research article spectral separation for multispectral...

Research ArticleSpectral Separation for Multispectral Image ReproductionBased on Constrained Optimization Method

Bangyong Sun12 Han Liu2 and Shisheng Zhou1

1 School of Printing and Packing Engineering Xian University of Technology Xian 710048 China2 School of Automation and Information Engineering Xian University of Technology Xian 710048 China

Correspondence should be addressed to Bangyong Sun sunbangyongxauteducn

Received 11 May 2014 Accepted 2 June 2014 Published 22 June 2014

Academic Editor Qingrui Zhang

Copyright copy 2014 Bangyong Sun et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The constrained optimizationmethod is employed to calculate the colorant values of the multispectral images Because the spectralseparation from the 31-dimensional spectral reflectance to low dimensional colorant values is very complex an inverse processbased on spectral Neugebauer model and constrained optimizationmethod is performed Firstly the spectral Neugebauer model isapplied to predict the colorantsrsquo spectral reflectance values and it ismodified by using theYule-Nielsen 119899-value and the effective areacoveragesThen the spectral reflectance rootmean square (RRMS) error is established as the objective function for the optimizationmethod while the colorant values are constrained to 0sim1 At last when the nonlinear constraints and related parameters are setappropriately the colorant values are accurately calculated for the multispectral images corresponding to the minimum RRMSerrors In the experiment the colorant errors of the cyan magenta and yellow inks are all below 25 and the average spectral erroris below 5 which indicate that the precision of the spectral separation method in this paper is acceptable

1 Introduction

The objective of color reproduction is to obtain the samevisual perception of the original images and it is mainlyimplemented based on themetameric reproduction principle[1 2] However when the illuminants or observers changethe color consistency between the original and the hardcopy is hardly maintained Thus in many high-accuracyreproduction areas the originals are represented as multi-spectral images not the common 119877119866119861119862119872119884119870 images [3 4]If the imagersquos spectral information is reproduced correctly thehard copy will look the same as the original under differentilluminants

Within the multispectral image reproduction workflowafter the spectral reconstruction [5ndash7] and gamut mappingprocess [8ndash10] the image pixelrsquos spectral values should beprecisely converted into ink values for printing while theconversion process is often defined as spectral separation[11 12] For most printers the primary inks are cyanmagenta yellow and black hence the input spectral imagesrsquo

reflectances are transformed to119862119872119884119870 values during spectralseparation

In fact as most of the multispectral image pixels are31-dimensional it is difficult to calculate the colorant val-ues from the spectral data straightly Most of the spectralseparation processes are based on the spectral predicationmodels and iteration methods The spectral predicationmodels can be used to calculate different ink combinationsrsquospectral values And the iteration of the separation processwill stop when the image pixelrsquos spectral matches with thepredicated spectral Several spectral predication models canbe used for spectral separation such as multiinterpolationtechniques [13] spectral Neugebauer model [14 15] Yule-Nielsen model [16 17] and Kubelka-Munk model [18 19]Because the spectral Neugebauer model uses less samplecolors and often generates acceptable accuracy it is widelyapplied to the spectral separation process However there aremany factors which influence the separation accuracy In thispaper the spectral Neugebauer model is modified and a non-linear optimization method is analyzed in order to improve

Hindawi Publishing CorporationJournal of SpectroscopyVolume 2014 Article ID 345193 8 pageshttpdxdoiorg1011552014345193

2 Journal of Spectroscopy

the multispectral imagersquos spectral separation accuracy for119862119872119884119870 printers

2 Modification of Spectral Neugebauer Model

21 The Expression of Spectral Neugebauer Model The spec-tral Neugebauer model is a halftone color predication modelwhich calculates the spectral reflectance values within thevisual wavelength from printersrsquo colorant space In fact it isdeveloped fromMurray-Davies model which is a monochro-matic model [20] When a primary ink is printed on thepaper if the spectral reflectance of the solid and substrate arerepresented as 119877120582119905 and 119877120582119904 respectively and the patchrsquos dotarea is given then its reflectance values 120582 can be predictedby using Murray-Davies model as follows

120582 = 119886119905119877120582119905 + (1 minus 119886119905) 119877120582119904(1)

where120582 is thewavelength of light within 400 nmndash700 nmand119886119905 is the fractional dot area of the printed patch

When the monochrome Murray-Davies model isextended to predict color halftones the spectral Neugebauermodel is generated Take the cyan magenta and yellowcolorants printing for example eight possible colors existin the halftone patch which are white (bare substrate) cyanmagenta yellow red (magenta + yellow) green (cyan +yellow) blue (cyan + magenta) and black (cyan + magenta+ yellow) respectively These eight halftone colors areusually defined as Neugebauer primaries When the spectralreflectance values of the primaries are measured the halftonepatchrsquos overall reflectance can be predicated by using thespectral Neugebauer model as follows [21]

120582 =

8

sum

119894=1

119908119894119877120582119894 (2)

where119877120582119894 is the 119894thNeugebauer primaryrsquos reflectance value atfull colorant coverage and119908119894 is the corresponding weightingfactor calculated by the dot areas of the cyan magenta andyellow inks If 119888 119898 and 119910 represent the cyan magenta andyellow inksrsquo area coverage respectively the eight Neugebauerprimariesrsquo weighting factors can be deduced using Demichelequations and the full expression of (2) is written as follows

120582 = (1 minus 119888) (1 minus 119898) (1 minus 119910) 119877120582119882 + 119888 (1 minus 119898) (1 minus 119910) 119877120582119862

