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A

Method

to

Construct

a

Form

from

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Andreas NORDGREN

KejoUniversity

fieescpt#<\

lmages

This

_paper

describesa method torelate formimpressions

todesign_parameters;a mapping of image-space to

design-space v[a a neural network solution, A survey designed by

thelaguchimethod was used tocollect dataon how altering

various design_parametersof an automobile affects itsimage.

Principal

Component

Analysiswas _performedtoextract

cor-related factorsfromthisdataand each sample includedinthe

survey was

described

inthisnew space

by

calculating

its

fac-torscore.

A

neuralnetwork was constructed and trainedwith the$e samples, which a[lowed a

CAD-system,

based

on this

neural network, toautomatically

_generate

3D-models

corre-sponding toany

form

impression

_presented

to

it.

These

results show that

it

is

possib[etogivea

design

system a `sense' _ot

shapes,

_prev[ously

restrictedonlytothedesignen

1.

Introduction

Withthe fiercecompetition inthe automotive industry,itis absolutelyessential

to

have

the

access tomodern

CADICAM-systems inorder todevelop new cars ina short amount of time.A new model needs not onlytofulfilltheoftenconflicting

demands of the_potentialcustomers, butalso tobring some-thingnew

-

functions,features,outstandlng qualityor

innova-tivedesign

-

tostand out among thecompetitors. Thereare

methods toincludethe customeris voice invarious stages of

thedevelopment of a new mode], butwhen itcomes tothe

de$iredimage,theysuffer fromthesubtleties of form

impres-sions, Whereas customer demands for

_properties

such as

passenger

space, fueleconomy, _performanceand safety are easy to_quantifyand consider inthedesign_process,theform

impressionisa subtle association or a feeling,and thusfar

lesseasy torelate todesign_parameters.Such a form

impres-sionisoften expressed innatural Ianguage,which israther subjectiveand

differs

from

customers tocustomers.

CADICAM-systems are very helpfulinthedesign and

manufacturing _process,

but

they

have

no sense ofcreativity orknowledge about what

kind

ofform

impressions

certain shapes wil]_give.Ithasalways beentheroleofthedesignerto

interpretsubtleties incustomer demands fora design,transfer

itintosurfaces and curves, and create a_productthatwil[ ap-pealtothe targeted _groupof customers. Howevec thisisnot an easy thingtodo

-

itrequire$ experience and $ensitivityto

current trends,or better_yet,thetrend forthe coming _years. For

instance,

what shapes and curves willgivean

impres-sion of a sporty and _powerfulcar,

_yet

with a classicIookand elements of

formality

init,toa young woman? lstheresome set ofproportionsthatwillyielda

form

impression

that coin-cides wi±

h

what thetargetedcustomer

desires?

Knowing

such a set ofproportionswou[d

be

very valuable

in

creating suc-cessful cars.A

_good

designer

_probably

hasafeelingforthese

proportions,

but

it

would certainly

be

valuable toalso

have

thistypeofsensitivitybuiltintoa CAD-system, and beable

tovisualizehow various form impressionswill affectthe

de-sign parameters.By

learning

tomap

image-space

to

design-space, thistype ofsystem could be used intheeariystages ofthe

design

processtosuggest

design

parameters,or

by

the reverse mapping, validate how the form impressionchanges

afterare-design,

The

method

described

in

thispapercan

be

used as afoundationtodevelopa designsupport system with these

features.

Thus

this

method

has

the

potential

to

shorten

the design_proces$,become avaluable too[ inthe creative

process,as we]1 as validate thatthe car reflects customer

re-quirementson theformimpression.

2.

Method

The method _presentedinthis_paperuses several techniques fromstatistics, multivarjate analysis and artificial neural

net-works, and thesections belowdescribehow thesetechniques were appl[ed and what assumptions were made.

2.1. DesignParameters

The

first

step of thismethod istodecidea set ofdesign

pa-rameters thatcan adequately describetheshape in

_question.

For

thiswork, a sedan typeofcar was considered and

12

parame

±ers

for

the

basic

_proportions

of theside

_profile

shape

were decidedas shown inFigure1

.

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Fig.2.IWoDesignParametersforCrossSectionProfileShape rameters of thissetup _provideda basiccontrol _poiygonwhich laterwas used to _placethecurves and surfaces forthecar's

body.

