Three-dimensional structure perception of paired-dot and unpaired-dot spherical surfaces : The effects of the vantage point and the object's rotation axis predicted by the generic-view principle

The Japanese Psychonomic Society

NII-Electronic Library Service

TheJapanesePsychonomicSociety

77ieimanes'elk)uixato.rtts,ciconomicSciEncg/

1999,Vol,I8,Ne.1,9

-22

Original

Articles

The

Three-dimensional

structure

_perception

of

paired-dot

and

unpaired-dot

spherical

surfaces

:

effects

of

the

vantage

_point

and

the

object's

rotation

predicted

by

the

generic-view

_principle

Michiteru

Ki'rAzAKi"

and

Shinsuke

SHn{oJo"'

Udeiversity

of

7iokJ,e'

and

Ctilttb"iia

b2stitute

of

Ttrchnolczg{)'**

.axls

We examjned applicability of thegeneric-view principle to the extraction of structure

frorn

motion.

In

particular we manipulated the angle betweell_thelineof sight and therotation nxis of the spherical surface that was definedby moving _pairedor unpaired random

dots,

The

image motions of thesphere were categorized using an aspect _graph and ussigned values of _genericnessl

acciclentalness,

The

generic

image

motions elicited clearerlmore depththan theaccidental ones

in

the paired-dot stimuli, bejng mostly consistent with the _predictions of the generic-view

principle.Cf'heeffect of the_genericimage rnetion was

ress

intheunpaired-det stimuli than inthe

paired-dotstimuli. Itissuggested thatthe combination of the _{generic-viewprinciple}and the

relative-inotion

hypothesis

could betterexpluin _perception of _the rotating sphere ingeneral.

Thus, both of them seem

to

contribute totheproccssingof structure

from

motion.

Key

words: generic-view principle,three-dimensional motion structure

from

motion, paired

randoni

dots,

unpaired.random

dots

'

Introduction

The human observer can perceive

three-climensional

<3-D)

structure

from

two-dimensional

(2

D)

motion without any other cue such as binecular

disparity,shading, textureor occlusion, This

phe-nomenon was firstreported by Miles

(1931),

and is now called the Kinetic Depth

Effect

<"J'allach

&

O'Connelr,1953)or

Structure

From

Motion

(UIIman,

1979).

Wallach

and

O'Connell

(1953)

founcl

that "simulta･

neous change of lengthand orientation of a contour"

was an essentia] condition for the

Kinetic

Depth

Effect

(see

also

Johansson

&

Jansson,

1968)

by

using

* _Departinent

of

Psychology,

Graduate

School of

Humanities and Sociology,Universityof Tokyo,

7-3-1Hongo, Bunkyo-ku, Tokyo, ]13-O033

'"

_Computation

and

Neural

Systems,

Division of

Biology,

California Instituteof Technology,

Pasadena, CA 91125,U.S.A.

thesilhouette of rotating solid objects and wire-frame m6dels. Ullman

(1979)

investigatedstructure frorn

motion using the computational approach, and

showed that 3visual frames of 4nonplaner points are

computationallyltheoretically suMcient

for

recover-ing

3-D

structure with the

"rigiclity

constraint". This study

had

so much

impact

on theresearch field_that

many researches

have

fecused on two issuesever

since: on the minimal information for recovering

structure computationally and psychophysically

(e.

g.,Longuet-Higgins, 1981;

Hoffman

&

Bennett,

1986;

Bennett

&

Hoffman, 1985;

Bennett,

Hoffman, Nicola

&

Prakash,

1989;

welr reviewbd by Braunstein,

Hoffman, Shapiro,Andersen & Bennett,1987)and on

thevalidity of therigiclity constraint as a predictor of

psychophysical

data

(e,

g,,Braunstein

&

Andersen,

1984;

Ullman,

1984

a;

Ullman,

1984

b;

Braunstein

&

Andersen,

1986;

Ullman,

1986;

11'odd,

1984). From

thesestudies, itseenis to be obvious that the rigiclity

constraint or the relaxed version of it

(Ullman,

10 The

Japanese

Journal

of

Psych

1984a; Hildreth,Grzywacz & Adelson, 1990)would

contribute tothe process of structure

from

motion.

However,

the rigidity constraint isnot enough to explain thevarious aspects of structure from motion.

Itwas

founcl

that velocity _{gradientfrelative}motien

(Braunstein,

1962; I.iter,

Braunstein

&

Hoffman,

l993),

segmentation boundaries

(Ramachandran,

Cobb

&

Rogers-Ramachandran, 1988),and surface

interpolation

(Ramachandran,

et al., 1988; Treue,

Husain

&

Andersen,

1991

;IIildrcth,Ando, Andersen

& Treue, l995;Treue,

Andersen,

Ande

&

Hildreth,

I995)

could also contribute to the structure-from-motlon _process.

VLrehave applied the `Generic-view

principle'

(de-scribed

in

detail

in

the next section) to 3-D inotion

perception and suggested thatthisprinctple,if

util-izedus a constraint, weuld well _predictthe human

perceptionof 3-D mution of a single

bar

and

double-bar

(Kitazaki

& Shimojo, 1996). The original

rig{d-ity

constraint and the algorithrn

(Ullman,

1979)

do

not offer the solution for the ambiguity

in

`'deteriorated-infonnation" _{situations such as the}

sin-gle straight

bar

in

Kitazaki and Shimojo study.

Urlman also macle a remark that sume additional

assumptions are required to interpretthe

image

inotion of peor

information

such as two _pointsor a

line,

An

example of such an aclditional assumption would

be

the"maximal extension assumption" that

had

been

employed

by

Johansson

and

Jans$on

(1968).

The maximal extensiun assumption states that the

line

with maximum lengthina 2-D

image

sequence should

be

on the frontal-parallel_plane und that

it

should app]y to a limitedsequence such as 30 cleg rotation.

Johansson

and

Jansson

(1968)

showed that thismaximal extension assumption,

in

addition tothe

rigidity con$traint, could uniquely _{predictperception}

of the 3'D rotation of a

linelbar,

that

is,

theexact

slant and tiltof the line.However, the assumption was yalid only

if

thepossibtlityof translation indepth

was excruded a

Pn'on'.

