Colorimetric characterization of a desktop drum scanner using a spectral model

Rochester Institute of Technology

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Theses

Thesis/Dissertation Collections

7-1-1994

Colorimetric characterization of a desktop drum

scanner using a spectral model

Ming-Ching James Shyu

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Recommended Citation

Colorimetric Characterization of a Desktop Drum Scanner

Using a Spectral Model

Ming-Ching

James

Shyu

B. S. National Cheng-Kung University (1983)

M. S. Colorado State University (1988)

A thesis submitted for partial fulmlment

of the requirements for the degree of

Master of Science in Color Science

in the Center for Imaging Science

in the College of Imaging Arts and Sciences

of the Rochester Institute of Technology

July 1994

Ming-Ching

1. Shyu

Signature of Author

Mark D. Fairchild

Accepted by

College of Imaging Arts and Sciences

Rochester Institute of Technology

Rochester, New York

CERTIFICATE OF APPROVAL

M. S. DEGREE THESIS

The M. S. Degree Thesis of Ming-Ching James Shyu

has been examined and approved

by two members of the color science faculty

as satisfactory for the thesis requirement for the

Master of Science degree.

Dr. Roy Berns, Thesis Advisor

Thesis Release Permission Form

Rochester Institute of Technology

Center for Imaging Science

Title of Thesis:

Colorimetric Characterization of a Desktop

Drum Scanner Using a Spectral Model

I, Ming-Ching James Shyu, hereby grant permission to the Wallace Memorial Library of

R.

I. T. to reproduce my thesis in whole or in part. Any reproduction will not be for

commercial use or profit.

Colorimetric

Characterization

of a

Desktop

Drum Scanner

Using

a

Spectral Model

Ming-Ching

James Shyu

Athesissubmittedforpartialfulfillment oftherequirementsforthedegreeof

MasterofSciencein ColorScience intheCenterfor

Imaging

Science

intheCollegeof

Imaging

Arts andSciences

oftheRochester Instituteof

Technology

ABSTRACT

Ascanner characterizationmethodbasedon ananalytic spectral model wasderived.

Themethodfirstmodeledthespectralformationof eachmedium_usingeitherBeer-Bouguer

LaworKubelka-Munktheory. Scanner digitalcountswerethen_empiricallyrelatedtodye

concentrations. Fromtheseestimateddyeconcentrations, either spectral _{transmittance}or

spectral reflectancefactorcouldbepredicted. Theseestimated spectraldatawere used to

calculate tristimulus values and then color differences forthe target object. A Howtek

D4000

desktop

drumscanner was_{colorimetrically} characterizedaccordingly. The average

Acknowledgments

I wishto express _my gratitudeto the

following

sources ofsupportin completion ofthis

thesis:

Dr.

Roy

Berns forguidance and

inspiration,

Dr. Mark Fairchildand staffs oftheMunsell Color Science Lab forall_{the support,}

Mr. TaekKimofDupont

Printing

and

Publishing

forthespectral_{measurements,}

Dupont

Printing

and

Publishing

for financialsupport,

HowtekInc. forpartialdonationoftheHowtekD4000 drumscanner,

My

wife

Yu-Ling

forallthe encouragement,myparents and in-lawsfortheir

fully

Dedicate

to

Yu-Ling,

Table

of

Contents

Table of Contents i

ListofTables iv

ListofFigures vi

1. Introduction 1

2. Background 4

3. Scanner Characterization Process 13

3. 1 Material Analysis 14

3.1.1 Spectral Model- Transparent Material 15

3. 1.2 Spectral Model

- Opaque Material 18

3.1.3 Derivation of Unit Absorptivities 20

3.2 PredictionofActualConcentrations 22

3.3

Building

Characterization Model 25

3.3.1

Linearizing

Scanner Signals 27

3.3.2

Relating

Scanner ReadingstoConcentration 28

3.4Model Verification 29

3.5Comparison with prior spectral methods 32

4.Experimental 33

4.1 Target Objects 33

4.2

Metrology

and

Colorimetry

34

4.3Spectral Measurement 37

4.3.1 TransparentTarget 37

4.4 System Configuration 38

5. ResultsandDiscussion 40

5.1 Transparent Material- Kodak Ektachrome

40

5.1.1 MaterialAnalysis 40

5.1.2PredictionofActualConcentrations 45

5.1.3 Image

Scanning

46

5.1.4

Building

Characterization Model 47

5.1.5 Performance Verification 69

5.2 Transparent Material

-FujiFujichrome 72

5.2. 1 Material Analysis 72

5.2.2 PredictionofActual Concentrations 77

5.2.3 Image

Scanning

78

5.2.4

Building

CharacterizationModel 78

5.2.5 Performance Verification 86

5.3 Opaque Material Kodak Ektacolor Plus Paper 89

5.3. 1 Material Analysis 89

5.3.2PredictionofActualConcentrations 94

5.3.3 Image

Scanning

95

5.3.4

Building

CharacterizationModel 96

5.3.5 PerformanceVerification 105

5.4OpaqueMaterial- FujiFujicolorPaper 108

5.4.1 MaterialAnalysis 108

5.4.2PredictionofActualConcentrations 113

5.4.4

Building

Characterization

Model 114

5.4.5 Performance Verification 124

6. Conclusions 131

References 134

Appendix A:Spectral Weightings for

Calculating

TristimulusValues 139

Appendix B: Spectral

Property

oftheTarget Materials 141

AppendixC:ProgramtoPredict Concentrations 145

Appendix D: Program to Calculate Color Difference 155

Appendix E: ProgramtoretrieveRaw Scanner Digital Counts 163

List

of

Tables

TABLE I. List ofpublished scanner characterization results 12

TABLEn. Resultsoftheprincipal component analysisonKodak IT8.7/1 target 42

TABLEHI. Regressionresults

-rampeigenvectors againstglobaleigenvectorsfor

Kodak IT8.7/1 target 43

TABLE TV. Regressionresultsofthe3

by

3model(12-bitscan)for Kodak IT8.7/1

target ; 50

TABLE V. Regression results ofthe 3

by

11 model (12-bit _scan) for Kodak

1T8.7/1 target 55

TABLEVI. Regressionresultsofthe3

by

1 1 model(8-bit scan) for Kodak IT8.7/1

target 61

TABLE VII. Performance summary of 3 different scanner models for Kodak

IT8.7/1 target 66

TABLE vm. Resultsoftheprincipal component analysis onFuji IT8.7/1 target 74

TABLE DC Regressionresults

-eigenvectors against global -eigenvectors for Fuji

IT8.7/1 target 75

TABLE X. Regressionresults ofthe 3

by

1 1 model (12-bitscan) for Fuji IT8.7/1

target 81

TABLE XI. Resultsoftheprincipal component analysis onKodak Q-60Ctarget 91

TABLE XII.Regressionresults

-rampeigenvectorsagainst global eigenvectorsfor

Kodak Q-60C target 92

TABLE XIII. Regression results ofthe 3

by

1 1 model (8-bitscan) for Kodak

Q-60Ctarget "

TABLE XTV. Resultsoftheprincipal component analysisonFujiIT8.7/2target 110

TABLE XV. Regressionresults

-rampeigenvectors against globaleigenvectorsfor

Fuji IT8.7/2target Ill

TABLE XVI. Regressionresultsofthe3

by

1 1 model _{(8-bit scan)}forFuji IT8.7/2

target 118

TABLE XVII. Regressionresults - theindependentFujicolortarget's_eigenvectors

againsttheFuji IT8.7/2target'seigenvectors 130

List

of

Figures

FIG.3-₁

. Overalldataflowofthecharacterization method 14 FIG. 3.1-1. Optical geometry oftransmittance and opaque materials 15

