A Numerical Minimization of Perceptual Error for the Linear Chromatic Adaption Transform

A numerical minimization of perceptual error

for the linear chromatic adaptation transform

R. Costantini, M. Ansorge, J. Bracamonte,and F. Pellandini

Institute of Microtechnology, University of Neuch^atel

Rue A.-L. Breguet 2,CH-2000 Neuch^atel, Switzerland

Tel. +41 32718 34 10;Fax +41 32718 34 02

e-mail:[email protected]

Abstract

Inthis paper, newsensors for the chromatic adaptation

transform(CAT)arefound. Theyhavebeenobtainedby

theindependent numerical minimization of6 perceptual

errormetricsover16correspondingcolorpair(CCP)data

sets, includingLam's set,using as startingpoint for the

minimization 4 known and commonlyused sensors. An

analysis of their performances has shown that the best

performance is always achievedby the sensors resulting

fromtheminimizationprocessoverLam'sdataset. Some

oftheseperformancesarestatisticallyequivalentto-and

evenbetterthan-thoseobtainedusingtheCMCCAT2000

andthenonlinearBradfordtransforms. Thisresultrein-

forcesboththeuseofLam'ssetasagoodrepresentation

fortheotherCCPdatasets,andtheeortsmentionedin

theliterature towards the removalof thenonlinearity of

theCAToftheCIECAM97model.

Keywords

Chromatic Adaptation Transform, Color Constancy,

ColorAppearance,ChromaticAdaptationSensors.

Introduction

Whenwe look at anobject separately undertwo dier-

entilluminationconditions,forexampleunderatungsten

lampandadaylightillumination,wemaintainalmostthe

sameappearanceofthecolorsoftheobject,eventhough

thevisualstimuliarequitedierentinthetwosituations.

Thisisduetoanaturalmechanismofadaptation tothe

changeinilluminationconditions,innertothehumanvi-

sualsystem,andcalledchromaticadaptation. Thepersis-

tenceofthesamecolorappearanceinpresenceofillumi-

nationvariationsiscalledcolorconstancy.

Thephenomenonofcolorconstancywasknownsincethe

nineteenth century. Helmholtz, Ives, Hering, and Hel-

son [1 ], rst conducted tests to nd a model for such

adaptation of the human visual system. As a result of

their eorts, the von Kries adaptation model was cre-

ated[2, 3 ]. Thismodelmainlyreliesontwo hypotheses:

1) Theadaptation is done by a separatedscalingof the

threephotoreceptorresponsesofthehumanvisualsystem

withoutchangingtheir sensitivity shape; 2) The scaling

coeÆcientsare adjustedtokeepthe adaptedappearance

Thersthypothesismeansthat,whileadaptingforanil-

luminantchange,theconeresponsesdonotinterferewith

eachother, butarejustscaledbyamultiplicativefactor.

The second hypothesis suggests that the scaling factors

are regulated by some consciousperception ofthe scene

illuminant,andit iscommonlyreferred toasthe Illumi-

nationEstimationHypothesis.

This model has been extensively tested up to now. It

hasbeenfoundthat itiscoherentwithmanyresultsob-

tainedduringsubjectivevisualtestsconductedinlabora-

tory[5 ,6 ,7],andthatitcanwellexplainsomephenomena

suchas the goodadaptation to yellow-blue shifts ofthe

color componentsofanilluminant,and the bad adapta-

tiontored-green shifts[1 ]. Anyway,it isstillconsidered

asanincompletemodelbecauseofitsextremesimplicity.

The chromatic adaptation should in fact also take into

considerationothervariables,suchas thecorrelation be-

tweenspatiallylocalchromaticsignalsacrossilluminants,

andthedesensitizationcausedbytheeyemovementacross

spatialvariations[4 ]. Moreover, theilluminationestima-

tion hypothesis has been recently reviewed [8 ], demon-

stratingthatitisnotvalidifformulatedintermsofcon-

sciousperception.

Despite these observedlimitations, the vonKries model

isstillavalidmodelforthehumanchromaticadaptation,

and itssimplicity constitutes anadvantage for thecom-

putationalaspectofcolorconstancy,i.e.,toachievecolor

constancyforanarticialvisionsystem. Thisisnecessary,

since systemslike scanners,cameras, video displaysand

soon,usedierentkindsoflighttoacquireorreproduce

an image, and theydo nothave the ability to adaptto

illuminationchanges. Then,itis necessarytoimplement

an operation that transforms a color obtained from one

mediaundercertainlightconditionstothecorresponding

colorusedinanothermedia,suchthattheperceivedcolor

appearanceinthetwocasesisthe same. Thisoperation

correspondstoachromaticadaptation transform.