In

fact,

subjects perceived

translation indepth when the

image

contajned L-D stretch and 2'D translation

(Kitazaki

&

Shimojo,

1996). Thus the rigidity assumption, even with the

additional

L`maximal

extension" assumption, is

insulficient

to predict

3-D

motion perceptiun of a

onomic

Science

Vol.

18,No. 1

single straight bur. This isso mainly

because

it

does

not solve theambiguity between rotation in

depth

and

translationin

depth.

On the other

hand,

our

predic-tions

based

on thegeneric-viewprinciplewere

consts-tentwith theperception of

discriminating

3-D

reta-tion indepthfrom 3"D translation

in

depth

of a single

straight bar.

We

have

speculated thatthegeneric-viewprinciple

isnot incompatible with the rigidity constraint, but

rather cooperates with itin_general. Inour _previous studies, we adopted only a

bar

or

double-bar

as a

stimulus so thatwe could cbnsider allcombinations of motion components such as rotation, translation,

and stretching. ConsequentlyL one would argue that

thegeneric-view principlecould be applied only to

3-D motion of such simplest structure. To examine

this issue,we adepted a rotating spherical surface

with multiple dots as a stimulus and tested whether

the _{generic-viewprinciple}can predict the

3-D

percep-tionof thestimulus.

Generic-view

Principle

We assurne thatthevisual system's selution shoulcl

beprobabilisticallyor statistically appropriate inthe

real world. Inother words, generic views of a

lar

object should befavored over accidental views of

ethers. For most object$, there istypicallyat

least

one view that

has

invariant propertiesover large

changes of the vantage _point. This isthe `LGeneric

View".

On

theother

hand,

the'`Accidental View" is

defined

as an

image

class that

is

chungeable with

slight _positionalchanges of the vantage point. The

generic･view principlestates that the visual system

interpretsa 2-D imuge as a _genericview of a

3'D

obj ect,

but

not as an accidental view of another object

even ifit

is

possib]e theorctically.

This princip]e

has

already

been

applied to many

different

domains

of vision and cognition, such as

machine vision

(Binford,

1981;

"'itkin

&

baum, 1983;

Lowe,

1985;Malik, 19S7),3'D object

recognition

from

components

(Biederman,

1985>,

shape from silhouette

(Richards,

Koenderink &

Hoffman, 1987), surface _perception of untextured

stereograms

(Nakayama

&

Shimejo,

1992),

tienof

line

drawings

(Albert

& Hoffman, inpress),

The Japanese Psychonomic Society

NII-Electronic Library Service

TheJapanesePsychonomicSociety

M.

KiTAzAici

and

S.

SmMoJo

:

Generic-view

(Freeman,

199Lt;Freeman, 1994), and color con-stancy

CBrainard

&

Freeman,

_1994).

'T'hus,

thiswould

be a good candidate

for

a _generaltheory of vision.

"Fe

hax,e

attempted to apply this_principleto3-D

inotion, or dynamic scene

interpretation.

In

the

present stucly, we

deal

_{particulEtrly･}with 3-D niotion of aspherical surface

defined

by

randorn dots,Itisan

especially suitable stirnu]us for our _purposc because

thestatic 2-D image of the 3-D sphere isalways a circle

from

a]] _possiblevantage _pointsso thatthe

prejected Z

-D

irnagesare al]generic views

in

termsof n static image. By using thisas a stimurus, we can

investigatethe

dynarnic

application of the

generic-view principlewithout contarriination of any static

aspects.

Paired-dots and IJnpaired-dots

Spherical

Surface

and Vantage Points

Inthe _presentstudy, we firstemployed u spherical

$urface

definecl

by

paired

dots

as motivated by

Qian,

･Andersen

_and

_AdeLson

_(t994

_{a) study}

_(Experiments

₁

and 2),

The

relationship of the _present study with

their

finclings

wi1] becliscussed laterin

General

Discus-sion. A spherical surface definedby _paired random

dots was sirriulated

in

a ,',-D scene

(see

Figure1)i),

that was rotating around the vertical axis. Note that

the coordinate system that we adopted here was

environment-based and was neither dependent on

vantage points ner on object rotation. The v･antage point was as$umed tobe at various _positions around

thesphere, but always to

look

through the origin

(O,

O,O),which was the center ef thesphere. The

ortho-graphic projectionwas adepted inthis_paper.Inother

DWe

used theterms "paired

dots"and `'unpaired

dots"

in

avery specitic way to indicatethetypes

ef spherical surface

defined

by

dots

in

a 3-D scene, as indicated

in

Lhe text.

"'e

used the

phrases,2-D paired dotsand 2'D unpaired

dots,

only to

indicate

thestirnuli employed

by

Qian

et a]

(1994

a). InExperiments

1

and 2,all dots

were _paired on the surface of a 3'D sphere

model

(see

Figure

1and Method of Experiment

1),and their_projected2--Dimage motions werc

used as stirnuli. Itwas certainly truethut the

offset-position iniagemotion inExperiments ] and 2contained unpaired detson its2-D irnage. Yet,we never employ such usage of theterm in order to avoid confu$ion.

Princip]e

for

Rotating

Spherical

Surface

11

words, _the

distance

between

the vantage _pointand

thesphere ",as assumed infinitery]eng _thatthe

per-spective didnot appear inany image mot.ion.

All

dots

were simurated on the spherical surface, and _pairedso

thateach _pairhad thesame coordinates on the X'Y

plane but

different

ones en the Z axis at the initial

posltion.Thus, when the vantage _pointwas at

(U,

O,

]

k)

{`k'

is.

an arbitrary nurnber Iarger than the

radius of the sphere), al] _paired dots appeared as

paired at the same _position on the projectecl 2-D

image _plane,thenmoved

in

opposite directions.This

was similar tothe2-D _paired stimulu$ employed

by

Qian

et al.

(1994a).