+ (1 minus 119888)119898 (1 minus 119910) 119877120582119872 + (1 minus 119888) (1 minus 119898) 119910119877120582119884

+ (1 minus 119888)119898119910119877120582119877 + 119888 (1 minus 119898) 119910119877120582119866

+ 119888119898 (1 minus 119910) 119877120582119861 + 119888119898119910119877120582119870

(3)

When the 119862119872119884 three-color spectral Neugebauer model isextended to 119862119872119884119870 four colors there are 16 Neugebauerprimaries and the weighting factors are listed in Table 1 (119888119898 119910 and 119896 represent the cyan magenta yellow and blackinkrsquos area coverage)

Table 1 The respective fractional area coverages of the CMYKcombinations

Index Weighting factor Fractional area coverage1 119908119908 (1 minus 119888) lowast (1 minus 119898) lowast (1 minus 119910) lowast (1 minus 119896)

2 119908119888 119888 lowast (1 minus 119898) lowast (1 minus 119910) lowast (1 minus 119896)

3 119908119898 (1 minus 119888) lowast 119898 lowast (1 minus 119910) lowast (1 minus 119896)

4 119908119910 (1 minus 119888) lowast (1 minus 119898) lowast 119910 lowast (1 minus 119896)

5 119908119896 (1 minus 119888) lowast (1 minus 119898) lowast (1 minus 119910) lowast 119896

6 119908119888119898 119888 lowast 119898 lowast (1 minus 119910) lowast (1 minus 119896)

7 119908119888119910 119888 lowast (1 minus 119898) lowast 119910 lowast (1 minus 119896)

8 119908119898119910 (1 minus 119888) lowast 119898 lowast 119910 lowast (1 minus 119896)

9 119908119888119898119910 119862 lowast 119898 lowast 119910 lowast (1 minus 119896)

10 119908119888119896 119888 lowast (1 minus 119898) lowast (1 minus 119910) lowast 119896

11 119908119898119896 (1 minus 119888) lowast 119898 lowast (1 minus 119910) lowast 119896

12 119908119910119896 (1 minus 119888) lowast (1 minus 119898) lowast 119910 lowast 119896


14 119908119888119910119896 119888 lowast (1 minus 119898) lowast 119910 lowast 119896

15 119908119898119910119896 (1 minus 119888) lowast 119898 lowast 119910 lowast 119896

16 119908119888119898119910119896 119888 lowast 119898 lowast 119910 lowast 119896

In fact the spectral Neugebauer model is also suitable formulti-ink color systems If119901 colorants are included as follows

119888 = [1198881 119888119895 119888119901]

119879

119888119895 isin [0 1] for 119895 isin 1 119901 (4)

there will be 2119901 Neugebauer primaries and their weightingfactors can be determined by the following equation [11 22]

119908119894 =

119901

prod

119895=1

119888119895

if colorant 119895 is part ofthe 119894th Neugebauer primary

(1 minus 119888119895) else(5)

It can be concluded that the primariesrsquo area coverages areexpressed as fractions of the total area and they satisfy theconstraint sum2

119901

119894=1119908119894 = 1

Because there are only eightNeugebauer primaries withinthe spectral Neugebauer model for three-color printers thepredication accuracy is very limited In order to employmore measured halftone patches as Neugebauer primariesthe cellular spectral Neugebauer model is frequently usedin which the colorant space is divided into more cellularsubdomains [23] For example when the individual inkrsquos areacoverages are partitioned into two parts with three points[0 50 and 100] the119862119872119884 colorant space will be dividedinto eight cellular subdomains

22 The Optimization of Spectral Neugebauer Model Thereare actually several reasons which decrease the predica-tion accuracy of the spectral Neugebauer model such asthe dot gain light scattering and penetration and nonlin-earity between the summed and the individual primariesrsquoreflectances For the purpose of reducing the influenceof these factors some optimization approaches should beperformed

Journal of Spectroscopy 3

221 Calculating the Effective Area Coverage Values Withinthe spectral Neugebauer model the colorantsrsquo area coveragesare employed to calculate the primariesrsquo weighting factorsthus the spectral predication accuracy is highly dependenton these area coverage values and it is significant to obtaintheir optimal values For halftone color reproduction imagesthe change in dot diameter is the critical factor for the printimage transfer and these changes usually lead to tonal andcolor shifts For a monochrome halftone patch its spectralreflectance is usually calculated from the remitted lightreflectance of solid and halftone areas as follows

119886119905 =

119877120582119898 minus 119877120582119904

119877120582119905 minus 119877120582119904

(6)

where 119886119905 is the predicted area coverage and 119877120582119898 is themeasured reflectance values of the halftone patch Becausethe reflectance values change with the wavelength the min-imum reflectance value within 400 nmsim700 nm is usuallyused Actually in conventional printing techniques a widelyadopted form of area coverage is deduced from the opticaldensity values and (6) is written as

119886119905 =

1 minus 10minus119863119903

1 minus 10minus119863119905 (7)

where 119863119905 is the optical density of solid tone and 119863119903 is thehalftone optical density

When the halftone patch ismeasuredwith a densitometerit is not the geometrical area coverage (the ratio between dotsand white paper on the measuring patch) but the ldquoopticallyeffective area coveragerdquo The difference between geometricand optically effective area coverage is due to the fact of lightpenetration and trapping For example as shown in Figure 1part of the arriving light penetrates into the paper betweenthe dots at the unprinted areas and are trapped under thedots during reflection thus this light seems to be absorbed(as shown in Figure 1) [24]