Inmanyapplications,thetransformationislinearandcan

berepresentedbya33matrixwhoseroleis toobtain

the post-adaptation cone response of the visual system

to the color stimuli. It is in fact in this space that the

adaptation takesplace. Theaim ofthe present paperis

toproposeseveralcandidatesforthismatrix,andtocom-

paretheperformanceobtainedbyusingthemtothoseob-

tainedby theBradford [9], the CMCCAT2000 [15 ], and

theSharpCAT[11 ]. TheseknownCATsdierfromeach

other,sincetheyhavebeenobtainedbyusingaminimiza-

tiontechniqueoverdierentcorrespondingcolorpairdata

setsanderrormetrics,asitwillberecalledinthefollowing

sections.

The ChromaticAdaptation Transform

Let(X1;Y1;Z1)indicatetheCIEXYZcolorcoordinateof

a sample under a certain reference illuminant I1. The

chromaticadaptation transform is used to estimate the

color coordinates (X

2

;Y

2

;Z

2

) which would produce the

samecolorappearanceofthesampleunderI1 foranob-

serveradaptedtoanilluminantI

2

,denotedastestillumi-

nant. Inotherwords,thechromaticadaptationtransform

isusedtoobtainthecorrespondingcolorunderilluminant

I2. Thistransformisobtainedasfollows:

"

X2

Y

2

Z2

#

=T 1

2

6

4 R

0

w

Rw

0 0

0 G

0

w

G

w 0

0 0

B 0

w

B

w 3

7

5 T

"

X1

Y

1

Z1

#

(1)

whereR

w

;G

w

;B

w and R

0

w

;G 0

w

;B 0

w

arethe RGBcolor

components of the reference and test illuminations, re-

spectively. As it can be noticed, Eq. 1 represents the

formulation of the vonKriesmodelas mentionedinthe

introduction. Infact, accordingto thismodel,theadap-

tationisdoneseparatelyfor eachcolorchannel,andthis

isrepresentedbytheuseofadiagonalmatrix. Moreover,

this adaptation does not take place in the XYZ space,

butin atransformed cone space obtained by the use of

thematrixT.

To nd a suitable matrix T, Lam [9 ] created at Brad-

fordUniversityadatabaseofcorrespondingcolorpairsby

subjectiveinspectionof58dyedwoolsamplesconsidering

twodierentilluminationconditions. Usingthisdatabase

hefoundatransformthatmapscorrespondingcolordata

pairs,minimizingacertain perceptualerror metric. The

transform,knownas Bradfordtransform, isnonlinear in

the blue component of the tristimulus values. In most

applications, however, the linear form is used instead,

thusdiscarding the nonlinearity inthe blue component.

Thematrix T corresponding to this transform, denoted

byTBFD inthispaper,isgiveninTable 1.

Finlayson et al. [11 , 13 ] proposed a method to obtain

dierent matrices, based on numerical minimization of

theeuclideandistanceintheCIEXYZspacebetweenac-

tualandpredictedcorrespondingcolors,whilepreserving

white, i.e., no errorsin the achromatic transform. This

transformresultedinsharper,moredecorrelated, sensors

withrespecttotheBradfordtransform.Thecorrespond-

ingT matrixisdenotedbyT

Sharp

,cf. Table1.

Anotherproposal,correspondingtothematrixTvonKries

in Table 1, was formulated by Hunt, Pointer, and Es-

tevez[12 ],andconsistedinamatrixwhichlinearlytrans-

forms the tristimulus values XYZ to relative cone re-

sponses(LMS sensors).