FIG. 3.3-1.Plotsofnormalized _{scanner readings against concentration readingsfor}

spectrallynon-selectivecolors ₂₇

FIG. 3.4-1. Flow chart of the characterization process 31

FIG. 4.1-1. Sample images ofthe targetmaterials 36

FIG. 5.1-1. MaximumtransmittanceofKodak IT8.7/1 target 41

FIG. 5.1-2.Eigenvectors ofKodak IT8.7/1 target 45

FIG. 5.1-3. Predictedspectraltransmittancefactors fromthe tristimulus _matching

algorithm 46

FIG. 5.1-4. Histogramofthe

AE*ab

from the tristimulus _matching algorithm for

Kodak IT8.7/1 target 46

FIG. 5.1-5. Example plots ofthelinearizationprocess for Kodak IT8.7/1 target 49

FIG. 5.1-6. Concentration differences from the 3

by

3 model prediction (12-bit

scan)against actual concentrationsfor Kodak IT8.7/1target 51 FIG. 5.1-7. Histogramofthe

AE*ab

errorfromthe 3

by

3 model (12-bit_scan) for

Kodak IT8.7/1 target 52

FIG. 5.1-8. Color differenceversus

L*,

C*ab

andhab from the3

by

3 model

(12-bit scan) for Kodak IT8.7/1 target 53

FIG. 5.1-9. Concentration differences fromthe 3

by

11 model prediction (12-bit

scan) against actual concentrationsfor Kodak IT8.7/1 target 56

FIG. 5.1-10. Histogramofthe

AE*ab

errorfromthe 3

by

11 model (12-bitscan)

for Kodak IT8.7/1 target ₅₇

FIG. 5.1-11. Color difference versus

L*,

C*ab

and

hab

fromthe 3

by

11 model

(12-bit _{scan) for Kodak IT8.7/1 target 58}

FIG. 5.1-12. Concentration

differences

from the 3

by

11 modelprediction (8-bit

scan)against actualconcentrationsfor Kodak IT8.7/1 target 62

FIG. 5.1-13. Color difference versus

L*,

C*ab

andhabfromthe3

by

1 1 model

(8-bit scan) for Kodak IT8.7/1 target 63

FIG. 5. 1-14. Histogramofthe

AE*ab

errorfromthe3

by

1 1 model _{(8-bit scan) for}

Kodak IT8.7/1 target ₆₄

FIG. 5.1-15. Model performance analysis for the _gray balanceofKodak IT8.7/1

target ₆₇

FIG. 5. 1-16. Modelperformance analysisforthehueshiftofKodak IT8.7/1 target....69

FIG. 5.1-17. Color difference versus

L*,

C*ab

andhab fromthe 3

by

11 model

(12-bitscan)foranindependent Kodak Ektachrometarget 70

FIG. 5.1-18. Histogramofthe

AE*ab

errorfromthe 3

by

11 model _{(12-bit scan)}

foranindependent Kodak Ektachrometarget 71

FIG. 5.2-1. Maximum transmittance of Fuji IT8.7/1 target 73

FIG. 5.2-2. Eigenvectors of Fuji IT8.7/1 target 76

FIG. 5.2-3. Histogram ofthe

AE*ab

fromthe tristimulus _matching algorithm for

Fuji IT8.7/1 target 77

FIG. 5.2-4. Exampleplots ofthelinearizationprocessfor Fuji IT8.7/1 target 80

FIG. 5.2-5. Concentration differences fromthe 3

by

11 model prediction (12-bit

FIG. 5.2-6.Color differenceversus

L*,

C*ab

andhab fromthe3

by

11 model

(12-bit_scan)for Fuji IT8.7/1 target 83

FIG. 5.2-7. Histogramofthe

AE*ab

errorfromthe3

by

1 1 model _{(12-bit scan)} for

Fuji IT8.7/1 target 84

FIG. 5.2-8. Model performance analysisforthe_{gray balance} ofFuji IT8.7/1 target 85

FIG. 5.2-9. Modelperformance analysisforthehueshift ofFuji IT8.7/1 target 86

FIG. 5.2-10. Histogramofthe

AE*ab

errorfrom the 3

by

11 model (12-bit _scan)

foranindependent Fujichrometarget 87

FIG. 5.2-11. Color difference versus

L*,

C*ab

and hab from the 3

by

11 model

(

12-bit_scan)for independent Fujichrome target 88

FIG. 5.3-1. Maximumreflectance ofKodak Q-60Ctarget 90

FIG. 5.3-2. EigenvectorsofKodak Q-60C target 93

FIG. 5.3-3. Measured and predicted spectral reflectances from the tristimulus

matching algorithm for Q-60C target 95

FIG. 5.3-4. Histogram ofthe

AE*ab

from the tristimulus _matching algorithm for

Kodak Q-60C target 95

FIG. 5.3-5. Exampleplotsofthelinearizationprocessfor Kodak Q-60C target 99

FIG. 5.3-6. Concentration differences from the 3

by

11 model prediction (8-bit

scan) against actual concentrationsfor Kodak Q-60Ctarget 102

FIG. 5.3-7. Color difference versus

L*,

C*ab

andhab fromthe3

by

11 model

(8-bit scan) for Kodak Q-60C target 103

FIG. 5.3-8. Histogram ofthe

AE*ab

errorfrom the 3

by

11 model(8-bit scan) for

Kodak Q-60C target 104

FIG. 5.3-9. Model performance analysis forthe _gray balance of Kodak Q-60C

target 104

FIG. 5.3-10. Modelperformance analysisforthehueshift ofKodak Q-60C target 105

FIG. 5.3-11. Histogramofthe

AE*ab

errorfromthe3

by

1 1 model_{(8-bit scan) for}

anindependent Ektacolorpapertarget 106

FIG. 5.3-12. Color differenceversus

L*,

C*ab

andhabfromthe3

by

1 1 model

(8-bit_scan)for independent Ektacolorpapertarget 108

FIG. 5.4-1. Maximum reflectance of Fuji IT8.7/2 target 109

FIG. 5.4-2. Eigenvectors of Fuji IT8.7/2 target 112

FIG. 5.4-3. Histogramofthe

AE*ab

fromthe tristimulus _matching algorithm for

Fuji IT8.7/2target 113

FIG. 5.4-4. Exampleplotsofthelinearizationprocessfor Fuji IT8.7/2target 116

FIG. 5.4-5. Concentration differences from the 3

by

11 model prediction (8-bit

scan)against actual concentrationsfor Fuji IT8.7/2target 119

FIG. 5.4-6. Histogram ofthe

AE*ab

errorfromthe3

by

1 1 model(8-bitscan)for

Fuji IT8.7/2target 120

FIG. 5.4-7. ColordifferenceversusL*.

C*ab

andhab fromthe 3

by

11 model

(8-bit_scan)for Fuji IT8.7/2target 121

FIG. 5.4-8. Modelperformanceanalysisforthe gray balanceofFuji IT8.7/2target 123

FIG. 5.4-9. Model performanceanalysisforthehueshift ofFuji IT8.7/2target 123

FIG. 5.4-10. Histogram ofthe

AE*ab

errorfromthe 3

by

11 model (12-bit scan)

foranindependentFujiEktachrometarget 125

FIG. 5.4-1 1. Colordifferenceversus

L*,

C*ab

andhab fromthe 3

by

1 1 model

FIG. 5.4-12.Measuredand predicted spectral reflectances ofindependentFujicolor

papertarget 127

FIG. 5.4-13. Maximumreflectances ofFuji IT8.7/2 target and the independent

Fujicolor target 128

FIG. 5.4-14. Rotatedeigenvectors oftheindependentFujicolortargetandtheFuji

1. Introduction

Inthe graphic arts color reproductionprocess, aphotographicoriginal is captured

by

an analytical deviceandthenrecomposed

by

asynthetic mediumfromwhichforms the

reproduction. Agoalofthereproduction processistomakethereproduced coloridentical

to the original when

they

are viewed side-by-side under a specific _viewing condition.

However,

this goal is not always achieved _{satisfactorily due} to the lack of_processing

accuracy.

Therefore,

an accurateinputanalyticaldevice isa_{necessity in}thereproduction

system. The focusofthis thesisisto_{colorimetrically}characterize a

desktop

drumscanner

serving as an analytical device in order to enhance the _accuracy of graphic arts color

reproduction.