The above phenomenon is called ldquolight gatheringrdquo andit causes the dots to appear optically larger than they are inreality For this reason the optically effective area coverageconsists of the geometric area coverage and the optical areagainThe optical area gain is usually defined as dot gain valueincrease and it is calculated from the area coverage of the filmas a master for platemaking and the tone value printed on thesubstrate via the printing form The area coverage of the film(or the pixel values after color separation for Computer-to-Plate techniques) is called theoretical value 119886119905 and the printedhalftonersquos area coverage is the effective value 119886eff thus the dotgain 119885 is 119885 = 119886eff minus 119886119905 In fact dot gain essentially dependson the paperrsquos surface and its absorptionink setting behaviorthe ink rheology the blanket printing pressure and so on

In order to acquire the real area coverage for the spectralNeugebauer model all the spectral reflectance values withinthe visual wavelength are considered during the effective areacoverage calculation By using the least squares analysis (6)is described into a spectral form

119886eff = (119877120582119898 minus 119877120582119904) (119877120582119905 minus 119877120582119904)119879

times [(119877120582119905 minus 119877120582119904) (119877120582119905 minus 119877120582119904)119879]

minus1

(8)

Ink

Paper

Figure 1 Light gathering in the area of the inked paper surface

As we measure the reflectance from 400 nm to 700 nm withthe interval of 10 nm all the reflectance terms above are 1times 31 row vectors while the superscripts 119879 and minus1 indicatematrix transpose and inverse respectively Because most ofthe reflectances within 400nmndash700nm are involved duringeffective area coverage calculation in (8) it is usually moreprecise than (6) and (7) and we use this equation for spectralpredication in the experiment

222 Calculating the Optimal 119899-Values As a result of lightpenetration and scattering effect the relationship betweenmeasured and predicted reflectance is nonlinear for theMurray-Davies and spectralNeugebauermodels An effectivesolution for this problem is to add an exponent 1119899 to thereflectance values which is developed by Yule and Nielsen[25] Taking the Murray-Davies model for example themodified form can be described as follows

120582 = [119886eff1198771119899

120582119905+ (1 minus 119886eff) 119877

1119899

120582119904]

119899

(9)

where 119886eff is the effective area coverage value and 119899 is aparameter accounting for light spreading in paper and itis referred to as the Yule-Nielsen 119899-value Generally themodified Yule-Nielsen model is more accurate than theoriginal Murray-Davies model Likewise the Yule-Nielsenmodel can be extended to the spectral Neugebauer modelwhich is called Yule-Nielsen spectral Neugebauer (YNSN)model as follows

120582 = [

8

sum

119894=1

1199081198941198771119899

120582119894]

119899

(10)

Because the 119899-value is not a constant it is significant toacquire the optimal value for the specific halftone patchesPearson [26] recommended using 119899 = 17 by testing a varietyof substrates halftone screens and area coverages and mostof his experiment results showed that using 119899 = 17 alwaysimproved performance over using 119899 = 1 However Wybleand Berns have noted that values of 119899 greater than 2 are oftenrequired for modern high-resolution printers [27] Arney et


Spectral reflectance

YNSN model CMYK outputY

N

CMYK(k) ΔR120582 lt 120576

CMYK(k + 1)

Figure 2 Diagram of spectral separation process based on optimization method

al [28] analyzed the process of light spreading in paper andapproximated 119899-value as

119899 = 2 minus 119890minus119860119896

V119901 (11)

where119860 is a constant relating to dot geometry 119896119901 is a constantrelating to modulation transfer function and V is the halftonedot frequency in dots per millimeter In addition ShiraiwaandMizuno interpreted the 119899-value in another form [29] and(9) is modified as follows based on it

120582 = [119886eff(119877120582119904119879119899

120582)1119899+ (1 minus 119886eff) 119877

1119899

120582119904]

119899

(12)

where the solid inkrsquos reflectance 119877120582119905 is replaced by the term119877120582119905119879119899

120582and 119879120582 is the ink transmittance It should be noted

that this model is valid only for integer values of 119899-value andthe overall effect of this is to make the predicted reflectancelower which is consistent with the fact that the Murray-Davies model overpredicts reflectance values

In this paper we use a spectral-error-comparing methodto find the optimal 119899-value Firstly the YNSN model isestablished with the 119899-value initialized from 1 and then acertain number of testing patches are selected to calculate theYNSN modelrsquos spectral error We set 119899-value ranging from 1to 5 with the increment Δ119899 = 01 thus when all the spectralerrors of different 119899-values are obtained and compared theoptimal value is determined corresponding to the minimalspectral error

3 Spectral Separation Based onConstrained Optimization Method

For 119862119872119884119870 printers it is very difficult to convert the 31-dimensional spectral reflectances into the 4-dimensional119862119872119884119870 colorant values However as the 31-D spectralreflectance can be precisely predicted from 119862119872119884119870 values byspectral Neugebauer model it is more feasible to convert thespectral separation process into the constrained optimizationprocess based on the spectral predication model Actuallythe spectral separation is an iteration process where theoptimal 119862119872119884119870 values are continually searched until thepredicated spectral values match well with the given spectralreflectances Generally the spectral separation workflowbased on constrained optimization method can be describedas in Figure 2

It can be seen from the separation workflow that theobjective function and the nonlinear constraints should beaccurately defined for the optimization problem Becausethe major purpose for printing multispectral images is toreproduce the same spectral reflectance values the objectivefunction is defined as the spectral reflectance error

Δ119877120582 =

10038171003817100381710038171003817120582119862119872119884119870 minus 119877120582image