Thenonlinear Bradfordtransform was embedded inthe

CIECAM97 color appearance model [10 ], but new ef-

forts concentrated on removing its nonlinear correction

intheblue channel. These eorts gave origin to acom-

pletely linear CAT, called CMCCAT2000 [15 ] and here

denotedbyT2000. Thistransformrepresentsacandidate

forthesubstitutionofthenonlinearBradfordCATinthe

CIECAM97. The scientic community is currently dis-

cussingif thistransform representsthe onlyvalid candi-

date or if there are some other equivalent or even bet-

ter transforms. Some comparative studies between the

Sharp and the other transforms [13 , 16 , 14] put in ev-

idencethat thestandardizationof CMCCAT2000 isstill

premature,sincemanyothermatricesensuringequivalent

performanceshavebeenfound,thusshiftingtheproblem

to: 1)Thechoiceofthecriteriatoestablishwhichofthe

newCATsisthebest;2)Thevalidityofthischoice,con-

sidering the important experimental errorsthat are still

presentintheavailableCCPdatasets.

The MinimizationProcess

Asillustratedintheprevioussection,thematricesT cor-

respondingto thedierent CATsproposedinthelitera-

tureare the result ofan error minimization process ap-

pliedovercertainCCPdatasets. Theythusdiereither

duetothechoiceoftheperceptualerrormetric,ordueto

thechoiceoftheCCPusedfortheminimizationprocess.

The idea of the present paperis to separately minimize

dierent error metrics usingdierent CCP data sets, in

ordertocomparethebestresultsfound.

Wehavechosentousesixdierenterrormetricsandsix-

teen dierent CCP data sets. Table 1 summarizes our

choices. Therstthreeerror metrics,denotedbyfPEM

=1,2,3g, correspond respectively tothe meanof three

knowncolor distanceformulas. Theotherthreemetrics,

denotedbyfPEM =4, 5,6g correspond respectivelyto

the RootMean Squared (RMS) error of thesecolor dis-

tances. These error metrics are computed between the

CCPdata,obtainedbyperceptualtests,andtheirpredic-

tion obtained fromEq.1. The aim of theminimization

processistondamatrixT thatminimizesacertainer-

rormetricoveragivenCCPdataset. Wehaveconsidered

theCCPdatasetsatdisposalfrom[17 ]whichcorrespond

tothoseusedbySusstrunk[14,16] tocompareCATs.

We have chosen a modied descent minimization

method to nd the optimal coeÆcients of the 33 T

matrix. Sincethis minimizationmethodconvergestolo-

calminima,wehavechosenfourdierentstartingpoints,

corresponding to the matricesshowninTable 1, which

leadusto1664=384resultingmatrices.

ForeachcoeÆcientoftheTmatrix,adisplacementÆtwas

applied,i.e. weformedanewmatrixwithcoeÆcients:

t ij

new

=t ij

+Æt ij

(2)

wheret ij

withfi;j=1;2;3gisthe(i;j)coeÆcientofthe

T matrix. IftheerrormetricobtainedovertheCCPdata

set usingthis newmatrixhas asmaller value thanthat

obtainedfortheprecedingmatrix,thenthisdisplacement

iskept,otherwisewechangedthedirection,i.e.:

t ij

new

=t ij

Æt ij

: (3)

Thisis doneindividually for eachof thenine coeÆcient.

We iterate the process until a stable value of the error

metricisreached.

This minimization process was repeated 384 times, one

for each combination of the starting point (SP), error

metric(PEM), and CCP data set, resulting inas many

matricesobtained at theendof theprocess, denotedby

M

(SP;PEM;CCP)

according tothe correspondingparame-

ters. ForexamplethematrixM

(4;2;13)

wasachievedusing

the T

vonKries

matrix (SP= 4) as starting point for the

minimizationofECIE94(PEM=2)overthe\Breneman

1"dataset(CCP=13).

Tests and Results

Theperformancesofthe384matricesfoundinthemini-

mizationprocesswerecomparedto thoseobtained using

the Sharp, the linear and nonlinear Bradford, and the

CMCCAT2000transformsoverthesixteenavailableCCP

data sets. We have chosento use the same comparison

testas in[13 ], i.e., at-Studenttest with95% condence

interval. The null hypothesis was that the mean dier-

encebetweenthepredictionerrorsobtainedusingrespec-

tivelythereference andtesttransforms, isequalto zero,

wherethepredictionerrorsareexpressedintheELabor

E

CIE94

perceptual metric. Incase the null hypothesis

wasrejected,wedeterminedwhichfromthereferenceand

testtransformsprovidedthebestresults.