Intraditionalprinting, thescanningoperationis done

by

a skilledcraftsman_usinga

"high-end"

scanner. Thescanneris usually inthe million-dollar range and equipped with

very sophisticated color correction controllers. Based on accumulated _experience, the

craftsman adjusts the controllers to convert the image

density

ofthe original to screen

percentages of the separations for press printing. Since the craftsman has profound

knowledge about howthe screen

density

willtranslate into color-ink onpaper, accurate

color reproduction_{may be}achievedinsuch a_closed-loopenvironment.

Meanwhile,

thecolor reproduction

industry

hasexperienced significantchangesdue

tothe adventof electronicimage processingtechnology. Thedevelopmentofthe

desktop

electronic scanner provides a more productive andless expensive methodthan traditional

high-end scanningin colorreproduction. Despitethis technological advance, two issues

The first issue is that the users ofthe

desktop

systemdo not always have good

color separation skill compared withthe_printingcraftsmen. Sincetheusers ofthe

desktop

scanneraremost

likely

artists withexpertise notinoffset_printing,the

desktop

systemhas

toprovide a vehicleto assurethe_accuracyofthecolor reproduction. The secondissue is

that the reproduction synthetic medium _may not be limited to ink on paper. Since the

reproductioncouldbecarried outinanopen-ended system withadditionaldifferentmedia

such as CD

ROM, CRT,

film recorder, or digital color _{printer, the scanning} operation

designedforthe close-loopedink-on-paperprocess is not adequateto assure_accuracy of

the color reproduction for open-ended media.

Consequently,

colorimetric _accuracy

independent fromthe output media is required for the

desktop

scanner to provide good

color reproduction quality. Scanner colorimetric characterization is the _{first step in}

achieving device independentcolorforthisopen-endedcolor reproduction system andthe

scanner is also the first device in the color reproduction chain.

Therefore,

it becomes

criticaltohavethe_{scanning device colorimetrically}characterizedtorecordtheimagesignal

faithfulto theoriginal.

There aretwo general approaches in scanner colorimetric characterization: direct

tristimulus value _matching and spectral matching. Both approaches usethe set ofthree

digital counts fromthe threeprimary sensorsinthescannertoderiverequisite data. The

directtristimulus_matchingapproach mapsthedigitalcountsto tristimulusvalues througha

set ofcharacterizationfunctions. Thespectralmatchingapproachreconstructs thespectral

dataoftheoriginal

by

a spectral model andthencalculatesthetristimulusvalueswiththe

There have beenseveral recent articles

describing

thecolorimetriccharacterization

of

desktop

scanners based on the tristimulus _matching approach,1"3

to be discussed in detail in the

following

chapter. A few articles have described the colorimetric

characterization of

desktop

scanners based on the spectral _matching approach.4'5 _The

tristimulus approach iseasier toimplement since it does not require a spectral analysis.

However,

the spectral match approachhasnot_onlytheadvantage ofhigher_{accuracy but}

alsoin

functioning

well undermultipleilluminantsand not

being

susceptibletoproblems of illuminantmetamerismincomparison withthe tristimulus_matchingapproach. Thespectral

matchingapproach waschosen asthesolecharacterizationmethodinthisthesis.

Theoverall objectiveofthisthesiswastoachievecolorimetric characterizationof a

Howtek D4000

desktop

drum scanner suchthat the scanner's output could be translated

into accurate colorimetric signals of the target object. The scanner was treated as a

densitometer where the scanner digital counts were related to the material's dye

concentrationsinordertoreconstructthespectralinformationofthephotographic original.

Thespectralinformationwas usedtocalculatetristimulusvalues andthenCIELAB values

asthefinalresultofthecharacterizationprocess. In a similar mannertocurrent practicein

the _printing

industry,

photographic materials were used as the target objects. CIE

illuminant D50andtheCIE 1931 2 degreestandard colorimetricobserver6

were usedinall

the computations as recommended

by

the Committee for Graphic Arts Technologies Standards (CGATS).7 The performance ofthe characterization method was evaluated

quantitatively

by

AE*ab

color differences between instrumental measurements and the characterized scanner output ofthe test targets. These results were also comparedwith

2. Background

There havebeen several articles

describing

the colorimetric characterization of

desktop

scanners. In _{general, their} methodologies can be categorized as operator

intervention,8 _polynomial regression,9'10

multidimensional interpolation,11'12 multi

channelanalysis,13-14

and spectral modelanalysis.4-5

They

allshare onecommon goal: to

achieve the smallest

AE*ab

difference between the original and the transformed digital

signals.

Ideally,

this goal could be achieved _easily with a simple 3

by

3 matrix if the

scanner's sensor spectral sensitivities are a linear combination of a set of CLE color

matching functions. This has been proven _{mathematically}

by

Schrodinger15 that in

transforming

fromone set of primaries toanother set of_primaries,thenew primaries will

be homogeneous linear functionsoftheoldprimaries. Thistopicwas revisited_recently

by

Gordon and Holub.16 Gordon andHolub also cautioned thatifthe sensors'

sensitivities

are not linear combinations ofcolor _matching

functions,

nonlinear transformations are

neededtorelatetheRGB digitalcountstoXYZtristimulusvalues. Thisisthe typicalcase.

Wandell and Farrell8 utilized the 3

by

3 transformation and also analyzed the

residualdistribution betweenthemeasured and predictedtristimulus values.

They

found

thattheerror cloud was_principally scatteredinonedirectionand proposedto add afourth

channel_alongthecolor coordinates where most ofthecharacterization errorwas observed.

By

visually evaluating

images,

theusercould use a slidertocorrecttheestimatedcolorand

to reducethetransformationerror. Intheir experiment,thecharacterizationresultsof aHP

13.2)

for the direct 3

by

3 transformation and improved to an average

AE*ab

of 1.7

(maximumat

6.2)

with userintervention_alongthefourth dimension. Theoperationof user

intervention did improvethecoloraccuracy;

however,

itadded considerableburdenonthe

desktop

userforextra color adjustment

likely

_reducingproduction speed.

The 3

by

3 transformationfailedtorelatethe scannerdigital countstotristimulus values because the scanner responsivities were not a linear combination of CIE color

matching functions. One could ask the question: _why not build a scanner

having

responsivitiesthat are alinearcombinationofCIEcolor _matching functions? Vrhel and

Trussell have addressed this question

by deriving

a method to select color filters and

imaging

illuminants for scanner systems.13 _A

vectorspace approach combinedwith set theoreticalmethods was usedto synthesizethedesired filters with as few basis filters as possible.14 _Optimal

nonnegativesets offilters were derived

by

this method forseveral

viewing illuminants. Simulations wereperformedon343 spectralreflectance patchesfrom a color copier. The simulation results under illuminant D65 were as follows: average

AE*ab

of2.3 unit (maximumof

10.7)

fortheoptimal3

filters,

average

AE*ab

of0.35unit

(maximumof

1.3)

fortheoptimal4

filters,

average

AE*ab

of0.34unit(maximumof

1.4)

for the optimal 5 filters. The constraint of nonnegative terms for the filters' spectral

response would ensure that thefilters are_physically conceivable. Howevertheseresults

were allfromcomputersimulation;it isnot clearthathowfeasible it istomanufacture such

filter sets with good signal-to-noise performance and with reasonable cost from commerciallyavailablefiltermaterials.

polynomial regression ormulti-dimensionalinterpolation. Thetechnique ofpolynomial

regression17 _{is based on the}

following

theory: _assuming the _processing error in the

scanningelementsfollows a normal

distribution,

aregression equation canbeestablished

torepresent the_{relationship between}thepredictor variables- RGB

digitalcounts andthe

response variables - their

corresponding XYZ values. North9 performed stepwise

polynomial regression for a

Sharp

JX450 flat-bed scanner with 125 color patches of

photographic material and achieved results where86%ofthepredictions werelessthan2.0

AE*ab. Berns10_{performedstepwise polynomialregression with200}

photographicsamples

basedon _{photographing} aMunsell BookofColorand achieved an average

AE*ab

of 1.6

units (maximumat

4.5)

forilluminantD50. Kang2performed polynomialregressionfora

Sharp

JX450scanner_usingaKodakQ60Cphotographic standard andachievedanaverage

AE*ab

of2.8 for a 3

by

3 matrix, an average

AE*ab

of2.5 for a 3

by

6 matrix and an

average

AE*ab

of1.9 fora3

by

14matrix. Moreresults are listed in Table I.