10038171003817100381710038171003817 (13)

where 120582119862119872119884119870 is predicated reflectance values using YNSNmodel and 119877120582image is the multispectral imagersquos reflectancevalues The iteration process in Figure 2 will stop whenthe difference of (13) is smaller than a threshold value 120576predefined

In addition as the colorant values have the specific scalerange the nonlinear constraints can be defined as follows

0 le 119886eff le 1 sum119886eff le 119886limit (14)

where 119886 = 119888119898 119910 119896 and 119886limit represents the limit of thetotal ink amount Thus the nonlinear optimization processfor spectral separation is described as

min 10038171003817100381710038171003817120582119862119872119884119870 minus 119877120582image

10038171003817100381710038171003817

st 119886eff isin [0 1]

sum119886eff le 119886limit

(15)

It should be noted that the use of an optimizationtechnique may lead to a nonoptimal solution (eg a localminimum will stop the iteration process) as Mahy andDelabastita presented [30] Thus Gerhardt and Hardeberg[11] analyzed the parameters which determined the rightcolorant combination obtained including the limitations onthe minimum difference between the desired value and itsestimation difference between colorant values in successiveiterations and initial guess values to start the iterative search

4 Experiment and Analysis

In the experiment the cyan magenta and yellow inks areused to print the multispectral images and the three-colorspectral Neugebauer model is employed for spectral pred-ication The halftone patches are printed with a HP digital


Table 2 The colorant and spectral reflectance error for 50 testing halftone samples

ΔC ΔM ΔY Δ119864119888119898119910

RRMSAvg (error) 143 226 221 385 00047Std (error) 098 154 200 213 00030Max (error) 454 607 723 986 00128

0

01

02

03

04

05

06

07

08

09

1

400 450 500 550 600 650 700

Refle

ctan

ce

Wavelength (nm)

W

Y

M

R

C

G

B

K

Figure 3 Spectral reflectance data of eight Neugebauer primaries

printer and the spectral reflectance values are measuredwith an X-Rite 530 spectrophotometer with geometry (119889 10∘)under aD65 illuminant Take the eight Neugebauer primariesof 119862119872119884 space for example the spectral reflectances within400 nmndash700 nm are illustrated as in Figure 3

Besides 50 testing halftone patches are selected to test thespectral separation method in the paper Firstly the testingpatches are printed with the defined ink values 119862111987211198841and then the spectral reflectance values 1198771205821 are measuredSecondly by using the spectral separation method describedin Sections 2 and 3 new ink values 119862211987221198842 are calculatedfrom the measured spectral reflectance 1198771205821 At last whenthese 119862211987221198842 values are printed and measured new spectralreflectance values 1198771205822 are obtained The difference of 119862119872119884values between 119862111987211198841 and 119862211987221198842 and the spectral errorbetween 1198771205821 and 1198771205822 are calculated to test the separationaccuracy [23 31]The119862119872119884 ink difference and the reflectanceerror are expressed as follows

Δ119864119862119872119884 =radicΔ1198622+ Δ119872

2+ Δ1198842 (16)

where Δ119862 = |1198621 minus1198622| Δ119872 = |1198721 minus1198722| and Δ119884 = |1198841 minus1198842|While for the spectral errors the reflectance rootmean square(RRMS) difference is represented as

RRMS = radicsum120582[1198771205821 minus 1198771205822]

2

119873

(17)

where 119873 is the dimensionality of spectral reflectance 1198771205821is the input and given reflectance values and 1198771205822 is newlypredicted 119862119872119884 inksrsquo reflectance values and they are bothscaled to 0sim1 The RRMS error reveals the matching degreeof two spectral reflectance values so it may favorably evaluatethe precision of spectral separation method

In Table 2 the errors in the form of Δ119862 Δ119872 Δ119884 andRRMS are listed where the Avg(Error) represents the averageof the errors Std(Error) is the standard deviation of theerrors and Max(Error) is the maximum of the errors

From Table 2 it can be seen that the differences of inkvalues are about 2 and most of the spectral reflectanceerrors are below 5 which indicates that the accuracy of thespectral separationmethod in this paper is acceptable For allthe 50 testing halftone patches the colorant errors of cyanmagenta and yellow inks are shown in Figure 4

The spectral reflectance error is depicted in Figures 5 and6 In Figure 5 the distribution of RRMS errors for 50 halftonepatches is listed while in Figure 6 the original and newlyseparated spectral reflectance values are compared and it canbe seen that these two figures match very well

5 Conclusions

The spectral separation algorithm is significant for the multi-spectral image printing devices which can calculate the accu-rate colorant values In the traditional printing process the


0 10 20 30 40 500

1

2

3

4

5

Testing sample

ΔC

(a) The errors of cyan ink

Testing sample0 10 20 30 40 50

0

1

2

3

4

5

6

7

ΔM

(b) The errors of magenta ink

0 10 20 30 40 500

1

2

3

4

5

6

7

8

Testing sample

ΔY

(c) The errors of yellow ink

0 10 20 30 40 500

2

4

6

8

10

Testing sample

998779E

CMY

(d) The combined errors of three inks

Figure 4 Colorant errors of cyan magenta and yellow inks

0 10 20 30 40 500

0002

0004

0006

0008

001

0012

0014

Testing sample

RRM

S

Figure 5 Spectral reflectance error of the 50 halftone patches


400 450 500 550 600 650 7000

01

02

03

04

05

06

07

08

09

Wavelength (nm)

Refle

ctan

ce

(a) Measured reflectance values

400 450 500 550 600 650 7000

01

02

03

04

05

06

07

08

09

Wavelength (nm)