Differenttypes of vehicles have some fundamental

differ-ences

in

their

basic

shapes, and

therefore

the

design

param-etersforone type of car do not necessarily correspond well to

thatofanother type.

Furthermore,the

decision

of

design

parametersisnot

lim-itedtobasicproportionsofthecar

-

dependingon the type ofshape the

designer

is

working on, itispossibleto define

designparametersfreely,as longas theyhave a significant

effect on theshape. Inmost cases the

designer

has

many constraintstofollow,and theseconstraintsshou[d becaretully considered when

deciding

the

design

parametersand their

range.

Only

two parameterswere used forthecross section shape of the car inorder to minimize the samples needed forthe survey

(Figure

2).The focuswas on _provingthatthe method works rather than tomake a _{production-quality}model, and

thereforethissimplification was made. ai sets the tumble-home,theangle ofglassfromthe

beltline

totheroof as viewed fromthe frontor the rear of thevehicle, while tvi controls the shoutdeltwidth ofthecar,

2.2. Form lmpressionAttributes

lnorder todescrlbean image innatural language,aset of tenattributes were chesen as

_parameters

torepresent the

form impressionof a shape, as _perceivedby a customer.

A 5-pointscale was used to

put

weights on each attribute,

thereby_yieldinga form impressionvector Fliketheone in

lable1

.

Ahigherweight signifiesahighercorrelationtothe

at-tribute.

Ttable.1

.

Weighted SetofAttributes CuteSportyCIassicFermalPewerful

2 s 3 3 4

ModernRebustSpaciousSleekLuxurious

4 4 1 4 3

2.3.

Survey

and faguchi Method

A survey was designedand conducted inorder tocollect

dataon the

form

impressions

of various shapes, The aim for

thissurvey was to _provethe methodology, not to_gatherdata foran in-depthanalysis offormimpressionsforcars, and the results should

be

vlewed with consideratlon tothescarce amount ofdatacol]ected.

Everydesign

parameter

wilfi_givea contribution to

the

form

impression,and thereforetheymust all

be

accounted forand

changed uniformly torthesamples

included

in

thesurvey,

fofacilitatethecreation of samples and ensure a minimum of samp[es with uniformly changed _parameters,thelaguchi

Anethodwas used fordesigningthesurvey, Each

parameter

fortheside _profileshape was

given

threelevelstochange

be-tween,and using theorthogonal array developedbylaguchi

[1],

27 differentsamples were

given.

Eachsample consisted

of a si[houette of the side _profileof thecar, as displayedin

Figure3.The front_parameter$were restrictedtotwo levels

in

order to minimize the contribution tothesurvey with four

samples

(omitted

from

Figure

3),

Furthermore, thesurvey was dividedintoseparate _partsfor thecross section and side _profileshapes, inorder tosimplity

thesurvey by_presenting2D-silhouettesinsteadofmore

com-plex3D-models,Viaa web-browser interface,thesesamples

were _presentedto21 individualsconsisting ofmen and

wom-en intheages between

20

and

30

_yearsold.

The

`average'

model inFigure3 was created withthe

_parameters

_given

by

thesecond level,and displayedas an example toeach indi-vldualbeforethesurvey was

_given.

The

form

impressions

for

thesamples were collected and saved ina database.When thesurvey was completed bythe

group,

theaverage response foreach model was calculated and used as a value to de-scribe theformimpression.

Forthiswork, the

_permissible

range ofthe

[evels

were rather

large

in

order tocreate siightlyexaggerated samples which

wouid be easierto separate forthe _peopletakingthe survey.

For

example, the

hood

was _givenlevelsof30-, 50-,and

70-]ength

unitstochange between.[na _production

environ-ment, thedesignteam willaiready have an ideaor concept

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of what typeof cartheywjll develop,and ±heywillalso have toconsider many engineering and manufacturing constraints. Thesefactorswili[eadtoa much smaller range of _permissible values

for

_the

levels,

and thuscreate more realistic samples which show lessvariation.

2.4.

Data

Processing

by

FactorAnalysis

The datafromthesurvey

_provided

amultivariatedatasetof

12_parametersmeasured over

27

samples, yieldinga 27×12

primarydatamatrix, However,_thisdatasetshowed thatsome attributes hadsimilarities and were correlatedtoeach othen fo eliminate

thls

overlap ofmeaning,

Principal

Component

Analy-sis

{PCA)

was used toextractcorrelatedfactors.