Kang

also

included a_{gray balance} routinein his

implementation,

which forced the_gray patches to

haveequal amount ofRGB digitalcounts.

Berns3 _further

concentrated on thecolor correction operation of the system and

performed a regression from the digital counts

directly

to CIELAB values. The

characterization was performed on a

Sharp

JX610 scannerwithaKodak Q60Creflectance

target and a Macbeth Color Checker chart; the result was an average

AE*ab

of 1.8

(maximumat

8.8)

fora3

by

9matrix. Otherthan _usingtheKodak Q60Cas atest_target,

Clippeleer18_{applied polynomial regression on aflatbed CCD} scanner withanAgfachrome

IT8.7/1 standard and achieved an average

AE*ab

around2.5 (maximumat around

9.0)

fora

(maximumat around

5.0)

fora3

by

27 matrix and around 1.0(maximum at around

3.5)

fora3

by

64matrix.

Severalissues exist when _using the regression technique. One is the regression

function can not be extrapolated beyond the range of the known predictor variables.

Another issue is how to interpret _any physical _{meaning for} the non-linear polynomial

terms.

Moreover,

itis_very difficulttocalculatetheinverse transformationfroma

high-order polynomial regressionfunction.

Fortunately,

thisisnot requiredinthisapplication.

Multidimensional interpolation techniques with table look _up were then considered as

another approachtoscannercharacterization.11'19

Theideaofmulti-dimensional interpolation is basedonthemathematicalprinciple

that _any smooth function can be approximated

by

_many contiguous linear segments.

Together,

allthe smalllinear segmentsdefinethe systemresponsecharacteristic between

the input domain and the output domain.

Treating

a scanner as a black

box,

the

input/output relationship canbecharacterizedbetween the systeminput (scanner values)

and the system output (tristimulus _values) with a

look-up

table

by

the interpolation

technique.

Thereareseveral waysto subdividethedomainspaceintosubspaces. Twotypical

ways are cubic subspace division and tetrahedral division. The cubic interpolation

techniqueuseseight corners of a cube tointerpolate betweentwo3-dimensionalspaces. It

is a straight-forward operation to _map a uniform orthogonal cube in six flat plans to

another solid form

having

eightcorners in another space. However

inversely,

_anyeight

Thetetrahedralinterpolationtechniqueis basedonthephenomenonthatfourpoints

define a unique tetrahedron.

Consequently,

a subcube divided into tetrahedrons in one

color space canbe

linearly

relatedtoa pointinthe

corresponding

tetrahedron intheother

color space and the forward or _{inverse relationship is} a unique one-to-one mapping.

Hung1! _{appliedtetrahedralinterpolation}

andLUTtechnique

(33x33x33)

tocharacterize a

Sharp

JX450 scanner with 125photographic color patchesforilluminantD65 and resulted

in an average

AE*ab

of 1.1 with a maximumerror of9.9. For_comparison,

Hung

also

appliedpolynomialregression onthesameconfigurationand got anaverage

AE*ab

of4.7

(maximum at

12.9)

for 1st order _regression, 2.8 (maximum at

8.2)

for 2nd order

regression and2.2 (maximumat

7.8)

for 3rdorder regression.

To comparetheperformancedifference betweenvariousLUTsizes, Hung12used

an analytical model to generate 65x65x65 data points and tested the data with

5x5x5,

9x9x9,

17x17x17 and 33x33x33 linear tetrahedral LUT. In the case of Beer's law

simulation, the average

AE*UV

errors were

5.4,

1.4,

0.4 and 0.1 for

5x5x5,

9x9x9,

17x17x17 and 33x33x33 tetrahedral

LUTs,

respectively. The maximum

AE*UV

errors

were

18.7,

6.0,

1.7 and0.5 respectively.

Hung

suggestedthat the suitable sizeforaLUT

model _showing a small enough error _may result from 17x17x17 to 33x33x33

look-up

tables.

However,

a 17x17x17LUT implies 4913 measurements in each oftheinput and

outputdomains.

Hung12 _{had furthercombined the tetrahedral} and LUT technique with nonlinear

interpolation. He adjustedtheRGB digitalcounts with "tonecurve

adjustment"

using

one-dimensional LUTs similar to the gray balance routine

Kang

used. The results of this

simulatedtest databasedonBeer'slawmodel. Underthesame_{condition, the}regression

techniqueresultedAE*uverrorof 15.1 (maximumat

52.3)

for 1storder_regression,AE*uv

of5.5 (maximum at

29.4)

for2nd order regression and AE*uv of2.1 (maximum at

8.8)

for3rdorderregressionrespectively. From_{these results,}itseemedthatthenon-linear

one-dimensionalinterpolationcombined with multi-dimensionaltetrahedrallinear interpolation

producedabetterresultthan theregression method.

Unfortunately,

these testresults were

not available in

AE*ab;

neitherhas there _{been any further} published results on scanner

characterization_usingthis technique.

RodriguezandStockham4proposed amethod whichtreats thedigitalcounts ofthe

scanner output as the scanner

density

readings and relates them

directly

to colorimetric

quantities based on the assumptions that the system responsivities of the scanner are

narrow, like delta

functions,

andthespectral characterization ofthe scanned photographic

materialis known.

They

usedNewton'smethodtoestimatethedye densitiesof each color

patch withthe transparent film'sspectral characterizations ofthe_{dye according}toBeer's

law. Beer's law20'21 _{statesthat the}

density

spectrum of a color patchis

linearly

relatedto

theconcentrationsofthedyesand itsspectraltransmittancecanbe reconstructed with the

density

spectrum asfollowing:

K(k)

=

ko(A.)

+

Ci ki(X)

+

C2 k2(k)

+

C3 k3(A,)

+... +

Cn kn(X)

T(A.)

=

I(X)/I<A)

=e-Kft)

where

kr/A,)

isthe spectral

density

ofthebaseand

kn(A)

istheunit_absorptivity spectrumof

thenthdyeinthematerial.

Cn

isthe associated concentration of eachnthdye.

Io(A)

isthe

factor. For a photographic material, the scanner's digital counts can be related to the

concentrations of_{the cyan,}magenta andyellowdyes andthen thespectralinformation as

wellasthetristimulusvalues canbecalculatedaccordingly. More detail aboutBeer's law

is discussed inthe

following

chapter.

RodriguezandStockhamappliedthespectral methodforaHell 3000series drum

scanner with a Kodak Ektachrome Q-60 test target. An iterative method was used to

estimatethe dyeconcentrations fromthescannerdensities.4-22 WiththeEktachrome dye

spectral

density

curvesprovided

by

the manufacturer, theestimated concentrations were

usedtoreconstructtheestimated spectrumbasedonBeer's law. Theestimated spectrum

was fed into scanner model equations to generate the predicted scanner densities. The

scanner model equations werebasedonthephysicalchannel responsivities ofthegraphic

artsscanner. The difference betweenthepredicted scannerdensitiesandtheactual scanned

density

readings was usedtocalculatetheincrementoftheestimatedconcentrations. The

iterative algorithm was based on the

theory

that when the concentrations are _correctly

estimated, theestimated spectrum wouldbe identicalto theactualspectrum,therefore,the

difference betweentheestimatedand actual scannerdensitieswouldbenegligibleandthe

iterationcanbeended. Notethat thisiterationcriterionwas notbasedon_{CIE colorimetry}

and the spectral

density

ofthe

base, kn(A),

was notinvolved in the computation.

They

achieved thecharacterizationforaverage

AE*ab

lessthan2 and maximum values ofless

than4.

Viggiano andWang5 appliedtheBouguer-Lambert-Beer modelto calibrateaflat

bedscanner with aKodak Ektachrome Q60Ctarget.