Refle

ctan

ce

(b) New reflectance values by spectral separation

Figure 6 Comparison of the original and newly separated spectral values of the 50 testing samples

multispectral images are firstly converted into the CIE colorvalues under specific illuminant and then the colorant valuesare calculated from the CIE colors Because the connectionspace is the 3-dimentional CIEXYZ or CIELAB under oneilluminant the original and reproducedmultispectral imagescannot keep same color appearance under different observingcircumstances In this paper the spectral separation methodis employed to calculate the spectral reflectancersquos colorantvalues and the purpose of which is to generate the identicalspectral values of the input multispectral images Thus theoriginal and reproduced images reveal the same visual colorsunder different illuminants The accuracy of the spectralseparation method is evaluated in the experiment Theexperiment results show that the colorants errors of threeinks are about 2 and the average spectral error is below5which can guarantee the spectral consistence between theoriginal and the printed multispectral images

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors gratefully acknowledge the financial support byresearch foundation of Department of Education of ShaanxiProvince (no 11JK0541) Doctor Foundation of Xirsquoan Uni-versity of Technology (no 104-211302) and ldquo13115rdquo CreativeFoundation of Science and Technology (no 2009ZDGC-06)Shaanxi Province of China

References

[1] I Zjakic D Parac-Osterman and I Bates ldquoNew approach tometamerismmeasurement on halftone color imagesrdquoMeasure-ment vol 44 no 8 pp 1441ndash1447 2011

[2] M Rump and R Klein ldquoSpectralization reconstructing spectrafrom sparse datardquo Computer Graphics Forum vol 29 no 4 pp1347ndash1354 2010

[3] N Hagen and W Kudenov Michael ldquoReview of snapshotspectral imaging technologiesrdquo Optical Engineering vol 52 no9 Article ID 090901 2013

[4] F Wang A Behrooz M Morris and A Adibi ldquoHigh-contrastsubcutaneous vein detection and localization using multispec-tral imagingrdquo Journal of Biomedical Optics vol 18 no 5 ArticleID 050504 2013

[5] P Xia Y Shimozato Y Ito et al ldquoImprovement of colorreproduction in color digital holography by using spectralestimation techniquerdquo Applied Optics vol 50 no 34 pp H177ndashH182 2011

[6] P-Y Ren N-F Liao B-H Chai W-P Yang and S-X LildquoSpectral reflectance recovery based on multispectral imagingrdquoOptical Technique vol 31 no 3 pp 427ndash433 2005

[7] Z Liu X-XWan X-GHuang Q Liu andC Li ldquoThe study onspectral reflectance reconstruction based on wideband multi-spectral acquisition systemrdquo Spectroscopy and Spectral Analysisvol 33 no 4 pp 1076ndash1081 2013

[8] H Li J Feng W Yang et al ldquoSpectral-based rendering methodand Its application in multispectral color reproductionrdquo Laserand Optoelectronics Progress vol 47 no 12 Article ID 1223012010

[9] P Urban and R S Berns ldquoParamer mismatch-based spectralgamutmappingrdquo IEEETransactions on Image Processing vol 20no 6 pp 1599ndash1610 2011

[10] B Sun H Liu S Zhou and W Li ldquoA color gamut descriptionalgorithm for liquid crystal displays in CIELAB spacerdquo TheScientific World Journal vol 2014 Article ID 671964 9 pages2014

[11] J Gerhardt and J Y Hardeberg ldquoSpectral color reproductionminimizing spectral and perceptual color differencesrdquo ColorResearch and Application vol 33 no 6 pp 494ndash504 2008

[12] P Urban and R-R Grigat ldquoSpectral-based color separationusing linear regression iterationrdquo Color Research and Applica-tion vol 31 no 3 pp 229ndash238 2006


[13] D-W Kang Y-T Kim Y-H Cho K-H Park W-H Choeand Y-H Ha ldquoColor decompositionmethod for multi-primarydisplay using 3D-LUT in linearized LAB spacerdquo in ColorImaging X Processing Hardcopy and Applications vol 5667 ofProceedings of SPIE pp 354ndash363 San Jose Calif USA January2005

[14] C Lana M Rotea and D E Viassolo ldquoRobust estimationalgorithm for spectralNeugebauermodelsrdquo Journal of ElectronicImaging vol 14 no 1 pp 1ndash10 2005

[15] S Xi andY Zhang ldquoNeugebauer reflectancemodel of frequencymodulation halftone imagerdquo Optik vol 124 no 15 pp 2103ndash2105 2013

[16] B Wang H Xu M Ronnier Luo and J Guo ldquoMaintainingaccuracy of cellular Yule-Nielsen spectral Neugebauer modelsfor different ink cartridges using principal component analysisrdquoJournal of the Optical Society of America A Optics and ImageScience and Vision vol 28 no 7 pp 1429ndash1435 2011

[17] M Hebert and R D Hersch ldquoYule-nielsen based recto-versocolor halftone transmittance prediction modelrdquo Applied Opticsvol 50 no 4 pp 519ndash525 2011

[18] C Sandoval and D Kim Arnold ldquoDeriving Kubelka-Munktheory from radiative transportrdquo Journal of the Optical Societyof America A Optics and Image Science and Vision vol 31 no3 pp 628ndash636 2014

[19] L M Schabbach F Bondioli and M C Fredel ldquoColor predic-tion with simplified Kubelka-Munk model in glazes containingFe2O3-ZrSiO4 coral pink pigmentsrdquoDyes and Pigments vol 99no 3 pp 1029ndash1035 2013

[20] J Seymour and P Noffke ldquoA universal model for halftonereflectancerdquo in Proceedings of the Technical Association of theGraphic Arts (TAGA rsquo12) pp 1ndash40 March 2012