The goalof PCA is

to,

via analysjs of eigenvectors and

eigenvalues, finda transformation matrix thatwill

_provide

a

new set of coordinate axes where _the

data

can

be

projected insuch away thatthevariance ismaximized along

subse-quent,orthogonal axes

(Principal

Component

Axes).Aseach

extracted factoraccounts forlessand iessvariance _inthe data,itis_possjb[eto obtain a reduction ofparameterswhile

preserving

most oftheinformation

in

_the

dataset

{Gorsuch

[2]).

Thisreduction in_parametersisimportantinorder tolowerthe

dimensionalityof the_problem

-

according to

Friedman

[3],

a

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function

defined

in

high

dimensional

space jslikelytobe more complex thanone

in

a

lower

dimensionalspace, and theretore harder

for

thenetwork tosolve.

The number of

factors

toextract israther subjective and

thereare many techniquesavailabletoajd inthisdecision,

Generally,

asufficientnumber of factorsmust beextracted

toaccurately reproduce thedatamatrix fromfactorloadings

and

factor

scores, butthe_goalotthisanalysjs

is

stilltoextract

a limitednumber of factorsthatwill contain themaximum amount of

information.

A

Scree

lest,developedbyCattell

_[4],

was _performed

but

_provided

inconclusiveresults.According

to Figure4,the number ofextracted factorsshould beeither

fouror six.The Kaiser

Criterion

[5],

which statesthatonly fac-torswhose eigenvalues are_greaterthan 1.0should bekept, suggested thatthe

first

three

factors

would sufficetoexpress

mo$t of the informationcontained inthedataset,Therefore,

with theresult$ fromthesetwotests,we

decided

toretainfour factors,which accounted for

90.3%

ofthevariance,

lnaddition toextracting theprincipalcomponent axes, the

PCA also _providedthe factorloadingmatrix which contains

thevariable loadingson each oftheretained axes, thus

dis-playing

thecorrelationsbetweentheattributes and thefac±ors.

Inthenext step of thefactoranaiysis the _principalaxes were

Varimax-rotated

_{algorithm

fromHarman

_[6])

in

order to

force

them toalignas closely as _possiblewith strongly correlated

subsets among theformimpressionattributes,

The

idea

ofthis

procedureistoobtain a simpler structure which heipinthe

interpretationand labelingofthefactors.Inasimple structure each factorloadshighlyon afewvariables, and each variable

loads

highly

on on]y one factor.Furthermore,variables that

lable.2,Varimax RotatedFactorLoadingsforAttribute$ Factor1Factor2Factor3Factor4 Cute

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loadheavilyon thesame factorare related, whereas unrelated

variables would loadon differentfactors,Forthesignificance of theseloadings,Hairet al.

[7]

suggest a guideiinewhere loadingslangerthan ±O.5can beconsidered as _practically sig-nificant, thatis,they haveameaningful effectonthe varlables, The rotated

factor

loadings

are

displayed

in

lable

2

with the significant loadingshigh[ighted,

An

analysis ofthistablecan

givean

interpretation

ofthe

factors,

but

for

the

function

ofthe system

described

in

_thispaper,a

formal

labe[ingofthefactors was not necessary, and thereforeomitted.

Withthisfactorloadingmatrixitwas

_possible

to

_project

the

samples, expressed with theiroriginalform impression at-tributes,intothenew space spanned bytherotated _principal cornponent axes bycomputing thefactorscores

(coordinates

in

PC

space)

for

each sample. The

factor

score matrix Swas

given

byi

S-XB

(1)

where X isthe

data

matrix, standardized with mean

O

and

standard deviation1_, and B isa score coefficient matrix such

±hat:

B-ACi

{2)

A istherotated factorloadingmatrix, and C represents the variance-covariance derivedfromthe retained factors,_given by:

C-ATA

(3)

The factorscores could be calcula ±ed with

(l)-(3),

and every

sample was _projectedintothenew fouFdimensional

image-space.2.5.

System

Construction

UsingNeuralNetwork

The most importantcomponent ofthissystem istheneural

network, Itisresponsible foraccurately mapping the

image-space tothedesign-spacespanned bythedesign

_parameters.