"rhen

the vantage _point "'as

locatedapart from

(O,

O, ±IO, the image motion was

rather similar tothe 2-D unpaired stimulus employed

by

them.

Let us now consider all _possiblevantage _points

nrou"d _the sphere and projected retinal image

motions

(Figurel).

The outer spherical surface

consisting of vantage _pointsissegrnented according

tothequalitative c]ass of the

image

motion, to make an `'aspect

graph"

(Koenderink

&

van

Doorn,

1976;

Gigus & Malik, 1990; Kriegnian

&

Ponce,

1990;

Ponce & Kriegman,

1992).

At

two singular points on

theaspect graph,theobserver obtains "samc-position

&

collinear"

imagc

motions, where _thepaired

dots

appear at the same _positionand move collinearl>,

in

opposite directionsto each other. At other twe

singular _points,theobserver obtains

L`co-axis"

image

motion$, where all the

clots

are

just

rotating around

the common center.

On

the horizontal arc, _the

obsen･,er obtains "apart-position & collinear" image motions, where thepaired dotsappear at horizontally apart _positionsand move col]inear]y

in

opposite

directions.

On

the vertical arc, the observer obtains

"offset-position" _image

motions, where the paired

dotsappear at vertically offset po$itions and move in

different

djrections.

From all the other vantage

points,the

image

mot{ons are a mixture of the

"apart-position

&

collinear" and the "offset-position"

image

motions, and named "apart- _&

offset-position"

image

lnvtions.

The genericness of

image

motions

for

a spherical

stirface

defined

by

_{paired detsis}assumed tobe inthe

followingorder : "apart-

&

12 TheJapanese

_Journalof

PsychonomicScience

Vol.

18,

No.

1

<>

saertlowaSeti8n ap.ar,t2-sl/fi',ti.en

.co-axls

I offsetJPosition

image

motions apart-& offset-position coordinate system

Figure

1.

Schematic

representation of paired random

dots

on a spherical surface and

its

orthogonally projected

image motions. The outer sphere indicatesthe aspect _graph

(see

text).

The

right-bottorn

indicates

the

coordinate systern used inthe text; the center of the sphere was the origin

(O,

O,O),and all axes were set

environmentally so thatthecoerdinate was

invariant

with thevantage-point change.

position"="apart-pusition

&

collinear" >"same

posi-tjon

&

collinear"="co-axis". This is

determined

automatically by thesizes of vantage _points'areas in

the aspect graph.

Accerdingly,

the generic-view principle preclictstheclarity of 3-D perception or the

amount of _perceived depth inthe same order.

We

comparecl theeffects of these image-motion typeson

3-D

perceptionof the sphericul surface definedby

paired random

dots

in

Experirnents

1

and 2to see if

theresults are consistent with thegeneric-view-basecl

predictions. Then, inExperirrient3,we adopted a

spherical surface

defined

by unpairecl!ordinary

ran-dom

dots

as thestirnulus, and investigatethe effects

of itsimage-rnotion types on the 3-D _perception,

again with regard tothe generic-view-based

predlc-tiOllS.

Experiment

1

We

first

investigated

the qualitative

differences

in

depth

effect among three

image-motion

types:the

same-position

&

collineur

image

motio'n, the

apart-position

&

collinear

image

motion, and the

offset-2) The

"apart-&

offset-position" image metion

was net included inExperiment 1 or 2. We

conducted another experiment which we

do

not

report heretocornpared thatirnagernotion with

theothers, and found thatthe "apart- &

position"image motion

had

a similar effect to

that obtained

in

the "offset-position"

_image

motlon.

The Japanese Psychonomic Society

NII-Electronic Library Service

TheJapanesePsychonomic Society

Dv･I.KiTAzAK]and

S.

SmMoJo:

Generic-view

position image motion

(see

Figure

1)Z}.

Method

Subjects. Four subjects

(all

males, ages ranged

from

21

to

26)

participated

in

the experiment.

Three

subjects were naive to the _purpose of the experiment

ancl one was thefirstauthor. Thcy allhad normal or

cerrected-to-nonnal visual acuity.

Stimuli. The $timulus

displays

consisted of

ortho-graphic projections of

dots

on a sphere

(radius

5.0

deg

in

visual angle). The luminance of detswas 6.93

cdlrn2 and that of the buckground was

O.Olcd/m2.

Alr

dotswere _pairedso that each _pairhad tbesame

coordinates on the X-Y _plane

but

different

ones on

the

Z

axis at the

initial

position

(We

employcd an

environment-defined, not viewer-dependent, coordi-nate system todescribe the stimuli :See Figure2).

The

dots

on thevirtual sphere rotated for2s at

30.0

degfs

(5.0

rpm) around _the Y axis.

The

lifetime

of

each dot _pair was limited to 167ms and the

dots

appeared and

disappeared

asynchronously, inorder to

exclude the _possibleartifact of the dots'long

tra-jactories.

The

number of dots disp]ayedat a timc

was

50

(25

pairs>.

Design.

Three different vantage

_,points

were

adopted for experimental cunditions as shown

in

Figtire2

(See

also Figure1).

In

the

"same-position

&

collinear'' condition, the vantuge peint was at the

coordinate:

(x,u,z)=(O,O,

±

fe)

(`k'

was an

arbi-fi2ts?n

Figure2. The stimulus conditions of

Experiment

1

The coordinate system was environment-based

and never

dependent

on thevantage _point.Three

image motions defined by the vantage _points

were used as stimuli.

PrincipleforRotating

_Spherical

_Surface

₁₃

trary number

lager

than the radius of the sphere), so

thatall _paireddotsappeared at the same _positionon

the 2-D image _plane,then moved

in

opposite

direc-tionscollinearly.

In

the "apart-position _&

collinear"

condition, thevantage point was

horizontally

shifted

5.0

deg,

so that all _paired

dots

appeared at the

positions apart horizontallyon the 2-D image _plane, then moved inopposite

directions

collinearly.