[21] T Bugnon and R D Hersch ldquoCalibrating ink spreading curvesby optimal selection of tiles from printed color imagesrdquo Journalof ELectronic Imaginig vol 21 no 1 Article ID 013024 pp 1ndash152012

[22] B Wang H Xu and L M Ronnier ldquoColor separation criteriafor spectral multi-ink printer characterizationrdquo Chinese OpticsLetters vol 10 no 1 Article ID 013301 2012

[23] J Guo H Xu and L M Ronnier ldquoNovel spectral characteriza-tion method for color printer based on the cellular Neugebauermodelrdquo Chinese Optics Letters vol 8 no 11 pp 1106ndash1109 2010

[24] H Kipphan Handbook of Print Media Springer Berlin Ger-many 2001

[25] J A C Yule and W J Nielsen ldquoThe penetration of light intopaper and its effect on halftone reproductionsrdquo TAGA Proc vol3 pp 65ndash76 1951

[26] M Pearson ldquon value for general conditionsrdquo TAGA Proc vol32 pp 415ndash425 1980

[27] D R Wyble and R S Berns ldquoA critical review of spectralmodels applied to binary color printingrdquo Color Research andApplication vol 25 no 1 pp 4ndash19 2000

[28] J S Arney C D Arney M Katsube and P G Engeldrum ldquoTheimpact of paper optical properties on hard copy image qualityrdquoin Proceeding of the International Conference on Digital PrintingTechnologies pp 166ndash167 1996

[29] Y Shiraiwa and T Mizuno ldquoEquation to predict colors ofhalftone prints considering the optical property of paperrdquoJournal of Imaging Science andTechnology vol 37 no 4 pp 385ndash391 1993

[30] M Mahy and P Delabastita ldquoInversion of the Neugebauerequationsrdquo Color Research and Application vol 21 no 6 pp404ndash411 1996

[31] S Shen and R S Berns ldquoColor-difference formula performancefor several datasets of small color differences based on visualuncertaintyrdquo Color Research and Application vol 36 no 1 pp15ndash26 2011

Submit your manuscripts athttpwwwhindawicom

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SpectroscopyInternational Journal of


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the multispectral imagersquos spectral separation accuracy for119862119872119884119870 printers

2 Modification of Spectral Neugebauer Model

21 The Expression of Spectral Neugebauer Model The spec-tral Neugebauer model is a halftone color predication modelwhich calculates the spectral reflectance values within thevisual wavelength from printersrsquo colorant space In fact it isdeveloped fromMurray-Davies model which is a monochro-matic model [20] When a primary ink is printed on thepaper if the spectral reflectance of the solid and substrate arerepresented as 119877120582119905 and 119877120582119904 respectively and the patchrsquos dotarea is given then its reflectance values 120582 can be predictedby using Murray-Davies model as follows

120582 = 119886119905119877120582119905 + (1 minus 119886119905) 119877120582119904(1)

where120582 is thewavelength of light within 400 nmndash700 nmand119886119905 is the fractional dot area of the printed patch

When the monochrome Murray-Davies model isextended to predict color halftones the spectral Neugebauermodel is generated Take the cyan magenta and yellowcolorants printing for example eight possible colors existin the halftone patch which are white (bare substrate) cyanmagenta yellow red (magenta + yellow) green (cyan +yellow) blue (cyan + magenta) and black (cyan + magenta+ yellow) respectively These eight halftone colors areusually defined as Neugebauer primaries When the spectralreflectance values of the primaries are measured the halftonepatchrsquos overall reflectance can be predicated by using thespectral Neugebauer model as follows [21]

120582 =

8

sum

119894=1

119908119894119877120582119894 (2)

where119877120582119894 is the 119894thNeugebauer primaryrsquos reflectance value atfull colorant coverage and119908119894 is the corresponding weightingfactor calculated by the dot areas of the cyan magenta andyellow inks If 119888 119898 and 119910 represent the cyan magenta andyellow inksrsquo area coverage respectively the eight Neugebauerprimariesrsquo weighting factors can be deduced using Demichelequations and the full expression of (2) is written as follows

120582 = (1 minus 119888) (1 minus 119898) (1 minus 119910) 119877120582119882 + 119888 (1 minus 119898) (1 minus 119910) 119877120582119862

+ (1 minus 119888)119898 (1 minus 119910) 119877120582119872 + (1 minus 119888) (1 minus 119898) 119910119877120582119884

+ (1 minus 119888)119898119910119877120582119877 + 119888 (1 minus 119898) 119910119877120582119866

+ 119888119898 (1 minus 119910) 119877120582119861 + 119888119898119910119877120582119870

(3)

When the 119862119872119884 three-color spectral Neugebauer model isextended to 119862119872119884119870 four colors there are 16 Neugebauerprimaries and the weighting factors are listed in Table 1 (119888119898 119910 and 119896 represent the cyan magenta yellow and blackinkrsquos area coverage)

Table 1 The respective fractional area coverages of the CMYKcombinations

Index Weighting factor Fractional area coverage1 119908119908 (1 minus 119888) lowast (1 minus 119898) lowast (1 minus 119910) lowast (1 minus 119896)

2 119908119888 119888 lowast (1 minus 119898) lowast (1 minus 119910) lowast (1 minus 119896)

3 119908119898 (1 minus 119888) lowast 119898 lowast (1 minus 119910) lowast (1 minus 119896)

4 119908119910 (1 minus 119888) lowast (1 minus 119898) lowast 119910 lowast (1 minus 119896)