They

performedan extensive analysis

to compensate for the scanner's nonlinear amplitude response function. The amplitude

response, sometimes referredto as "gamma

correction,"

wasincorporated

by

thescanner

manufacturer to account for the _nonlinearity

introduced

by

CRTs. As a result, the

amplitude response function should be compensated when _getting the actual sensor

readingsoftheobject

density

fromthescanner output.

They

used a non-linearfunctionto

model the amplitude response function ofa series of _spectrally non-selective tiles. In

addition,

they

performedaprincipal component analysis onthe

density

spectra of all the

patchestoobtain the spectral curves ofthedyeset ratherthan_{using data}supplied

by

the

manufacturer. An _{ordinary least-squares} algorithm was used in predicting each patch's

concentrations withthe derivedeigenvectorsfromthe principal componentanalysis. The

published characterization results were an average

AE*ab

of4. 1 anda90thpercentile of

6.2. Besides the procedural difference in estimating the concentrations (least-squares

algorithm versus iterative algorithm), the fact that Viggiano and

Wang

performed their

experiment on a flat-bed CCD scanner while Rodriguez and Stockhamused a high-end

drumscannercontributedto thelargeperformancedifference.

At the current state-of-the-art, all these published characterization results as

summarizedin Table Iare stillintherange of average errorslargerthan 1

AE*ab

unit with

themaximumerrors largerthan3

AE*ab

units.

Stokes,

etal23

foundthat the _{perceptibility}

threshold for images is around 2

AE*ab

units on average.

Therefore,

to have the

colorimetric errorintroduced

by

the_scanningoperationnottobeperceptible,itrequiresthe

maximum characterization error ofthe scannertobe around2

AE*ab

units.

Meanwhile,

sincethe scanner operationisthefirstelementinthecolor reproductionchain,it isdesirable

to

keep

the average characterization error as small as possibleto preventthe errorfrom

ofthis thesis was to achieve highercharacterization _accuracythan the published results

summarizedin Table I.

Method Author Avg.

AE*ab

Max.

AE*ab

3

by

3 WandellandFarrell8 4.9 13.6

3

by

3 WandellandFarrell8 3.6 13.1

3

by

(3+

1)

WandellandFarrell8 2.4 6.2

3

by

(3 +

1)

WandellandFarrell8 1.7 6.2

3simulatedfilters VrhelandTrussell13 2.3 10.7

4simulatedfilters VrhelandTrussell13 0.4 1.3

5 simulatedfilters VrhelandTrussell13 0.3 1.4

Stepwise Polynomial North9 2 N. A.

3

by

3+

Gray

Balance Kang2 _{2.8 N. A.}

3

by

6+

Gray

Balance Kang2 _{2.5 15}

3

by

14+

Gray

Balance Kang2 1.9 N. A.

1storder reg. Hung11 4.7 12.9

2nd order reg. Hung11 2.8 8.2

3rdorder reg. Hung11 2.2 7.8

5*5*5 LUT Hung11 1.1 9.9

3

by

6(SS

XYZ)

Berns3 3.6 22.1

3

by

9 (SS

XYZ)

Berns3 2.5 12.5

3

by

9 (SS

Lab)

Berns3 1.8 8.8

3

by

9 (SS .33)

Berns3 _2.4 9.2

3

by

3Polynomial Clippeleer11 2.5 9.0

3

by

8Polynomial Clippeleer11 2.0 9.5

3

by

27Polynomial Clippeleer11 1.5 5.0

3

by

64Polynomial Clippeleer11 1.0 3.5

Spectralmodel ViggianoandWang5 4.1

6.2(90%)

Spectral model Rodriguezand

Stockham4 _{<2 <4}

3.

Scanner

Characterization Process

Inthegraphic arts color reproduction_process,photographic materials arepresented

astheoriginal. Thescanner characterization methodinthis thesisutilizes thecolorimetric

andspectralproperties ofthephotographic materialtoformthebasis_{for characterizing}the

original. An analytical method is used in material analysis to decompose the spectral

informationofthetargetmaterialintounit absorptivities ofthe_primarydyes. Thescanner

istreatedas an

imaging

densitometer enablingthe_relationshipfromthescanner readings

by

thescannerto thedyeconcentrations ofthe targetmaterialtobemodeled. Thismodelis

then usedtopredictthedyeconcentrationsfromthescanner's digitalreadings for images

having

the same dye set. The predicted concentrations can be used to recompose the

spectral datawiththeunit absorptivities ofthedyes. The spectral data is

finally

used to

calculate colorimetric parameters of the original for defined observers and illuminant.

Color differencescanbeassessedbetweenthemeasured andthepredicted colorimetricdata

toevaluate themodel performance. Anobject-oriented representation ofthedata flow is

shownin Fig. 3-1. To havean objective performance_{verification,}anindependentoriginal

Scanner Digital Counts

J

c

CMY

Concentrations

f

Spectral Curves

J

c

TristimulusValues [image:31.571.114.246.84.330.2]

Color Difference Values

FIG. 3-1. Overall dataflowofthecharacterization method.

3.1 Material

Analysis

Therearetwogeneraltypesof photographic materials: transparentandopaque. As

shown in Fig.

3.1-1,

the optical _property of the material determines its viewing and

measurement conditions. The transparent material is viewed and measured with 0/0

geometry. Theopaquematerialis viewed and measured withd/0geometry.

Hence,

there

are different spectral models for each kind of material based on the Beer-Bouguer

theory20-21

andtheKubelka-Munktheory,20'24"26_{respectively.}

T

Transparency

isviewed under0/0_geometry

Opaquematerialisviewed

underd/0 geometry

FIG. 3.1-1. Optical geometryoftransmittanceand opaque materials.

3.1.1 Spectral Model - Transparent Material

The Beer-Bouguertheory20'21

states that the

intensity

of abeamofmonochromatic light i passing through a transparent material of thickness X suffers a _weakening of

intensity, di,

thatisproportionaltoits intensity:

di /dx=- K i

,

(D

where K is the absorption coefficient of the material. Integration of this differential

equationovertheentirethicknessofthematerialgives

ln(I/I0)

=

ln(Ti)

=

-KX,

(2)

or

I /

10

=Ti=_e-KX

where

Lj

is the

intensity

ofthemonochromatic _{light before passing}through thematerial;

after_passingthroughit is I. Ti istheinternaltransmittanceofthematerial.

For material with n layers ofdifferent colorants with asingle base substrate, the

totalabsorption,

K,

of unitthicknessX becomes:

K=

kt

+

Ki

+

K2

+ ... +

Kn

,

(4)

where

kt

is the absorption of the substrate without _colorant, and

Ki,...,Kn

are their

respective absorptions ofn colorants. With thefurther assumption that the unitspectral

absorptionproperties of eachdyeareinvariantwith_{concentration,}Eq.

(4)

becomes:

K=

kt

₊

ciki+c2k2 +... +cnkn,

(5)

where

kt

is the absorption of the substrate without _{colorant, ci,...,cn} are scalars

representing amount oftheconcentrations ofthevarious _colorants, andki,...,knaretheir

respective unitabsorption coefficients. Further expandingthedomain frommonochromatic

light tochromatic

light,

variables

T, Io,

I and K become functions of wavelength

(A)

as

follow:

I/I0(A)=Ti(A)

_

e-(kt(X)+Cl kl(k)+ C2k2(X,)+...+ Cn kn(A,))

}

(g)

Equation

(6)

formsthebasisofthespectral analysisfortransparentmaterials.

Since onlyphotographicmaterials are presented astheoriginal, several assumptions

are made _specifically about this material in order to be applicable to the Beer-Bouguer

theory:27

Nooptical_scattering,

No

fluorescence,

Refractive index

discontinuity

between material and air is not _{significantly}

influenced

by

thevariationofthedyeconcentrations.

The reversal film after _processing can be considered as a transparent medium

consistingof_cyan, magentaandyellowdyescoatedon abasegelatin.

According

to

Beer-Bouguer

theory

andtheprevious stated_assumptions,theinternaltransmittanceof a reversal

filmcanbe describedasfollow:

Tj(A)

=e~(

ks^

+ cc

kc^

+ Cm

km(A)

+cy

ky(A) )

?