Tohaveaglobalindicationoftheperformanceofapartic-

ulartransform,wecalculatedanindexwhichisthedier-

encebetweenthenumberoftimesthetesttransformwas

evaluated better, and thenumberoftimes it was evalu-

atedworsethanthe referencetransform. This was done

overthesixteenavailableCCPdatasets. Thisindex,de-

notedby In withn =1;2;:::;384, spansfrom In = 16

toI

n

=16, correspondingto thecases inwhichthe test

transformperformsrespectivelyworseorbetter thanthe

referencetransform for allthe 16CCP datasets consid-

ered. Incase In = 0, thetest and reference transforms

areconsideredequivalent. Moreover,wedenethefactor

AkindicatingthenumberoftransformswhoseindexInis

greaterthank,i.e.:

A

k

=#fn:I

n

>kg (4)

where the symbol # species the cardinality of the set

considered. InTable2weshowthenumberoftransforms

whicharestatisticallyequivalenttoorbetterthantheref-

erencetransformsaccordingtoA

k .

InTable3 we listthe transformsthat providedthebest

performance,includingthecorrespondingparametersthat

ledtothesetransformsafterapplicationoftheminimiza-

tion process. The index I

max

corresponds to the max-

imum value of In obtained among the 384 transforms

withrespecttothereferencetransformconsideredateach

time. As an example, the transform based on the ma-

trixobtainedstartingfromT2000(SP=3)byminimizing

E

CIE94

(PEM=2) overLam'sset (CCP=1)has an

indexImax=5comparingtheperformance tothelinear

Bradford transform, and this represents the best result

foundamongtheproposedtransforms.

Figures1{4illustratetheshapesofthe sensorsthat are

statistically equivalent to -or better than - a reference

transform,while Figure5comparesthereference sensors

to those correspondingto M

(4;2;1)

, whichrepresentsone

to thenonlinearBradfordtransform,as indicated inTa-

ble3.

350 400 450 500 550 600 650 700 750 800

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1

Sensors for which I _n > 0 (comparison with Sharp)

Wavelength (nm)

Normalized sensitivity

Figure 1: Sensitivity curvesfor the sensors statistically

betterthanthereferencetransform(In>0). Comparison

withSharptransform(forECIE94).

350 400 450 500 550 600 650 700 750 800

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1

Sensors for which I _n > 0 (comparison with BFD)

Wavelength (nm)

Normalized sensitivity

Figure 2: Sensitivity curvesfor the sensors statistically

betterthanthereferencetransform(I

n

>0). Comparison

withlinearBradfordtransform(forECIE94).

FollowingTable3,wealsoreportthreeamongthebest

matrices obtained, according to the t-Student test for

E

CIE94 :

M

(3;2;1)

=

"

1:1059 0:0642 0:1702

0:8630 1:8195 0:0435

0:0012 0:0053 0:9959

#

M

(1;5;1)

=

"

1:0922 0:0890 0:1811

0:8793 1:8121 0:0211

0:0023 0:0156 0:9868

#

M

(4;2;1)

=

"

0:9732 0:2000 0:1732

0:8509 1:8244 0:0265

0:0009 0:003 0:9994

#

(5)

Discussion

A certain numberofobservations canbemade fromthe

testswehaveperformed.

Firstly, it is clear from Table 2 that a certain number

350 400 450 500 550 600 650 700 750 800

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1

Sensors for which I

n > 0(comparison with CMCCAT2000)

Wavelength (nm)

Normalized sensitivity

Figure 3: Sensitivitycurvesfor thesensors statistically

betterthanthereferencetransform(In>0). Comparison

withCMCCAT2000transform(forE

CIE94 ).

350 400 450 500 550 600 650 700 750 800

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1

Sensors for which I

n >= 0 (comparison with BFD non Lin.)

Wavelength (nm)

Normalized sensitivity

Figure 4: Sensitivitycurvesfor thesensors statistically

equalto-or betterthan-the referencetransform(I

n

0). Comparison with nonlinear Bradford transform(for

E

CIE94 ).

reference ones, atleast fromthe statistical analysis per-

formedbythet-Studenttest. Thisshiftstheproblem in

establishingsomecriteriatochoose agoodCATmatrix.