In

the thirdcondition, '`offset-position"

condition, the

van-tage _peintwas vertically shifted 5.0 deg,so thatal]

paired

dots

appeared at the_positionswith a vertical

offset on the 2-D image _plane,then moved inthe

opposite directions.Three _pairsof conditions were repeated 48_times inrandom orcler.

Thus,

each

sub-ject

performed 144trials.

Apt,aratus. The experiment was

done

ina

semi-dark

rooin.

Stimuli

were _presented on a color

cathode-ray tube

(CRT)

display

(HITACHI

CM218

MU

O.31 mm _pitch21-inch

CRT;

1024'

768

_pixels;

vertical scanning frequency,

60.0

Hz) controlled

by

a

workstation

(SiliconGraphics

INDIGO).

The

subject's

head

was

loosely

stabilized

by

a chin-rest

and theviewing

clistance

was 57cm.

Procedintre.

Each

subject _performed

30

_practice

trials

followed

by

144 experimental trials,

Two

of

three conditions were randomly selected and

present-ed sequentially at each trial

for

paired cemparison.

AI] observations were made monocular]y, with the other eye occluded

by

an eye patch. The subject was

instructed

tochoose thestirnulus that_yieldedclearer

3

'D

structure percept or more amount of depth. We employed thisinstructionbecause some subject$

re-portedthat they

_did

not understand `clarity'

of

3-D

perceptionand itturnedout to

be

easier

for

them to

judge

amount of

depth

than

3-D

clarity,

Results

All

thesubjects _perceiveda significantly clearer

3-D

sphere or more depth in

the

apart-posion

&

col-Iinearcondition and the offset-position condition than

inthesame-position & collinear condition

(Figure

3

;

sign test

P<

.05).

It

is

consistent with theprediction

based

en thegeneric-viewprinciplebecause the

position

&

collinear and theoffset-position conditions

are more generic than the sarne-position

&

collinear

14 The

_Japanese

_Journalof

PsvchonumicScience VoL 18,

No.

I

The

offset-positfon condition w･as _preferredfor a clearer 3'D sphere over theapart-position & collineur eundition

by

all thesubjects

(statistically

significant

furthreesubjects ;sign test

P<O.5).

This

difference

was not _predicted from the _generic-view principle

because

both

were equally available

frem

vantage

points on an arc in the aspect _graph

(Figure1).

These two types of image motion, however, might

contain

different

typesof genericness.

W'e

hypothes-izethat there are two types of genericness inthe

paired-dotspherical surface.

One

isthe _genericness

relevant totheinstantaneousmotion of

dot

pairs,and

theother

is

reLevant tethe angle between the]ineof sight and thc rotation axis3). The offset-position

image motion contains

both

typesof thegenericness,

while the apart-position

&

collinear image niotion contains only the_genericnessre]evant tothe

instanta-neous motion of dotpairs. That wou]d

be

thereasun

why theformer elicited clearer clepthimpressionthan

the

later.

In this expcriment, three qualitativelydifferent

vantage _points were selected to show the basic or

categorical

differences

among the three types of

image motion, The next experirnent wus conclucted

in

order toevaluate the

diffcrences

more

quantitative-ly

among the

following

threeimage-motion types:

"the

same-position

&

collinear'',"the

offset _position", and "the

co-axis"

image

motiens. By shifting the

vantage _point vertically along

Y

axis, the

irnage

motion _graduallychanges from

`'the

same-position

&

collinear" image motion to "the

offset position"

image

motion, then reaches '`the

co-axis"

image

motion")

(for

details,

see the method inthe next experiment).

The pairedcornparison adopted

in

Experirnent

1is

verv sensitive tothe difference

between

two stimuli so

'that

it

was suitable

to

show the

fundamental

effect of

thegenericness. The pairedcomparison

is,

however,

net good

for

theexperimental designrequiring many

3)See also theintroductionof

Experiment

3about

thesetwo types of _genericness.

4)

Though

we could quantitativelymanipulate the

vantage _puintalong any axes or directions,the

v･antage _point was manipulated only alung

Y

axis

in

Experiment

2 inerder to compare the

result of thepuired-dot casc

(Experiment

2)

and

that of the unpaired-dot case

<Experiment

3).

The

results inthe ease of the vantage-point

manipulation along other axes or

direetions

wilr

be inferred

from

the result obtained

in

this

expenment. Subjects 100ts

90-g'gij:voopt

_60a2

soca

ts

40au1:

3ov-UU

20vtu10o

aP&arcto'rl:,nSeitat?noffset-position offset-position

v vm v

same-position SaMe-POSItlOn apart-position

&collinear

&collinear

&collinear

Compared Image Motion Types

of Experiment 1

The abscissa indicatescombinations of stimuli

The ordinate

indicates

thepercentage

juclgment

of the image motion at the

forthe c]earer 3 D _percept,ion.The dottedline

indicates

the

5%

significance level

Figure3. The results

Subject

MK

was the

first

author and theothers were naive.

presented forpairedcomparison.

upper row ofthe abseissa

The Japanese Psychonomic Society

NII-Electronic Library Service

TheJapanesePsychonomic Society

)vl.

Kri',xz,xK{

and

S,

SHm{o.]o:Generic-view･

Principle

for

cenditiuns

because

the number of trialsis easy to

explode.

Therefore,

we employed the subjective

adjustment method

in

thenext experiment

in

order to

investigaternany _{quantitatively-rnanipulatecl}

stimu-lusconditions,

Experiment

2

The

amount of the vantage-point shift, thatisthe angle

between

therotation axis and the

line

of sight,

was systematically manipulated and its effect on

depth was measurcd by thc subjective adjustment

method.

Method

Subjects.

Three

subjects

(a

female

ancl two males, ages ranged from 20to26)participated inthe experi-ment. All

the

subjects were naive

to

_thepurpose of the experiment. They all haclnormal or

corrected-to-normal visual acuity.

Stimtfii,

The

$timulu$

displays

were

identical

to

thoseinExperiment 1except fortheduration

(1

.5

s)

of thestimulus and the _positionsof thevantage _point as

described

inthe

following.

Design. The vantage _point was _{quuntitatively}

rnanipulated; vertical shift inincrements of O,5,15,

30,

45,

60,

and

90

cleg.