,ys

_ _{e-kg(X.) * e-(}cc

kc(A.)

+ cm

km(A,)

+Cy

ky(A.)

) /o-v

where_cc,cm and_cy aretheconcentrations and

kc(A),

km(A)

and

ky(A)

aretheunitspectral

absorptivities of cyan, magenta and yellow

dye,

respectively.

kg(A)

is the spectral

absorptivity of the base and can be separated out as the base transmittance, Tg(A).

Assuming

thechangeof refractiveindex betweenthebasematerial and airisnotinfluenced

by

differentamount ofdye_{concentration,}themeasurement of

Tg(A)

wouldbethenetbase

transmittance

including

therefractionfactor. Thetotal transmittanceofthetransparentfilm

becomes:

T(A)

=

Tg(A)

* e~(cc

kc(^)

+ cm

km(^

+cy

ky^ )

,

(9)

Further

dividing

Tg(A)

and_applyingthenatural logarithmfunctiononbothsides ofEq. (9):

K(A)

=

-ln( T(A)

/

Tg(A)

)

=

Consequently,

anygiven spectraltransmittanceofa coloronthefilm canbe decomposed

intoalinearcombination ofthedyeconcentrations anditsrespectiveunit absorptivity.

3.1.2 Spectral Model - Opaque Material

Themost common photographicreflectancematerialisphotographicpaper,which

has transparentdye layered on

top

of a paper base. The dye layer is considered as a

homogeneous layeroffinite thickness.

Scattering

occurs within the natural fiberpaper

base. Eventhough thepaperbaseisnot_opaque,

by backing

thepaper withblackmaterial

as recommended

by

CGATS.5-1993 standard,7

the measurement of the paper base is

equivalentto themeasurement of a mediumthatisthickenoughtobeopaque. As a_result,

the photographic paperis considered as atransparent dye layer in opticalcontact with a

scattering,opaque support. This has been described in detail

by

Berns.28

Kubelka and Munk24 described the_{relationship between} reflectance

(R)

andthe

proportionality constant of absorption coefficient

(K)

over_scattering coefficient

(S)

ofa

coloredlayeroffinitethickness

(X)

applied on abackgroundofknownreflectance

(Rg)

as

shown in Eq. 1 1.

R_l-Rg(a-bcoth(bSX))

a-Rg+

bcoth(bSX)

where a= 1 ₊

(K/S)

and b= (a2-l)1/2. The symbol

"coth"

is the hyperbolic cotangent

function and is defined as coth(bSX) =

[exp(bSX)

_{+ exp(-bSX)]} /

[exp(bSX)

exp(-bSX)]. For opaque materials, the thickness X is large enough to make the _exp(-bSX)

negligiblecomparedtoexp(bSX). Eq. (1

1)

canthenbesimplifiedas:

Roo=l+(K/S) [(K/S)2+2(K/S)]1/2,

(12)

Since onlyphotographic paperispresented asthe_original,several assumptionsare

made_specificallyabouttheopaque materialinordertobe applicableto theKubelka-Munk

theory

asfollows:

No

fluorescence,

Thescatter effect caused

by

thedye isnegligible,

Refractive index

discontinuity

between material and air is not _{significantly}

influenced

by

thevariationofthedyeconcentrations.

When assumingthe _scatteringcoefficient S inthedye layer is allowedto approach_zero,

Eq.

(11)

becomes:

R=

Rge-2KX,

(13)

whichis_verysimilartoEq.

(3)

describing

theBeer-Bouguertheory.

However,

it is noted

that the Beer-Bouguer

theory

is defined for collimated _{light (0/0 geometry)} while the

Kubelka-Munk

theory

is defined for diffused light (d/d geometry).20-27

Sincethe

Rg

is

measured onthefinishedpaperbasewithminimumdyeconcentration,theinfluence ofthe

refractive index

discontinuity

between the paper and the air wouldbe built into the

Rg

measurement automatically. Inaddition, the thicknesstermX in Eq.

(13)

canbeeliminated

since it is constant for given photographic paper. The spectral absorption ofthe

dyes,

K(A),

is derived as a functionof spectral reflectance factor

by

the inverseofEq.

(13)

as

follow:

Given that the photographic paper is a continuous-tone _material, it is assumed that the

absorption properties of a given area arethesum oftheabsorption propertiesofeach ofthe

cyan,magenta andyellowdyes:

Kmixture(A)=

Kc(A)

+

Km(A)

+

Ky(A)

,

(15)

With furtherassumptionthat theunit spectral absorption propertiesofthedyesareinvariant

withconcentration,Eq.

(15)

becomes:

K(A)=_cc

kc(A)

+_cm

km(A)

+

cy ky(A.)

,

(16)

wherecc, cm,

cy

arescalars_representingamountoftheconcentrationof_cyan,magentaand yellow dye respectively, and

kc(A), km(A)

and

ky(A)

are their respective unit absorption

coefficients.

Combining

Eq.

(14)

andEq.

(16)

together,thespectral reflectancedatacanbe

directly

relatedto thelinearcombinationofthedyeconcentrations andtheirrespective unit

absorptivities,as follows:

- 0.5

ln( R(A)

/

Rg(A) )

= _cc

kc(A)

_+cm

km(A)

+

cy ky(A)

,

(17)

or

R(

A)

=

Rg

(A)

* e"2( cc

kc^>

+ cm

km(x>

+y

ky(^

) .

(18)

Eq.

(17)

formsthe basisofthespectral analysisforopaquephotographic materials.

3.1.3 Derivation of Unit Absorptivities

The fact thatthe spectraldataof_every color onthephotographic material can be

transformedintoalinearcombination ofits primary dyes'

absorptivitiesandits respective

concentration provides afirm basis forstatisticalanalysis. Principalcomponent analysisis

concerned with _explaining the variance-covariance structure through a few linear

combination oftheoriginal variables (oreigenvectors).29

Consequently,

the_primarydyes'

absorptivities ofthematerial are_essentially theeigenvectors andtheconcentrationsofthe

dyesaretherespective scalarforeachvariableinthelinearcombination.

Whena_samplingpopulationis_{uniformly distributed for}a photographic material's

color _{gamut, the} eigenvectors from the principal component analysis would depict the

variation vectors _among all the samplings from their mean.

Ideally,

these "global"

eigenvectors should resemblethe_primarydyes' absorptivities since what makes thecolor

different is justtheconcentrationdifferencesoftheuniquedyes inthe material.

However,

principal component analysis

traditionally

tends to draw maximum explanation of the

variationofthefirsteigenvectorbeforefurther

deriving

consequenteigenvectors; thereis

no guaranteethatallthe_{primary dyes}willbetreated_{equally in}

deriving

theeigenvectors.

Fortunately,

there are rotationoptions29-30

availableinseveral statistical software

packages. One particular option is "equamax rotation", which equalizes the variance

betweeneach eigenvector. Howeverasindicated

by

Berns,27 _{thereis significantunwanted}

secondary absorptions in the global eigenvectors, which _{may be introduced}

by

the

"equamaxrotation"

tocompensatetheuneven_sampling ofthe colorgamut. As a _result,

further correction is needed. Separate analyses are performed to estimate each dye's

eigenvector(and

hopefully

its absorptivity) one at atime,

by

sampling along one single

primary with aminimum presence of other primaries. These three

"local"

eigenvectors

theoreticalspectral models and actual

behavior,

_{theselocaleigenvectorsdo}notrepresentthe

global variationfortheentire gamutpopulation.

A combined method was used

by

Berns27

where the global eigenvectors were

rotatedto match thelocal eigenvectors_minimizing sumofsquareserror. Since thelocal

eigenvectors are defined

by

the primaries

individually,

the rotation from the global

eigenvectorsto the localeigenvectors removes theunwanted _secondary absorptionwhile

preserving therepresentation oftheglobal variation. Multiple linearregression17

canbe

used:

b=(XTX)-1XTY

(19)

Y =Xb

wheretheYmatrixcontains the threelocaleigenvectors andtheXmatrix containsthe three

global eigenvectors. The 3*3 b matrix is the rotation coefficients from the regression

analyses and theestimatedmatrix Y are the _{resulting final}eigenvectors to describe the

absorptivities ofthe_{primary dyes.}

3.2

Prediction

of

Actual Concentrations

An analytical method was used to determine the concentrations needed to

colorimetrically match each color. This type of method is commonly referred to as

computer colorantformulationandhas been

long

usedinthepaint_matching

industry

with

satisfactoryresults.20-24-31 This analytical method estimatestheconcentration mixture of

the colorants with a numerical computation algorithm until the predicted and actual

tristimulusvalues are within a specified goodnesslevel.