Fairchild[18 ]recommendsthat thebestchoiceshouldbe

a CATwhichensures performances similarto thoseob-

tainedby the current CIECAM97 model. However, two

mainproblemsarestillnotconsidered: 1)TheCCPdata

setsusedforcomparisonsarestillaectedbyaconsider-

ablenoise;2)TheVonKriesmodelisstillfarfrombeing

complete,sinceitiseithertoosimpletodescribewhatac-

tuallyhappensinthevisualsystem,orthevisualsystem

applies a vonKries transformation to a combination of

theconesignals, ratherthanscalingindividualconesig-

nals[18 ].

Secondly,wehaveshownthatLam's databaserevealsto

represent quiteeÆcientlythe otherdatasetsusedinour

tests. Infact, itcanbe noticedinTable 3that thebest

performanceshavealwaysbeenobtainedbytheminimiza-

tion of Lam's CCP data set. In other words, the best

transform T that minimizes a certain error metric be-

tweentheCCPsofLam'sdatabaseand theirpredictions

obtainedfromEq.1,isthebesttransformforthepredic-

tion of the entire collection of 16 CCP data sets. This

is an important result, since it tends to show that it is

350 400 450 500 550 600 650 700 750 800

−0.2 0 0.2 0.4 0.6 0.8 1

1.2 Comparison between sensors

Wavelength (nm)

Normalized sensitivity

Proposed Sharp CMCCAT2000 BFD

Figure 5: Comparison between reference sensors and

M

(4;2;1)

, best sensor with respectto nonlinear Bradford

transform.

tionthat corroborateschoicesthat weremade inseveral

papers[13 ,14 ].

Thirdly,anotherinterestingresultisobtainedbythecom-

parisonwiththeCMCCAT2000matrix. Thismatrixwas

foundbyLietal.[15 ]bytheminimizationofE

Lab over

certain datasets, including Lam's dataset. InTable 3

weshowthat betterresultscanbeobtainedby minimiz-

ingtheRMSofE

CIE94 orE

CMC1:1

,whichareclearly

dierent from the perceptual error metrics used by Li.

We also show that in the minimization of the RMS of

ECIE94,equivalentresultsareobtainedbyselectingany

ofthefourstartingpointsconsidered. Thustheminimiza-

tiondoesnotdepend, inthiscase, onthe startingpoint

(Table3,rightcolumn,comparisonwithCMCCAT2000).

Itisinterestingtonoticethatthebestresults,apartfrom

theonecorrespondingtotheCMCCAT2000,areobtained

by the minimization of E

CIE94

(boldface values indi-

cated in Table 3), which can thus be considered as a

good error metricto takeinto considerationwhenmini-

mizingthecolordierenceinadataset.

Finally,Table3showsusthatsimilarorevenbetterper-

formances arefoundwithrespectto thenonlinearBrad-

ford transform. A better performance is obtained con-

sidering the mean E

Lab

error metric, while an equiv-

alent performance is obtained in the sense of ECIE94.

This reinforces the interest in orienting the research to-

wards removing the nonlinearity present in the CAT of

theCIECAM97model.

Conclusions

Inthispaperweshowthatnewsensorsforthechromatic

adaptationtransformcanbefoundwithrespecttothose

alreadyproposed. Theperformancesobtainedbysomeof

the new sensors are equivalent or even better for acer-

taindatabaseofcorrespondingcolorpairs. Weshowthat

Lam'ssetcansignicantlyrepresenttheotherconsidered

datasets,sincetheperformanceoftheCATobtainedby

theminimizationprocessperformedonLam'ssetpermits

to obtain the best performancesalso for the otherCCP

datasetsconsidered. Moreover,somesensorshaveproven

toensureaperformanceequivalenttotheoneobtainedby

thenonlinearBradfordtransform. Thissuggeststhatthis

substitutedby amore economic linear one, as it is cur-

rentlywished.

Acknowledgements

Thisworkwas part of aprojectsupportedbythe Swiss

Commissionfor TechnologyandInnovation(CTI)under

GrantC-4374.

Theauthorswouldalsoliketoacknowledgethekindand

usefuldiscussion withProf. SabineSusstrunkat Audio-

visualCommunicationsLaboratory (LCAV),EPFLLau-

sanne,Switzerland,whogenerouslygaveusimportantad-

vicetointerpretandhighlightsomeoftheresultsfound.

References

[1] J.A.Worthey,\Limitationsofcolorconstancy",Jour-

nalofOpt.Soc.Am.A,Vol.2,No.7,pp.1014{1026,

July1985.

