in horizontallymoving figures,in

from

Table

3,

there are significant

differences

spite of the existence of the

fact

that,

in

between

the _perceived

lengths

of

figures

ina rotating arcs, thisreduction _phenomenon

is

dynamic

state and those of these figuresina found only under the condition of a white

stationary state for

both

luminance

relation-

figure

on ablackbackground. Themosteasily

ships.

Comparing

Tables

1

and 2, we may proposed answer may

be

_{that the} reduction

interpretthese significant

differences

as

being

_phenomena seen in rectilinear motion and in

caused by the reduction _phenomenon. Then, circular motion have no relation to each other:

'

Table 3. The

p-valuest

of three figuresat three speeds for two luminance relationships ･ fortesting the hypothesisof

e=O

(i,e.

A=B)tt

Luminance relationship SpeedFigure 3cm 6cm 12cm

White figureand blackbackground 56cmis .4<p<.5

(t=,8936)

.05<p<.1

(t.:,1.9711)

.02<p<.05

(t=2.0850)

70crnls J .2<P<.3

(t=1.2632)

.Ol<p<.02

(t=3.1358)

.Ol<p<.02

(t=3.1800)

84cmts .OOI<p<.

(t=3.7650)

.OOI<p<.

(t=4.1123)

.OOI<p<.

(t=4.0340)

Ol Ol Ol

Blackfigureand white background 56cmis .4<P<.5

(t=.7650)

.02<p<.05

(t=2.6170)

.05<p<.1

(t=1.9504)

70cm/s .5<p<.6

(t=.6643)

.02<p<.05

(t=2.5000)

.02<P<.05

(t=:2.5045)

84cmls .05<p<.1

(t=2.1717)

.Ol<p<.02

(t==3.442O)

.02<p<.05

(t==2.8612)

tttThe

P-values

See Fig. 2 forwere

obtained from the results of definitionsof

di,

A and B.

50

Table 4.

speeds

The Japanese

Journal

of

The P-valuestof three figuresat three

between two Iuminance relationships

Psychonomic Speed 56cmls7ocm/sI84cmts Figure 3cm 6cm 12cm .9<P<1.0

(t=.1161)

.8<P<.9

(t=.1400)

.2<P<.3

I(t=-1,276s)

P=.6(t=-.5490) .2<P<.3

(t=-L1696)

.1<p<.2

(t=-L6041)

.9<P<1.0

(t=.0934)

.05<p<.1

(t=-2.2139)

.1<P<.2

(t.."1.840e)

1

t

The _P-valueswere obtained from the results

of t-testsbetween the corresponding groups

(cif=8-1=7,

two-tailed tests).

they

have

only externally sirnilarappearances,

coming from

different

sources,

However,

when

we look_{at the restricted range of}

figures

_and

speeds used

here

and the _{present general} state

of the _poor

knowledge

on the reduction phe-nomenon, itseems too dangerous to

jump

to

the conclusion that the

discrepancy

reported

here

in

length

change

between

horizontally moving figures and rotating _{arcs suggests} mutual

independence.

Summary

The

perceived

length

of

different

linear

figures

was measured under differentmoving speeds _and different

luminance

_{relationships}

between

figure

and

background.

The

method of limits was used in measurement.

The

stimulus

figure

was attached toa

belt

moving

horizontally

at a constant speed.

The

_perceivd

Science VoL l,No,1

length

in

a stationary state was also measured

for

different

exposure times corresponding to

thespeeds used,

in

order toobtain the relative

difference

between

the _perceived length of a

figure

in a stationary _{state and that} of the

figure in a

dynamic

state.

The

same reduc-tion tendencies were shown at

the

different speeds

despite

the

different

luminance

relation-ships.

References

Ansbacher, H.L. 1944 Distortionintheperception

of real rnovement. Iburnal

of

Experimental

Rsychology,34,1-23.

Marshall, A,J. & Stanley, G. 1964 The apparent length of lightand dark arcs seen _peripherally in rotary motion. Australian

lburnal

of

chegQgy, 16,120-12s.

Morinaga,S. Noguchi, K, & Ohishi,A, 1963On the reduction _phenomenon in _pereeption of moving figures.fournal

of

the Cellage

_of

Arts and Sciences,Chiba Uhaiversit],,4,'19-23.

(In

Japanese

with English summary)

Tanaka, Y, 1943a Perception of moving figures

(1),

lapanesefournai

of

Rsychology,17,333-352.

(In

Japanese)

Tanaka, Y. 1943b Perceptionof moving figures

(2).

laPanese

JbunutJ

of

ts'cholaev,

17,443-458.

(In

Japanese)'

Tanaka, Y, 1944 Perception of moving figures

(3).

fapanese

fournal

of

llsychogogy,19, 1-11,

(In

Japanese)

Tanaka, Y. & Nakajima,Y. 1970 Perception of moving figures:1,On thereduction phenomena.

laPaneseRsychologicalResearch, 12.172-175.