A _properfiyset up and trainedneura] network hastheability

to

_generalize,

thatis,

_produce

accurate outputs forinputsnot

encountered duringtraining.HoweveL itisdjfficulttoachieve good generalization,and inorder tomake a reliable system itisessential to make sure thatthe network solution is

ac-curate

by

validating

it.

Generalization

is

influenced

by

the

size and qua]ityofthe trainingset,the architecture of the neural

network, and thephysicalcomplexity of theproblem,

There

isa tradeoffto beconsidered regard[ng the tra[ningset

-

the

laguchi

method willminimize thesamples and make the

sur-vey easier to_perform,butat thesame time theneural network

trainingwill

benefit

from

a

iarger

dataset,

With

a

fixed,

small trainingsetand no way tocontrolthecomplexity ofthe

prob-Iem,thenetwork architecture was carefullychosen toable to

represent theunderlying problemand achieve a

_good

general-ization.

A

feed-forward,

back-propagating

neural network

(Haykin

[8])

was constructed withfournodes intheinputlayer

(image-space), and

1

2

nodes

in

the output

layer

(design-space),

corresponding tothedesign

_parameters

fortheside

_profile

shape. Thisnetwork uses

_gradient

descenton theerrorsto traintheweights, with adifferentiable activation functionofthe

weighted sum ofinputsv,definedby:

1

ep(v)=

(4)

1+expGvi

As

thissigmoid bounds theoutput

in

the

interval

O

to

1,

it

was necessary tonormalize the

design

parameters

for

the samples inorder to use them as the desiredoutput, or target values,forthetraining.

Witha hiddenlayerof nine nodes, a 4-9-12 structure of theneuralnetwork was used

for

thetrainingofthesideprofile

shapes.

fo

avoid overtrainingand

losing

theabilityto general-ize,errordecay was implemented intothe network, while a $mall

learning

rateand momentum providedstable and

ef-ficientlearning.The number of hiddenunits was a critical pa-rameter ofthenetwork

-

toofew units

in

thehiddenlayerwill

not _givethe network enough flexibilityto _properlyrepresent

theunknown underlying function,whereas too many units may leadtoa network thatalso fitsthenoise, not

iust

thesignal, leadingtooverfitting.

Neuralnetworks trainedwith a scarce amount of case$

are _pronetooverfitting, and validation must be_performed

T-iftyvmxrvsee

speclalissueotjapanesesocietyforthescienceofdesLgn

NII-Electronic Library Service

totestthe_performance of the network. The cross section

profile

$hapes were trainedseparately on a differentnetwork

architecture,with a datasetof fourcases, compared tothe

27 cases available fortheside _profile.Due tothelimited

data

available, theuse of a testset would waste a lotof datafor

the trainingand therefore multifold cross-validation methods

seemed appropriate forthissystem, as allthecases can

be

used inthe training.Leave-one-outcross-validation was

per-formed toestimate theperformanceof a number ofnetwork

models, and aid inthe selection ofthe

_best

model,

This

meth-od was also

implemented

to

incorporate

earlystopping

in

the

training.Withthese measures taken,

it

was

_possibly

toachieve a neural network with good generalizationdespitethesmall training$et.

2.6.

Automatic

Generation

of

3D-model

With

the

design

parameters

given

bythe neural network solution,a

3D-mode[

ofthedesiredcarcould beconstructed,

The

aim ofthissystem, programmed in

OpenGLTM,

was to

generate

a simple model and displaythe

_proportions

suggest-ed

by

theneural network so]ution,A series of seven Bezier

curves

(Farin

[9])

oforderfourwere

joined

togethertoformthe

midline,side

_profiie

curve inFigure5.

This curve was _{duplicated,transposed}a]ong thez-axis to formtheshouider-Iine curve. Withthesetwo curves laidout,

B6zier

surfaces were used toconnect thecurves and create thesurfaces forthemodel.

Bezier

curves passthroughtheirendpojnts, which allowed the endpoints forthesjdeprofilecurve to

be

_placed

according

tothesolution presented

by

the

neural network, and thereby

yieldthe desired_proportions.Furthermore,one desirable

featureof thiscurve was to allowforlocalchanges ofcontrol

pointswjthout affecting the shape of the whole curve.

There-forethe

_jolnts

were restricted totangent continuity

{C1

}.