[2] H. Helson, D.B. Judd, and M.H. Warren, \Object-

color changes fromdaylight toincandescent lament

illumination",Illum.Eng.Vol.47,pp.221{223,1952.

[3] D. Jameson, L.M. Hurvich,\Color adaptation: sen-

sitivity,contrast, after-images", inHandbook of Sen-

soryPhysiology,7/4,VisualPsychophysics,D.Jame-

son and L.M. Hurvich, eds. Springer-Verlag, Berlin,

1972,Chapt.22.,pp.568{581,especiallyp.569.

[4] Q. Zaidi, B. Spehar, and J. DeBonet, \Color con-

stancy in variegated scenes: role of low-level mech-

anism in discounting illumination changes", Journal

of Opt. Soc.Am. A,Vol. 14, No.10, pp. 2608{2621,

Oct.1997.

[5] D.H.Brainard andB.A.Wandell,\Asymmetriccolor

matching: howcolorappearancedependsontheillu-

minant", Journalof Opt. Soc. Am.A,Vol. 9,No.9,

pp.1433{1448,Sept.1992.

[6] D.H.Brainard,W.A.Brunt,andJ.M.Speigle,\Color

constancyinthenearlynaturalimage.I.Asymmetric

matches",JournalofOpt.Soc.Am.A,Vol.14,No.9,

pp.2091{2110,Sept.1997.

[7] D.H.Brainard,\Colorconstancyinthenearlynatural

image.2.Achromaticloci",JournalofOpt.Soc.Am.

A,Vol.15,No.2,pp.307{325,Feb.1998.

[8] M.D.RutherfordandD.H.Brainard,\LightnessCon-

stancy: A DirectTestoftheIlluminationEstimation

Hypothesis",draftpaper,April2001.

[9] K.M. Lam, \Metamerism and Colour Constancy",

Ph.D.Thesis,UniversityofBradford,UK,1985.

[10] CIE,TheCIE1997interimcolourappearancemodel

(simpleversion),CIECAM97,Vienna: CIEPub.131,

1998.

[11] G.D.Finlayson,M.S.Drew,andB.V.Funt,\Spectral

sharpening: sensortransformationsforimprovedcolor

constancy",JournalofOpt.Soc.Am.A,Vol.11,No.

5,pp.1553{1563, May1994.

[12] M.D.Fairchild, \Color Appearance Models", Addi-

[13] G.D. Finlayson and S.Susstrunk, \Performance of

a chromatic adaptation transform based on spectral

sharpening",Proc.IS&T/SID8thColorImagingCon-

ference,pp.49{55,Scottsdale,Arizona,USA,2000.

[14] G.D. Finlayson and S. Susstrunk, \Spherical sam-

plingandcolortransformations",Proc.IS&T/SID9th

Color Imaging Conference, pp. 321-325, Scottsdale,

Arizona,USA,2001.

[15] C. Li, M.R. Luo, and B. Rigg, \Simplications of

theCMCCAT97",Proc.IS&T/SID8thColorImaging

Conf.,pp.56{60,Scottsdale,Arizona,USA,2000.

[16] S.Susstrunk,J.Holm,andG.Finlayson,\Chromatic

Adaptation Performance of Dierent RGBSensors",

Proc.IS&T/SPIEElectronicImaging,SPIEVol.4300,

pp.172{183,January2001.

[17] Web site of the University of Derby, UK, Sept. 3,

2001,http://colour.derby.ac.uk/colour/info/catweb/

[18] M.D.Fairchild,\ARevisonofCIECAM97sforPrac-

ticalApplications",ColorRes.Appl.,Vol.26,2001(in

press).

[19] R.S.Berns,\Billmeyerand Saltzman'sPrinciplesof

ColorTechnology",3rdEd.,JohnWiley&Sons,Inc.,

N.Y.,USA,2000.

Biography

RobertoCostantiniobtainedhisElectronicsEngineer-

ingMasterDegreefromtheUniversityofTrieste,Italy,in

2000. His Master work was jointly conductedwith the

Image Processing Laboratory of Uni. Trieste and the

Institute of Microtechnology (IMT) of the University of

Neuch^atel (UniNe), Switzerland, where he nowis Ph.D.

student. His research is oriented towards video/image

compressionalgorithms,telesurveillanceapplications,and

colorconstancy.