5 119908119896 (1 minus 119888) lowast (1 minus 119898) lowast (1 minus 119910) lowast 119896

6 119908119888119898 119888 lowast 119898 lowast (1 minus 119910) lowast (1 minus 119896)

7 119908119888119910 119888 lowast (1 minus 119898) lowast 119910 lowast (1 minus 119896)

8 119908119898119910 (1 minus 119888) lowast 119898 lowast 119910 lowast (1 minus 119896)


10 119908119888119896 119888 lowast (1 minus 119898) lowast (1 minus 119910) lowast 119896

11 119908119898119896 (1 minus 119888) lowast 119898 lowast (1 minus 119910) lowast 119896

12 119908119910119896 (1 minus 119888) lowast (1 minus 119898) lowast 119910 lowast 119896


14 119908119888119910119896 119888 lowast (1 minus 119898) lowast 119910 lowast 119896

15 119908119898119910119896 (1 minus 119888) lowast 119898 lowast 119910 lowast 119896

16 119908119888119898119910119896 119888 lowast 119898 lowast 119910 lowast 119896

In fact the spectral Neugebauer model is also suitable formulti-ink color systems If119901 colorants are included as follows

119888 = [1198881 119888119895 119888119901]

119879

119888119895 isin [0 1] for 119895 isin 1 119901 (4)

there will be 2119901 Neugebauer primaries and their weightingfactors can be determined by the following equation [11 22]

119908119894 =

119901

prod

119895=1

119888119895

if colorant 119895 is part ofthe 119894th Neugebauer primary

(1 minus 119888119895) else(5)

It can be concluded that the primariesrsquo area coverages areexpressed as fractions of the total area and they satisfy theconstraint sum2

119901

119894=1119908119894 = 1

Because there are only eightNeugebauer primaries withinthe spectral Neugebauer model for three-color printers thepredication accuracy is very limited In order to employmore measured halftone patches as Neugebauer primariesthe cellular spectral Neugebauer model is frequently usedin which the colorant space is divided into more cellularsubdomains [23] For example when the individual inkrsquos areacoverages are partitioned into two parts with three points[0 50 and 100] the119862119872119884 colorant space will be dividedinto eight cellular subdomains

22 The Optimization of Spectral Neugebauer Model Thereare actually several reasons which decrease the predica-tion accuracy of the spectral Neugebauer model such asthe dot gain light scattering and penetration and nonlin-earity between the summed and the individual primariesrsquoreflectances For the purpose of reducing the influenceof these factors some optimization approaches should beperformed



119886119905 =

119877120582119898 minus 119877120582119904

119877120582119905 minus 119877120582119904

(6)


119886119905 =

1 minus 10minus119863119903

1 minus 10minus119863119905 (7)





119886eff = (119877120582119898 minus 119877120582119904) (119877120582119905 minus 119877120582119904)119879


minus1

(8)

Ink

Paper




120582 = [119886eff1198771119899

120582119905+ (1 minus 119886eff) 119877

1119899

120582119904]

119899

(9)


120582 = [

8

sum

119894=1

1199081198941198771119899

120582119894]

119899

(10)





N

CMYK(k) ΔR120582 lt 120576

CMYK(k + 1)



119899 = 2 minus 119890minus119860119896

V119901 (11)


120582 = [119886eff(119877120582119904119879119899

120582)1119899+ (1 minus 119886eff) 119877

1119899

120582119904]

119899

(12)








Δ119877120582 =

10038171003817100381710038171003817120582119862119872119884119870 minus 119877120582image

10038171003817100381710038171003817 (13)





min 10038171003817100381710038171003817120582119862119872119884119870 minus 119877120582image

10038171003817100381710038171003817

st 119886eff isin [0 1]


(15)






ΔC ΔM ΔY Δ119864119888119898119910


0

01

02

03

04

05

06

07

08

09

1

400 450 500 550 600 650 700

Refle

ctan

ce

Wavelength (nm)

W

Y

M

R

C

G

B

K




Δ119864119862119872119884 =radicΔ1198622+ Δ119872

2+ Δ1198842 (16)



2

119873

(17)





5 Conclusions



0 10 20 30 40 500

1

2

3

4

5

Testing sample

ΔC



0

1

2

3

4

5

6

7

ΔM


0 10 20 30 40 500

1

2

3

4

5

6

7

8

Testing sample

ΔY


0 10 20 30 40 500

2

4

6

8

10

Testing sample

998779E

CMY



0 10 20 30 40 500

0002

0004

0006

0008

001

0012

0014

Testing sample

RRM

S



400 450 500 550 600 650 7000

01

02

03

04

05

06

07

08

09

Wavelength (nm)

Refle

ctan

ce


400 450 500 550 600 650 7000

01

02

03

04

05

06

07

08

09

Wavelength (nm)

Refle

ctan

ce






Acknowledgments


References










































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



119886119905 =

119877120582119898 minus 119877120582119904

119877120582119905 minus 119877120582119904

(6)


119886119905 =

1 minus 10minus119863119903

1 minus 10minus119863119905 (7)





119886eff = (119877120582119898 minus 119877120582119904) (119877120582119905 minus 119877120582119904)119879


minus1

(8)

Ink

Paper




120582 = [119886eff1198771119899

120582119905+ (1 minus 119886eff) 119877

1119899

120582119904]

119899

(9)


120582 = [

8

sum

119894=1

1199081198941198771119899

120582119894]

119899

(10)





N

CMYK(k) ΔR120582 lt 120576

CMYK(k + 1)



119899 = 2 minus 119890minus119860119896

V119901 (11)