Allen20 _has

described

a tristimulus _matching algorithm for _matching opaque

samples or clear samples based on a pseudotristimulus match and Newton-Raphson

iteration. In Allen'salgorithm, itfirstestimatesinitialconcentrationsby:

c= _(WDO)'WDf

,

(20)

where c is the scalarmatrix of_{the colorants;} in this_thesis, cc, cm and

cy

are scalars of

concentrationtoeach of_{the cyan,}magenta and yellowdyeunit absorptivities as

c= Cc

Cm

Cy

(21)

Wx,

Wy

and

Wz

are the ASTM tristimulus weights7 _for

a given CIE observer and

illuminantcombination:

W=

Wx(Al)

. .

Wx(A.)

Wy(Al)

. .

Wy(JL)

Wz(Ai)

. .

Wz(A.)

(22)

D is the multiple-linear regression _weighting matrix, which is the partial derivative of

reflectanceortransmittancewith respectto absorptionforopaque ortransparentmaterials:

D=

'd(Ai)

0

0

d(Xi)

0 0

0

0

d(A)

(23)

O isthe matrix of unitspectral absorptivities

k(A)

foreachcyan, magenta and yellowdye

o=

kc(Al)

km(Al)

ky(Al)

kc(/Ln)

km(Ao)

ky(An)

(24)

fis thegivenspectral _absorptivity

K(A)

ofa standard color. Inthis_{thesis, f is}calculated

fromthe spectral measurement ofeach color

by

Eq.

(14)

for opaque materials or

by

Eq.

(10)

fortransparentmaterials:

IVstandard(/tl)

f=

Kstandard(An)

(25)

The firstestimationoftheconcentrations(Eq.

20)

are usedtocalculatethespectraldataand

then tristimulus values. Subsequentiterations

by

means ofthe Newton-Raphson method

canimprovetheprediction results towarda closer match and _stopthe iteration when the

tristimulusdifference have becomesmallerthan some goodness parameter. The iteration

algorithmis:

Acra

Ac,,

=

(WDO)

AX

AY

AZ

(26)

c=

cc+Acc

cm +

Acn

c +

Ac,,

(27)

Thegoodness parameterinthis thesiswas set as follows:

[(AX)2+(AY)2

<_0.001

,

(28)

wheretheperfect reflectancediffuser hasaYequalto 100.

Similartristimulus _matching algorithms wereproposed

by

Ohta.32'33 except that

his algorithm does not require spectral data of the standard. Both Allen's and Ohta's

algorithm can be traced back to the _pioneering work of Park and Stearns.34

Lately,

Berns27 _{has applied Allen's algorithm in}

predicting the dye concentrations of thermal

transferpaperwith good results.

3.3

Building

Characterization

Model

The

key

issue in

building

thecharacterization model is how torelate the scanner

output to the actual concentrations. With the _primary dyes' absorptivities, each color's

spectraldistributioncanbe first decomposed intotheconcentrations ofthe_{primary dyes}

by

the tristimulus_matching algorithm. Ifthescanner's sensor spectral responsivities are_very

narrow,the naturallogarithmofthescanner'sdigitalcount readings canberelatedfromthe

integral density35 _{to the analytic densities ofthematerial's atthe specific wavelength as}

follow:

Ja"

-ln(j

T(X)

S(X)

s(X)dX) =

-ln(T(X)-

5(A)-s{X)\

dX

)

,

(29)

where

T(A)

isthespectraltransmittanceorreflectanceoftheobject_propertyreceived

by

the

responsivity. The integral ofthe product of

T(A-),

_s(A) and

S(A)

_{is actually} the scanner

channel reading.

Whenthebandwidth_{dA is very}small,

T(A),

s(A)and

S(A)

are not changedwiththe

variance of

A.

Since

T(A),

_s(A) and

S(A)

are constant terms in the

integral,

they

can be

moved outside theintegral andEq.

(29)

becomes valid. As described in Eq.

(2)

andEq.

(5),

the -ln(T(A))is actuallythetotalabsorption

K(A),

whichisalinearcombination ofthe

products of each_primarydye'sconcentrationwithits unit_absorptivity . As aresult, after

applying the natural logarithm transformation on the scanner digital _counts, these

transformeddigitalvalues are

directly

relatedto thedyeconcentrations ofthe_{primary dyes.}

Fromthiscorrelation,a

training

model canbe derivedtorelatethescannerdigitalcountsto

the material's concentrations. However inreality, the scanner sensor responsivities _may

not be narrow enough such that theintegral interval dA is wider and

T(A),

_s(A) and

S(A)

are not constants in the integral.

Consequently,

Eq.

(29)

does not hold and non-linear

functions are needed to describe the _{relationship between} the integral

density

and the

analyticdensities.

Two steps are taken to derive the characterization model. The first _{step is} to

linearize the scannerdigital counts to the concentrations ofthe _spectrally non-selective

colors. Thesecond_{step is} torelatethelinearized digitalvalues to theconcentrations ofall

colors _considering the possible cross-talkbetween the scanner's channel responsivities.

Combining

these two steps together, thescanner digitalcounts canbetranslatedinto the

concentrationsofthe targetmaterial.

3.3.1

Linearizing

Scanner

Signals

Thepurposeofthelinearizationprocessisto

independently

relatethe red,greenand

blue digital counts torespective cyan, magenta andyellow concentrations. This can be

achieved

by

_regressingthescanner readings withtherespective concentrationsofthenon

selective colors.

However,

_{the red,} green andblue scanner readings (denoted

dr,

dg

and

db)

are not always

linearly

related to the material's concentrations. Fig. 3.3-1 is an

example plot ofthe scanner sensor readings (normalized between 0 and

1)

against the

concentrations of a_groupof_spectrallynon-selective colors.

u Q

Normalized Scanner_Reading

FIG. 3.3-1. Plots of normalized scanner readings against concentration readings for

Itisclearthatatransformationfunction isneededtolinearizethescanner readings

withthematerial concentrations. Stepwisepolynomial regression canbeusedtoderivethe

linearizationfunctionas:

P

=

(XTXrXTY,

D=

[P0

A

p\ p\

ft

][!

Nd

N]

N]

N* N'f.

(30)

where X is the 5thorder matrixof

Nd

and

Nd

is thenormalizedscannerdigitalcountin

natural

log

transformation. Y is the concentration matrix of _spectrally non-selective

colors. D isthepredictedlinearized digitalcount. Note that

/J0

termis needed tomodel

thepossibledarkcurrentinthescannersystem.

3.3.2

Relating

Scanner Readings to Concentration

Ideally,

ifthe scanner's sensor responsivities are narrow enough, the scanner's

readings wouldbethe linearcombinations ofthedyes' concentrations. Afterthe scanner

digital counts are transformed through the linearization process, a simple 3

by

3

transformation shouldbe able to relate the transformed digital values to the actual dye

concentrationsasfollow:

(3= (DTD)-1DTC ,

Per

P,

"A"

Hmr

Pmg

/L,

D,

Pyr

K

P,b

A.

(31)

where the

ft

terms are derived

by

regression.

Dr,

Dg

and

Db

are the transformed red,

green and blue scanner readings.

Cc

,

Cm

and

Cy

arethe predicted cyan, magenta and

yellowconcentrations ofthe targetmaterial.