One

of thcseconditions was

employed

in

random order

for

each tria].

Seven

conditions were repeated

24

times

in

random order

for

each session

(168

trials),

Apt)a7utzts.The apparatus was identicalto that in

Experiment 1.

Procedttre,Each subject _performed

35

_practice

trialsfollowed

by

168experimental trials.All

obser-vations were made monocularly, with the other eye

occluded by an eye patch. The subject

judged

the

perceivedamount of

depth

relative

to

the

horizontal

diameter on the 2-D image _planewith the

`Lbircl's-eye-view adjustment" method: after each stiniulus was presented, a

horizontal

line

whose

length

was the

same as the sphere's diameter and a vertical line whose

length

was adjustab]e

by

the subject appeared.

The subject was instructedtoconsider theimage of

linesas the bird'sview

(x-z

_plane)and the horizontal

lineas the horizontal

(x-coordinate-axis)

diameter of

thesphere, and toadjust the

length

ofthevertical

line

Rotating

Spherical

Surface

15

to

be

the same as theperceived

depth

(z-coordinate-axis diameter) of the sphere by moving the mouse.

Results

The functionof the_perceivecldepthamount against

the vantage-point shift was a skewed inverse-U'

shape

(Figure

4). The _peak varied ina range of 5-30

deg

across thesubjects.

At

the

O

deg

condition where

thestimulus was thesame-position

&

co]linear image motion, the subject _perceived

less

ameunt of

depth

than at the 5-v60deg conditions where the stimulus

was the offset-position image motion. Itisconsistent

with theresult of

Experiment

1,

The

least

depth

was

perceived ut the

90

deg

condition where thestimulus

was the co-axis

i]nage

motion.

We

would

like

to

interpretthat thisskewecl inverse-U

function

may

refiect a compromise between the _generic-view

princi-pleand some other principlesuch as thatof relative metien. NVe will

discuss

itfurtherinthe _general

discussion,

We

used so

far

the

image

motions

derived

from

the

paired dots on a spherical surface as stirnuli

(see

Figure1) and demonstrated the effects _predictedby

the _{generic-view principle.} The _paired clotson a

spherical surface are, hewever, a very special and

artificial set of stimuli. How about the _periectly

unpaired

(spatially

random)

dots

on a spherical

sur-face,

thatmight bemore general? To investigatethis

ImageMotion Types 100 gege S-N p,._tuo 80

:E

7o

ge

.N

6o

'sn

un_vd so

xg

4o e'

.9

ge

30 w"

Mi'

2o "10 o sthrneuesltlen [ellinear, /joffset-positionco-axus･Subje[tstHIMtYT-t KM O 10 20 30 40 50 60 70 80 90

Vantage-point Shifttdeg

Figure4. The results of Experiment 2

The

abscissa

indicates

the amount of

manipulated vantage-point shift

from

the

zontal arc on the aspect _graph, The ordinate

indicatestheestimated ratio of

depth

relative to

16 The

_Japanese

_Journalof

Psychonomic

point, we conducted Experiment 3using thespherical surface thatwas

defined

byunpaired

dots.

Experiment

3

For the unpaired

dots

(random

dots

without any

regularity) on a spherical surface

in

a

3-D

scene, the

relationship

between

the

rotation axis and thelineof sight could

be

described

interms of the angle

between

them:

it

is

either orthogonal, oblique, or collinear.

Unlike

the case of the paired-dot spherical surface

(see

also Figure1),thereare no

longer

any effects of

the

horizontal

shift ofthevantage _point

(because

the

dots

are "apart" to

begin

with).

Thus,

we manipulat･ ed onlv the vertical elevation of the vantage _point.

"We

made theaspect graph to

determine

the

generic-nesslaccidentalness.

Categorically

we have three

image-motion types forthe spherical surface defined

by

unpaired ranclom

dots

(Figure5).

The

ortho-graphic projectionwas again aclopted

here.

At two

singular points on the aspect _graph, the observer

obtains the "curl"

_image

_{motiun that contains only}

the curl component

(arl

dots

rotate around the

com-mon center and the relative positions of dots never change).

On

the horizontalarc theobserver obtains

the

[`shear

&

compression" image motion that con-tains the shear component

(the

speed of

dots

changes

in the perpendicular

direction

to the dots'moving

directien)

and thecempressive component

(the

speed

of

dots

changes along the

dots]

meving

direction)

without any curl component. On all theother vantage

peints, the

image

motion contains all of thecurl,the

shear, and the compressive components, thus was

curl curLshear&

compresslen

shear&compresslo

Figure5. The image-motion typesof the unpaired

random

dots

on a spherical surface

The

ihickness

uf trajectories

in

the

image

motions refiects thespeed of the

dets

(see

text).

Science

Vol.

18,

No.

1

nained the

`"curl,

shear & compression"

irnage

rnotion.

The order of genericnesswas assumed to

be

as

fol-lo",s:"curl,

shear

&

compression">"shear

&

com-pression">`icurl". The generic-view principlepre･

dicts

thattheclarity of 3-D perception or the amount

of depth should

be

inthe same order,

Inthecase of unpaired dots,we expected thebias

predicted

by

thegeneric-view principle would

be

less

obvious than inthecase of paired

dots.

It

would

be

so because all theimage motions of the unpaired-dot

spherical surface were similar togeneric views forthe

paired-dotspherical surface interms of 2-D pairedl

unpaired _pattern,se that the _geometrical

difference

umong generic and accidental image motions would

be

less_prorninentintheunpaired stimuli than inthe

paired stimuli. In other words, stimulj with the

paired-dot spherlcal surface were relevant

both

to the

genericvantage _pointsforthe instantaneousrnotion

of dot pairs and tethat

for

therotation axis,

but

the stimuli with theunpaired-dot spherical $urface were

relevant only tothe _generic vantage pointsiorthe

latter,

Thus,the _generic-vieweffect would

be

_greater

inthepaired-clotcase than inthe unpaired-dot case.