120582 = [119886eff(119877120582119904119879119899

120582)1119899+ (1 minus 119886eff) 119877

1119899

120582119904]

119899

(12)








Δ119877120582 =

10038171003817100381710038171003817120582119862119872119884119870 minus 119877120582image

10038171003817100381710038171003817 (13)





min 10038171003817100381710038171003817120582119862119872119884119870 minus 119877120582image

10038171003817100381710038171003817

st 119886eff isin [0 1]


(15)






ΔC ΔM ΔY Δ119864119888119898119910


0

01

02

03

04

05

06

07

08

09

1

400 450 500 550 600 650 700

Refle

ctan

ce

Wavelength (nm)

W

Y

M

R

C

G

B

K




Δ119864119862119872119884 =radicΔ1198622+ Δ119872

2+ Δ1198842 (16)



2

119873

(17)





5 Conclusions



0 10 20 30 40 500

1

2

3

4

5

Testing sample

ΔC



0

1

2

3

4

5

6

7

ΔM


0 10 20 30 40 500

1

2

3

4

5

6

7

8

Testing sample

ΔY


0 10 20 30 40 500

2

4

6

8

10

Testing sample

998779E

CMY



0 10 20 30 40 500

0002

0004

0006

0008

001

0012

0014

Testing sample

RRM

S



400 450 500 550 600 650 7000

01

02

03

04

05

06

07

08

09

Wavelength (nm)

Refle

ctan

ce


400 450 500 550 600 650 7000

01

02

03

04

05

06

07

08

09

Wavelength (nm)

Refle

ctan

ce






Acknowledgments


References










































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




N

CMYK(k) ΔR120582 lt 120576

CMYK(k + 1)



119899 = 2 minus 119890minus119860119896

V119901 (11)


120582 = [119886eff(119877120582119904119879119899

120582)1119899+ (1 minus 119886eff) 119877

1119899

120582119904]

119899

(12)








Δ119877120582 =

10038171003817100381710038171003817120582119862119872119884119870 minus 119877120582image

10038171003817100381710038171003817 (13)





min 10038171003817100381710038171003817120582119862119872119884119870 minus 119877120582image

10038171003817100381710038171003817

st 119886eff isin [0 1]


(15)






ΔC ΔM ΔY Δ119864119888119898119910


0

01

02

03

04

05

06

07

08

09

1

400 450 500 550 600 650 700

Refle

ctan

ce

Wavelength (nm)

W

Y

M

R

C

G

B

K




Δ119864119862119872119884 =radicΔ1198622+ Δ119872

2+ Δ1198842 (16)



2

119873

(17)





5 Conclusions



0 10 20 30 40 500

1

2

3

4

5

Testing sample

ΔC



0

1

2

3

4

5

6

7

ΔM


0 10 20 30 40 500

1

2

3

4

5

6

7

8

Testing sample

ΔY


0 10 20 30 40 500

2

4

6

8

10

Testing sample

998779E

CMY



0 10 20 30 40 500

0002

0004

0006

0008

001

0012

0014

Testing sample

RRM

S



400 450 500 550 600 650 7000

01

02

03

04

05

06

07

08

09

Wavelength (nm)

Refle

ctan

ce


400 450 500 550 600 650 7000

01

02

03

04

05

06

07

08

09

Wavelength (nm)

Refle

ctan

ce






Acknowledgments


References










































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



ΔC ΔM ΔY Δ119864119888119898119910


0

01

02

03

04

05

06

07

08

09

1

400 450 500 550 600 650 700

Refle

ctan

ce

Wavelength (nm)

W

Y

M

R

C

G

B

K




Δ119864119862119872119884 =radicΔ1198622+ Δ119872

2+ Δ1198842 (16)



2

119873

(17)





5 Conclusions



0 10 20 30 40 500

1

2

3

4

5

Testing sample

ΔC



0

1

2

3

4

5

6

7

ΔM


0 10 20 30 40 500

1

2

3

4

5

6

7

8

Testing sample

ΔY


0 10 20 30 40 500

2

4

6

8

10

Testing sample

998779E

CMY



0 10 20 30 40 500

0002

0004

0006

0008

001

0012

0014

Testing sample

RRM

S



400 450 500 550 600 650 7000

01

02

03

04

05

06

07

08

09

Wavelength (nm)

Refle

ctan

ce


400 450 500 550 600 650 7000

01

02

03

04

05

06

07

08

09

Wavelength (nm)

Refle

ctan

ce






Acknowledgments


References










































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0 10 20 30 40 500

1

2

3

4

5

Testing sample

ΔC



0

1

2

3

4

5

6

7

ΔM


0 10 20 30 40 500

1

2

3

4

5

6

7

8

Testing sample

ΔY


0 10 20 30 40 500

2

4

6

8

10

Testing sample

998779E

CMY



0 10 20 30 40 500

0002

0004

0006

0008

001

0012

0014

Testing sample

RRM

S



400 450 500 550 600 650 7000

01

02

03

04

05

06

07

08

09

Wavelength (nm)

Refle

ctan

ce


400 450 500 550 600 650 7000

01

02

03

04

05

06

07

08

09

Wavelength (nm)

Refle

ctan

ce






Acknowledgments


References










































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


400 450 500 550 600 650 7000

01

02

03

04

05

06

07

08

09

Wavelength (nm)

Refle

ctan

ce


400 450 500 550 600 650 7000

01

02

03

04

05

06

07

08

09

Wavelength (nm)

Refle

ctan

ce






Acknowledgments


References










































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of






























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

research article spectral separation for multispectral...

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