MichaelAnsorgereceivedEng. Dipl. degreeinElec-

tronicsin1980fromthe SwissFederalInstituteof Tech-

nologyinLausanne(EPFL),andthePh.D.in2000 from

UniNe. From1980to1986,hewasscienticstamember

at CEHS.A.inNeuch^atel,whichbecamepartof CSEM

S.A.in1984. In1986, hejoinedtheElectronicsand Sig-

nal Processing Laboratory (ESPLAB)at IMT,where he

ispresentlyheadingaresearchteaminvolvedinverylow-

powermultimediaprocessing.

Javier Bracamonte received his Ph.D. in EE from

UniNe in November 1997. He is currently senior re-

searcheratIMT,workinginalgorithmsandlow-powerim-

plementations for portable multimediaapplications. His

research interests include digital signal processing, im-

age/videocoding,andVLSIarchitecturesdesignfor low-

powerimage/videocompressionsystems.

Fausto Pellandiniobtained hisPh.D.fromthe ETH

Zurich in 1967. In 1972 he was appointed as professor

of electronics at UniNe where he was in charge of cre-

atingIMT UniNE,whichhe headed for 10years. Since

1975 he headsthe ESPLAB at IMT, where he leadsre-

searchactivitiesmostlyconcernedwithrecognition,com-

pression andcodingof information(speechand images),

algorithms and architectures for ultra low power signal

processing. From 1989 he is part-time professor at the

EPFL,whereheteaches signalsandsystemstheory.

CCPDataSets PEM (Perceptual Err. Metric) SP(Starting Point)

1!Lam 1!E

Lab

1!T

Sharp

=

"

1:2694 0:0988 0:1706

0:8364 1:8006 0:0357

0:0297 0:0315 1:0018

#

2!Helson

3!CSAJ

4!Lutchi 2!E

CIE94

5!LutchiD50

6!LutchiWF 2!TBF

D

=

"

0:8951 0:2664 0:1614

0:0367 1:7135 0:0367

0:0389 0:0685 1:0296

#

7!Kuo&Luo 3!E

CMC1:1

8!Kuo&LuoTL84

9!Braun&Fairchild1

10!Braun&Fairchild2 4!RMSofELab

11!Braun&Fairchild3 3!T2000=

"

0:7982 0:3389 0:1371

0:5918 1:5512 0:0406

0:0008 0:0239 0:9753

#

12!Braun&Fairchild4

13!Breneman1 5!RMSofECIE94

14!Breneman8

15!Breneman4

16!Breneman6 6!RMSofECMC1:1 4!TvonKries=

"

0:3897 0:6890 0:0787

0:2298 1:1834 0:0464

0 0 1

#

Table1: Listofdatasets,perceptualerrormetrics,andstartingpointsusedinthearticle [11 ,16 ,17 ,19 ].

Referencetransforms

PerceptualErr. Metric Sharp(A0) CMCCAT(A0) BFD(A0) Nonlinear BFD(A 1)

ELab 62 55 87 16

ECIE94 46 15 63 7

Table2: NumberoftesttransformswithIn>0(i.eA0)orIn0(i.e. A 1)withrespecttothereferencetransforms.

ReferenceTransforms E

Lab

E

CIE94

Sharp I

max

7 6

SP 2 3

PEM 2 2

CCPDataSet 1 1

CMCCAT I

max

5 1

SP 2,4 1,2,3,4,4

PEM 6,6 5,5,5,5,6

CCPDataSet 1,1 1,1,1,1,1

BFD I

max

5 5

SP 1,1,2,2,2,3,3,4,4,4 1,1,2,2,3,3,4

PEM 2,3,1,2,3,2,3,2,3,6 1,2,1,2,1,2,3

CCPDataSet 1,1,1,1,1,1,1,1,1,1 1,1,1,1,1,1,1

Nonlinear BFD I

max

3 0

SP 4,4 1,2,2,3,3,4,4

PEM 2,6 6,3,6,3,6,2,6

CCPDataSet 1,1 1,1,1,1,1,1,1

Table 3: Summary of the conditions (choice of starting point, minimizing function, and data set) that led to the

transformsensuringthebestperformancesincomparisonwiththereferencetransforms. TheSP,PEM,andCCPvalues

havetobereadinaverticalsense,asatripletwhichactuallyrepresentsthematrixM

(SP;PEM;CCP) .