In

order totestthisexpectation and toextend our analysis to morc general cases, we

investigated

the effect of angle

between

therotation axis and theline

of sight for unpaired

dots

on a spherical surface in

thisexperiment.

We

must note that this experiment was simllar to that of

Loomis

and

Eby

(1989)

(see

alse

Liter,

et al.,

1993)except mainly forthelifetirneof dotsand steps

ofthe vantage-point manipulation, The lifetimewas

limitedto 100ms or

166ms

in

our experiments,

but

was not limited in theirs.

We

will

discuss

the

differences

later.

Method

Subjects.

Four

subject$

(all

males, ages ranged

from 21to 27)_participated

in

theexperiment.

All

the

subjects were naive tothe purpose of theexperiment,

Thev

all

had

normal or corrected･to-normal visual acultv.

Stijuli. The stimurus

displays

consisted of

ortho-graphic projections of random

dots

en

the

sphere

(radiu$

5.0deg invisual angle). The luminance of

The Japanese Psychonomic Society

NII-Electronic Library Service

TheJapanesePsychonomic Society ImageMetlon Types 100 s 9o

'k1so

70 as

EE6o

':8

so a.N 4e y. o

.8

g

3o 1'-"20 MS

U

le o

M.

Ki't'AzAKi

and

S.

SHmroJo:

Generic-view

O.Ol

cdlm2. The

dots

on the sphere rotated for2s at

60.0degls

(10.erpm)

around the Y axis. The

life-tirneof each

dot

was

limited

to 1OOms and the

dots

appeared and

disappeared

asynchronous]y,

in

order to cxclude the _possibleartifact of the dots'long

trajec-tories. The number of dots displayedat a time was

50,

Design. The vantage _pointswere _{quantitative]y}

manipulated; vertical shift

in

increTnents

of

O,

5,

15,

30,45,60,ancl 90

deg.

One

of theseconditions was

employed inrandom order at each trial.Seven

condi-tionswere repeated 24_time$inrandom order foreach

session

(168

triaTs).

APParatus. The apparatus was identicaltothat in

Experiment

1.

Procedure. Each subject performed 35 practice

trials

followed by 168experimental trials.AII obser-vations were made monocularly, with the other eye occludecl by an eye _patch. The subject

judged

the perceived amount of

depth

relatiye tothehorizontal

diameter on a 2-D image planeinthesame way as in

Experiment

2,

Results

The amount of the _perceiveddepth didnot change

much at O'v30deg vantage-point conditions and

de-creasecl monotonically at

30--90

deg

conditions

except

for

one subject:

KM

(Figure

6).This result is

[emwhp[rauTblS:Iil

::/A'S,h.:a,i.g

LN

i

n-yAy

i

Sub'ectst･]KtTS-tKM-t-MN.

o lo 2e 3o 4o so 6o 7o so go

Vantage-point ShiftIdeg

Figure6. The results of Experiment 3

The abscissa indicates the amount ef

manipulated vantage-point shift

frc)m

the

hori-zontal arc on the aspect _graph. The ordinate

indicatesthe estimated ratio of depthrelative to

the

2･

D

horizontal

diameter,

Princip]eforRotating

_Spherical

Surfacc 17

differentfrom thatinthepaired-dotexperiment

(see

Experiment 2 and Figure4),

in

that there

is

llo

explicit _peak at 5'-30deg conditions.

Loomis

and

Ebv

(1989)

and

Liter

et al.

(1993)

showed a monotonically

decreasing

function

in

the entire range of vantage positions

frorn

O to

90

deg,

which isstilldifferent

from

ours.

The

difference

is

at

the OA--30deg conditions _;we have a relutively flat

curve hcre. Loomis ancl Eb},

(1989)

proposed the

relative-motion

hypothesis

that the

depth

from

rnotion is

perceived

by thecrude ancl

heuristic

way of

using the amount of relative-motion components on

2-D images, Their results were consistent with the

predictienby thishypothesis.

By

considering theresu]ts of E.xperiment 2 and of

Loomis

and

Eby

(1989),

thepresentresultseems to

be

intermediate

between

thepredictions

by

thegeneric･

view _principleund that

by

therelative-metion

hypoth-esis. Inother words, thepresent result coulcl not be

explained solely by the _{generic-view principre,}but

could well

be

if

thegeneric-viewprincipleiscombined

with therelative-motion

hypothesis.

We

will

discuss

this

further

in

the

General

Discussion.

General

Discussion

The

effects of the vantage-point mantpulation on

human il-D motion/structure _perception were

inves-tiR.ated with twe typesof stimuli : the _paired and the

unpaired random

dots

on spherical surfaces

(see

Figure1and Footnote 1inIntroductionfc)rtheexact

definitions>.

The results were predicted

by

the

generic-view principle,InExperiment 1 and 2,the

"apart-position _&

collineur" and the

'`offset-position''

image

motions that were _genericviews e]icited the

clearer 3-D motion perceptionthan theiLco-axis" and

the

"same-position&collillear"

image

motions that were accidental views. In Experiment 3,the `'curl, shear & compression" image motion that was a

generic view elicited clearer or more 3 D motion

perceptionthan the

'Ccurl"

irnagemotion thatwas an

accidental view.

The

differences

between

the "curl, shear

&

compression" and the"shear

&

cc)rnpression"

18 The

_Japanese

_Journalof

PsychonomicScience

Vol.

18,

No,

1

The

leyel

of

Explanation:relationship

to

Qian,

Andersen

&

Adelson's

study

v

Recently,

Qian,

Andersen and Adelson

(l994a)

found

that the

human

observer cannot perceive a

transparent motion when a display has

finely-balaneed

opposing motion signals inulllocalregions

(i.e.,

2"D

paired-dot motion

display,

where all

dots

are _pairedlecallyon 2-D image,and move inopposite

directionsfrom each other)

.