The interiorcontrol pointsalso

influence

theshape ofthe curve, but as thiswork focuseson the basic_proportions, these_polntswhere onlyused

to

givethecurve some

smooth-ness, and considered tohave no effect on the form impres-sion,

3.

Resultsand Discussion

Withthesimple CAD-system outlined inthe_previous sec-tion,itwas _possibletovisualize how changes of theattributes

weights, controlled by thedesigner,affecttheshape ofthe

can Figure6shows two models with formimpressionvectors

42fifty#ewvek:e

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vol.15-4 no.6e 2008

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Fig.6.Example of3D-models

R=l3333333333]andFle-[3333335533].

Thatis,the

_parameters

forRobust and Spacioushave been

increased,

resultingina model which seems tocarry those

features

bytheincreasedsize ofits

_glasshouse,

Thisshows

thatthjssystem

ha$

theabilitytoconstruct a numeric

3D-model tofitan image _thatiseasilyalteredbymanipulating the

weights ofthe

form

impressionvectot Adesignercan

_get

an

instantfeedbackon theshape

_given

by

any formjmpression,

and this

feedback

isstillcarryjng theinformationcollected in thesurvey,and thus

incorporating

thevoice ofthecustomer

in

the creativeprocess.

fo

conclude, a

3D-model

of acar was created

from

design

parameters,suggested bya neural network trained to relate

subtle form impressionsto

basic

proportions.

Validation

of

theneural network _performanceand avisual inspectionof the

created models indicatedthatthe system could _produce

ac-curate results. Thjsshows thatitis_possibietocreate a design support system with sensibility to shapes, which can aid the

designerinthecreativeprocess

by

v[sualizing

the

relationship

between imageand design,and _presentanumeric 3D-model.

Theseresults are

_promising

fortutureresearch

in

this

meth-od, which byno means isrestricted toonly

_proposing

basic

proportionsof a car, ltcould beused inany situationwhere

the design_parameters,relating toa speciflc image,are

de-sired, One caveat of thissystem isthefactthatform impres-sions are very complex, and not only associated witha

few

el-ements ofaproduct,Foracarferinstance,thecoloc material, sound,

details

inthe designand even themarketing effortto promoteaspecific

image

willallcontributetotheimpressions

people

get

when theysee it,Thus theextraction a few

param-eters

from

such a complex pictureisa simplificationof this

problem.

However,a largeset of _parameterswould leadtoa

survey withso many samples thatitwould bevirtually

impos-sibletocarryoutinan efficient mannen

References

1

.

laguchi,Genichi,

2005,

laguchi's

Quality

Engineering

Handbook, John Wiley&

Sons,

inc.,

Hoboken,

New

sey.2.

Gorsuch,RichardL, 1983, Factor

Analysis,

2"d

Edition,

LawrenceErlbaumAssociates,lnc.,Hillsdaie,

New

Jersey.

3. Friedman,J.H.,1995, "An _{overview of}

prediction

ingand functionapproximation," lnXL

Cherkassky,

J.H.

Friedman,and H.Wechsle4eds.,From

Statistics

toNeural Networks:Theoryand PatternRecognitionApplications, SpringeFVerlag,New Nbrk.

4.

Cattell,

R.B.,1966, The scree ±estforthenumber of

tors,MultivariateBehavioralResearch,1

{2),

245-276,

5. Kaiser,H.E, 1960, The application of electronic

puters

tofactoranalysis,Educationaland Psychological

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6.

Harman, H.H.,

1976,

Modern

Factor

Analysis,

3rd

Edition,

Universityof

Chicago

Press,

Chicago,

lllinois.

7. HainyJ.EJr.,Anderson,R.E.,

latham,

R.L,&BIack,W.C.,

1998,

Multivariate

Data

Analysis,

5'h

Edition,Prentice

Hail,

Upper

Saddte

Rive4New Jersey.

8. Haykin,

Simon,

1999,

Neural

Network$:

A

sive

Foundation,

2"d

edition,

Prentice-Hall,

lnc.,Upper

Saddle

River,

New

Jersey.

9.

Farin,

G.E,

1997,

Curves

and surfaces forcomputer

aided geometric

design

:A _{practicalguide,}4thEdition, Academic Press,San Diego,California.

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specialissueotjapanesesocletyferthescienceofdesign