However in reality, the scanner's channel responsivities are not always narrow

enoughto be

totally

linearly

independent. Unwantedcross-talk could existbetween the

scanner's channel responsivities. Stepwise regression with higher order polynomial

equationisusedtomodelthenon-linearrelationbetweenthetransformeddigitalvalues and

the material concentration

including

thecross-talk. Second order polynomial terms plus

r*g*b crosstermare oftenusedinthemodel. Themodel coefficientsforeachindependent

variableina matrixform isasfollows:

p

=

[ft

ft

ft

ft

ft.g

ft.

ft,fr

ft.r

ft.?

ft.

ft.4

Following

thestepwiseselection,some ofthesecoefficients will equal zero.

3.4

Model

Verification

Nowthatthescannerdigitalcountscanbetranslatedintothedyeconcentrations

by

thecharacterizationmodel,it ispossibletoreconstructthespectraldataofeach objectcolor

with the unit absorptivities of_{corresponding dyes}

by

Eq.

(9)

orEq.

(18)

describedin the

material analysis section. With the reconstructed spectral

data,

the model-predicted

colorimetric properties ofthe targetmaterial canbecompared withtheinstrument-measured

data. CIELAB colordifferences canbegenerated to assessthe model performance. The

complete process flow ofthecharacterizationmethodis summarized

by

the solid arrow

Throughout the derivation of the characterization _{model, the} spectral data

measurement, thematerial _analysis, andthe _scanningoperation are all doneon the same

targetobject. Itis doneso astoprovideaconsistent groundforthemodel

training

process.

However inreal-life applications,a characterizeddevicehastowork well withindependent

data.

Consequently,

an independent object of the same photographic material was

processed through this characterized scanner system. The colorimetric information

generated

by

thescanner systemiscomparedwiththemeasured colorimetricinformationof

the independent test target. This colorimetric difference data shall serve as the most

objective _{way inverifying}the modelperformance. Theprocess flowofthe independent

verificationisshowninthedotted lines in Fig. 3.4-1.

Measure Spectral Data

_ Analyze Material

Predict Actual Concentrations

Scan Object

\l/ w

Build Characterization

Model

Linearize ScannerSignals

Relateto

Concentrations

Apply

Model

Reconstruct

Spectral Curve

Calculate TristimulusValues

& Color Difference

1

AE*ab [image:48.571.140.432.82.630.2]

3.5 Comparison

with prior spectral methods

Themain resemblancebetweenthe scanner characterization methodofthis thesis

andpriorspectral methods(ViggianoandWang,5RodriguezandStockham,4-22

)

is theuse

of spectralmodels.

However,

thereare several majorfundamentaldifferences. Viggiano

and

Wang

used the results from a principal component analysis ofthe global

density

spectra as thematerial's unit absorptivities with whichtheconcentrations were estimated

with a general least-square algorithm. Rodriguez and Stockham used manufacturer

provided spectralabsorptivities andapplied an iterativemethodbasedonthe_matchingof

the scanner

density

readings to predict the actualconcentrations. The characterization

methodinthis thesisderived theunit absorptivities withtheglobal andthe_ramp spectral

dataofthe actual target andtheprediction oftheconcentrations is based on aniteration

method with the tristimulus _matching algorithm, which guarantees atrue visual match.

These differentmethodsresultin differentmodel performance.

4. Experimental

4.1 Target

Objects

Both opaque andtransparent materials were selected as the target objects in this

thesis. As described

by

McDowell,36 _{since the color reproduction in the graphic arts}

industry

is_{mostly based}on several typesofphotographic materials,it is thenpossibleto

definethe spectral rangeofthereproductioncolorwith severalparticulardyesets_among

the photographic materials. Based on _{this characteristic,} ANSI/IT8 committee has

completed two standards IT8.7/1 and IT8.7/2 for input scanner calibration with

transparentfilms andphotographicpaper_products, respectively. SincetheseIT8.7targets

are

becoming

the industrial standard reference in device _{characterization,}

they

were

consequentlyadoptedasthe targetobjectsfor

building

thecharacterization models.

There are certain limitations when _using these the IT8 targets. One is the _gray

balance ofthe neutral colors. Since thecolors on theIT8 targetare composed

by

three

spectrally selective

dyes,

not a single_spectrallyneutral

dye,

_anyminuteoff-balance _among

the threedyeswill altertheequilibriumoftheneutralgray, resulting ina colortint. As a

result, the neutral scale is not always without_any chroma. Another limitation is that the

reproducible gamut range is confined

by

the dye sets.

Any

color beyond the linear

combination of the three _{primary dyes is} not represented in the target's domain. In

addition, uniformity,stability andnon-fluorescencearefactorstobeconsidered.

In this thesis, Eastman Kodak

Company

Ektachrome Q-60E1

(IT8.7/1)

and Fuji

IT8.7/2 andKodak Ektacolor Q-60Cwere used asthereflectiontargets. Independenttest

targetswere createdwith a6x6x6 digital factorial design samplingand 18 levelsof neutral

patches. Theseindependenttargetsweregenerated withthesame photographicmaterialsas

the standard IT8 type targets. Throughout this

document,

the _numbering order for the

colors on eachtargetwas from the

top

to the_{bottom starting from} the leftand

lastly

the

graypatch_startingfromthe left. TheportraitimageontheKodakIT8targetwas notused.

Sampleimagesofthese targetsare shownin Fig. 4. 1-1

4.2

Metrology

and

Colorimetry

Thecommitteefor Graphic Arts TechnologiesStandards

(CGATS)

was accredited

by

theAmerican NationalStandards Institute in 1989toserve asthecoordinator of graphic

arts standards activities. As a_{result, the}CGATS.5-1993 standard,7_"Graphic

technology

-Spectralmeasurementand colorimetric computation forgraphic arts

images"

prepared

by

CGATS

Working Group

4,

was approved

by

theAmerican National Standards

Institute,

Inc. onMarch

22,

1993to_specifya_{methodology for}reflectanceandtransmittancespectral

measurement and colorimetric parameter computation for graphic arts images.

Consequently,

the CGATS.5-1993 guidelines is followed throughout this thesis when

possible.

(a)

fctfyVrf"ffr'*"""'"'"' i'

*..-:...-i.t- -'- ',fi" r' "

^11' -i

--' --i'i'-' '

ium'-|V.

WK !:,?"

H

^.ty^^MM^MiliM^^lS^MM M "llll 1?^.L.

''

M MilllllMMIH.MMIllll IIiII ',

'

[i^ . imwsi$. ""

-MUOiri.^Sr^-'ie^V.'J

(c)

^KOOJJ^EKTAOHjORmiSP^'RtpradWtion Gewfe-O-SGC

(d)

FIG. 4.1-1. Sample images ofthe targetmaterials:

(a)

Kodak

IT8.7/1,

(b)

Fuji

IT8.7/2, (c)

Kodak Q-60Cand

(d)

independenttest target. [image:53.571.105.408.87.620.2]

The CGATS.5-1993 standardis based on CIE illuminant D50 and the CIE 1931

standard observer as defined in CIE publication 15.2. The spectral data are collected

between 360nm and780nmineither 10nmintervalsand20nmintervals. The weighting

values _representing the product ofilluminant and standard observerfor 10 nm intervals

accounting for bandpass as described

by

ASTM

E-308,

which isused in this _thesis, are listed in Appendix A. It is noted thatifthemeasured spectral data are at a wavelength

greaterthan360nm, allthe_weightingvalueslessthan the firstmeasured wavelength shall

be summed and added to the _weighting value for the firstwavelength measured. Ifthe

measured spectraldataare at a wavelengthlessthan780_nm,allthe_weighting valuesless

than thefirstmeasured wavelength shallbesummed and addedtothe_weightingvaluefor

thelastwavelengthmeasured.

4.3 Spectral

Measurement

4.3.1 Transparent Target

The spectraltransmittance factorof eachtransparent sample wasmeasuredwith a

Photo Research Spectrascan PR-703ASpectraradiometerin DuPont

Printing

&

Publishing,

ADIP

Group

Color Laboratory. The PR-703ASpectraradiometermeasures intherange of

390 nmto730 nm with 2 nmincrement and5 nmbandwidth. A diffraction grating and

multi-element photodetector comprise the system.37 _{A tungsten} halogen

lamp

with

Corning

filt