They also foundthatthe

Vl cells of behaving monkeys do not _generally

dis-criminate

between

the

ba]anced

motio'n _pattern

(nontransparent

motion) and theunbalanced motion

pattern

(transparent

rnotion),

but

Dv{T

cells

do

<Qian

& Andersen, 1994). Accordingly, they _proposed a

two-stage computational model of motion _processing

fortransparentmoti,en _perceptjon

(Qian,

Andersen

&

Adelson, 1994b). They successfully demonstrated

correlation among psychophysical effects, physiologi･ cal mechanisms, and themodel's _predictionson

trans-parentmotion,

We

would Iiketoexplain thcirresurts

at another level. Their investigationsare at the mechanism level,whereas we offer a

fitnctional

and compulationat account.

"rhy

does

thevisual system

interpretthe 2-D paired-dot motion _pattern as the

nontransparent niotion,while the 2-D unpaired-dot

motion _pattern as the transparent motion?

What

guarantees itsvaliclity or itsadvantage over other

interpretations?The generic-view principleseems to

offer an account

fer

thesequestions.

It

isatthevery

accidental vantage point where we seethe 2-D

irnage

of _paired-dotsthatare moving inopposite

directions

and sharing the trajectory though on differentdepth

planes!surfacesinthe 3-D scene. On the other hand,

at thegeneric vantage _potntsthe

dots

on the

different

depthplanesfsurfacesin3-D scene move

in

unpaired

style and

do

not share the trajector},

in

2-D

image

motion. This may bethe

biological

reason why the visua] system would liketointerpretimage motion as

two surfaces

in

depth,

on]y

in

the]atterimage motion.

This

principleoffers a

functional

account

for

both

the

learningprocess and the competence of transparent

motion _perception. This explanatien isnot at all

incompatible with studies by

Qian

et al.

(1994a;

1994b) and

Qian

and Andersen

<1994).

Rather,their

electrophysiological

findingshnodel

offer a

feasible

way fer_thevisual $ystem toimplement the _principle.

The

present study w･as

inspired

by

theirstudy.

We

employed the similar stimuli

(paired

and unpaired

dots)to investigatethe $tructure from motion, and

showed the _{psychophysical}

data

and the

computatjonal account by the generic-view principle.

If

physiological study

is

conducted using the same

stimuli as ours,

it

would inturnoffer the

mechanical-levelexplanation and contribute thetotal

understand-ingof thestructure-from-motion perception.

Relationship to Relative-motion Hypothesis

Some aspeets of our results, however, were not

explained

fully

by

the generic-view principle,and

better explained

by

the relative-motion hypothesis,

which states thatthe

human

visual svstem

determines

.

depth

using the amount oi relative moion!shear

com-ponentsina crude and heuristicway. Yet,theresults

inthepresentstudy were not fullyexplained bythe

relative-motion hypothesis,either. For instance,the

function

that related

3-D

perceptionwith

vantage-peint shift was u skewed

inverse-U

shape

in

Experi-ment 2 and a horizontal-to-deelineshape

in

Experi-ment

3,

The _previousstudies showed anionotonically

decreasing

linear_profilewith the rotation-axis

manip-ulation that was equivalent toeur vantage-point shift

(Loomis

&

Eby,

1989;

Liter,

et al,,

1993).

Their

resu]ts were consistent with theprediction

based

on

the relative-motion hypothesisalone.

To furthcrcompare the _predictionbased on the

relative-motion

hypothesis

with that

based

on the generic-view principle, we conducted the simulatien

by

applying the shear componellt ef

Loomis

and

Eby

<1989)

(see

Appendix fermore details)te our stimu]i.

We also show the results of thesimulation with the

generic-view･predictionand the _{psychophysica]}

data,

for

the paired and the unpaired cases, side by side

(Figure

7).

The

psychophysical

data

obtained

by

the

present stucly were intennediate between thesetwo

different

predietions,so that the data would

be

well

explained

by

a combinationfsum of both _predictions.

The practicar

differences

of the _presentresults of

ours with the

data

of

Loomis

and

Eby

(1989)

rnight

be

causcd by themethodological differencesinuur study

such as the short-lifetime clisplayand the adopted

The Japanese Psychonomic Society

NII-Electronic Library Service

TheJapanesePsychonomicSociety

M. KiTAzA- and S.SHiMeJo:Generic-xriew

Paired-dot

sphere case

PrincipleforRotating

_Spherical

_Surface

Unpaired-dot

sphere case

19

SSiuudqtiQ!Lbase[LQ!L

rmulat b d RIt t H th

-#egeptEeU-esosm O 10 20304050 6070 vantage-point shift l Prditinba 8090deg dnnn-1

1:gaoU-tuesm

O 1020304050 607080 90

vantage-point shift / deg

Prini 1 thmo".u-o:dio utcoecu--utuapto O 45 go O 45 90 vantage-pointshift1deg vantage-pointshift/deg

p

thhIDt

t

1

eg

tu a

eg

tu es

･b

b'

-i

'n"

un

un

dii

di

rvi o-

.e.

.!

.-o.

,! es

X

M-e _ntes

i'

pt at

Vantage-point Shift ldeg Vantage-point Shift 1deg

Figure 7. [['op:The results of sirnulation

based

on the relative-motion

hypothesis

for

the paired･dot

(I.eft

column) and theunpaired-dot

(Right

culumn) cases.

We

calculated

`shear'

according to Loomis ancl Eby

(1989)

for

every one degree of vantage-point shift from O deg to 90 deg. )vliddle:The _predictionsof

genericness from the aspect _graph. Bottom: The _{psychophysical}

data

from

Experiment

2

(Lcft)

and

Experiment 3

(Right).

'

were employed enly

in

our experiments.

inthefigure,we interpolateamong threecategorical

We

must note thatthe_genericnesswas tentatively views and those values. Though Freeman

(1994)

defined

as continuously

(quantitatively)

changing showecl the way of _quantifyingthe _genericncssinthe

20

The

Japanese

Journalof

PsychonomicScience

Vor.

18,

No,

1

foundthe way of quantifying thegenericness

in

the

3'

D motion _perception.

W'e

could intheory_quantifythe

genericness,but thisneeds furtherinvestigations.

Integrated Framework & Bayesian Inference

theory

A combination of the relative-motien

hypothesis

and the _{generie-view principle}seems towell explain

our data inthe _presentstudy, The relative-motion

hypothesiscould beunderstood by assuming the

rigid-ityconstraint ina broad sense. The relative motion or shear component

in

the2

D

image

would leadto

3-D structurefdepth _perception

if

the visual system

prefersthe more rigid structure over the non-rigid

relutive rnotion inthe 3TD scene.

Thus,

the relative-motion hypothesiscan be considered a natural con-straint

based

en theprior probability ofa

3-D

scene7s property: rigidity.

On

theother

hand,

the

generic-ness lsconsidered a conditional _probabilityof a 2 D

image _given a 3'D scene

(Nakayuma

&

Shiinojo,

199Z; Freeman, 1994). Taken together, itis

suggest-ed thut the

human

vision oi structure-from-motion

can

be

explained

by

comb{ning thepriorprobability

of a 3-D scene

(relative

motionlrigidity) and the

conditional probability of a

2

D

view given a

3'D

scene

(genericness>.

Itisconsistent with the idea that the Bayesian

inference

theory

is

a general framework forvision

(Nakayama

&

Shimejo,

1992 _;Freeman, 1994_;Knill

& Richards, 1996;

Knill,

Kersten

&

Yujl]e,1996).

The visual processing ean

be

formulated

as

follow-illg:

p(sll)

-･

P(IIi7I

.pl

.(s)

where

S

means a scene

in

the realworld and Imeans

an image as visual

input,

"Je

can treat

P(l)

as a

normaHzation constant, so thatwe have

p(sll)ocp(IIS)p(S)

Here,

P(S)

is

a

Prior

of agiven scene. The

distribu-tion

P(S)

isthe prior probabilit}, of

different

collec-tionsof scene _propertiesthatare actuall.y occurn'ng in

our enviromnent.

On

the other

hand,

p(llS)

is

a

prebab{litydistril]utionspecifying therelutive

proba-bility

of obtaining

different

images frum the scene, i,

e., the

gdeelihood

.fltnction

for

S. The natural

con-straints such as rigidity or smoothness are considered

priorprobabilitiesofspecificscene _propertiesthat are

actually occurring and not negligible inour ecologi-cal environrnent, while the

genericnessfaccidental-ness of images isconsidered conditional probability

(likelihood)

forimages duringtheobserver's

locomo-tion.Thus,these are incorporated

into

the

following

equatlon:

p(SiJ)-p(IIS)p(S)

=(genericness

of I)

'(natural

constraint

for

S)

Moreover, we argue that

it

depends

on thesituation

how the _{generic-vie-,principle}interactswith other

natural constraints. We specu]ated that the

generic-view principle works with other constraint$

depend-ingon thesituation, and

has

an advantage especially

when the available

information

is

impoverishedl

deteriorated

and ambiguous,

lt

would

be

reasonable

to assume that the visual system isvery sensitive to

thequalitativechange ef

2-D

images with the slight

vantage-point change when the

informatien

is

lim-itecl,Inthe _previousstudies, thegeneric-view

princi-ple was successfully applied to such situationsl scenes:e.g., a single straight bar

(Kitazak{

&

Shimojo,

1996),

untextured stereogram$

(Nakayama

&

Shimojo,

1992),and subjective contour by sparse

inducers

(Albert,

1993).

The

difference

of rcsults

between ours inExperiment 3and

Loomis

and

Eby's

cou]d be interprctedbythis aspect. Since the

short-Iifetimemotion empleyed in our study is more

impoverished

than the

long-Iifetime

motion employed

intheirs,the generic･view effect should be _greuterin

our stimulus conclitions.

The

findingthatthe

view-point

dependency

was stronger

for

the recognition of

wire-forms than forthat of surfaces and volumes also would support the idea

<Rock,

Wheeler,

&

Tuder,

1989

:

Farah,

Rochlin,

&

Klein,1994).

Appendix

NNie

app]ied the simulation of shear component

by

Lommis and Eby

(1989)

forour stirnuli in

Experiment

2

(I'aired-dot

spherical surface) and

Experiment

3

(Unpaired-dot

spherical surface). Three arbitrary

dots

were randomly selected from a frame and their

`shear'

was calcLilated

froin

theirpositions on the

2

'D

image and those at the next frame

(Figure

8).

"re

The Japanese Psychonomic Society

NII-Electronic Library Service

TheJapanesePsyc)onomic Society

)v'T.

KiTAzAici

and

S.

SHi"･ioJo

:

Generic-view

Frame1

dabl

b adcal c Frame 2 dab2 a dca2 dbcl b dbc2 c

shear= log(ddbbC,2illdd".bb2i

)

+

log(

ddC,a,2i

lldd."bbi2

)

'

Figure8,

The

definition

of the shear component

adopted

by

Looinis

and Eby

(1989)

and used in

Figure7

We

can calculate theshear component

by

using

thisformulatien when two

frames

(Frame

1and

2)of threedots

(Dot

a, b,and c) are available.

two successive framcs. Inother words,

if

even one of

the three dots disappeared inthe next

frame,

a new

set of three

dots

was selected randomry again.

One-hundred

sets of three dots were randomly

selected and used

for

the shear calculation foreuch

trial, Ten trials were conducted foreach

vantage-pointcondition. We adopted 91steps of thevantage

pointevery one

clegree

frorn

O

deg

condition to

90-deg

cendition

(see

also the Methods of Experiments 2 and 3)

.

All

thecalculated shear components

(relative

value) were _plottedagainst the vantage-point shiftin

the top row of Figure7.

Acknowledgments.

A part of thisresearch was presented at the

Associ-ation

for

Research

in

Vision

and

Ophtha]mology

(ARVO),

Fort

Lauderdale,

FL, 1996

(Kitazaki,

1996).

NX･'e

would

like

to thank Dr.

Johanna

MJ'eberforthe

careful Ehglishcorrection, Preparation of _thisarticle was supported

by

a

Grant-in-Aid

from

MESSC,

Japan

to MK, and by a grant from the

Human

Frontier

Science

Program to

SS,

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