Color gmut reduction techniques for printing with custom inks Sylvin M. CHOSSON *, Roger D. HERSCH * Ecole Polytechnique Fédérle de usnne (EPF) STRCT Printing with custom inks is of interest oth for rtistic purposes nd for printing security documents such s nknotes. However, in order to crete designs with only few custom inks, generl purpose high-qulity gmut reduction technique is needed. Most existing gmut mpping techniques mp n input gmut such s the gmut of CRT disply into the gmut of n output device such s CMYK printer. In the present contriution, we re interested in printing with up to three custom inks, which in the generl cse define rther nrrow color gmut compred with the gmut of stndrd CMYK printers. The proposed color gmut reduction techniques should work for ny comintion of custom inks nd hve smooth nd predictle ehvior. When the lck ink is ville, the lightness levels present in the originl imge remin nerly identicl. Originl colors with hues outside the trget gmut re projected onto the gry xis or onto desturted colors. Originl colors with hues inside the trget gmut hues re rendered s fithful s possile. When the lck ink is not ville, we mp the gry xis G into colored curve connecting in the 3D color spce the pper white nd the drkest ville color formed y the superposition of the 3 inks. The mpped gry xis curve is given y the Neugeuer equtions when enforcing equl mounts of custom inks. fter lightness mpping, hue nd sturtion mppings re crried out. When the trget gmut does not incorporte the gry xis, we divide it into two volumes, one on the desturted side of the mpped gry xis curve nd the other on the sturted side of the curve. Colors whose hues re not prt of the trget color gmut re mpped to colors locted on the desturted side of the curve. Colors within the set of printle hues remin within the trget color gmut nd retin s much s possile their originl hue nd sturtion. Keywords: gmut reduction, rtistic imging, color printing, custom inks. 1. INTRODUCTION Printing with custom inks 1,2,3 is widespred technique for protecting documents ginst nti-counterfeiting ttempts. In nknotes for exmple, designs re often printed with inks of which t lest one ink color vries long the length of the nknote, i.e. the ink color is liner interpoltion etween two given custom inks. In most nknote designs, the imge gmut is severely reduced to the gmut defined y few custom inks. In the context of nknote nd rtistic design, it would e extremely vlule to hve flexile tool le to crry out gmut reduction in order to mp color input imge to n imge with colors locted within the reduced gmut offered y the set of one, two or three custom inks, generlly without the lck ink. The prolem of color gmut reduction distinguishes itself considerly from the well-known prolem of gmut mpping 4,5. This is especilly the cse when the gry xis is not prt of the reduced trget gmut. In ddition, we ssume tht the trget gmut does not extend eyond the oundries of the originl gmut, for exmple the gmut of CRT monitor. There re however similrities etween gmut reduction nd gmut mpping. In oth cses, it is useful to work in color spce where the lightness is orthogonl to the hue-sturtion sections. This llows to first pply mpping on lightness vlues nd then to mp the hues nd sturtions. * Correspondence: E-mil: sylvin.chosson@epfl.ch; rd.hersch@epfl.ch; http://diwww.epfl.ch/w3lsp/ Proceedings of SPIE, Vol. 4663, 11-1, Sn Jose, US, Jn. 2. Color Imging: Device-Independent Color, Color Hrdcopy, nd Grphic rts VII.
et us formulte the gmut reduction prolem. Given reduced gmut given y few custom inks, crete mpping etween n originl "full" color gmut, e.g. the color gmut of CRT monitor nd the reduced gmut defined y the given set of custom inks. The proposed mpping should preserve color continuity nd whenever possile smoothness, i.e. continuous color wedge locted in the originl color spce should e mpped into continuous color wedge locted in the reduced trget gmut. In ddition, mong different possile mppings, the mppings preserving t lest to certin extent the originl colors will e preferred. For exmple, sturted colors locted in prts of the color spce common to oth the input nd trget gmuts should remin nerly identicl nd hues of originl colors should e preserved s much s possile. Methods for gmut mpping hve een proposed for the cses of one ink nd lck 6 nd for two custom inks 7 (duotone). oth methods try to mintin overll reltionships etween colors y llowing strong hue nd sturtion shifts. Our pproch consists in mpping colors outside the ville trget gmut hues s gry or s desturted pseudo-gry color nd colors inside the trget gmut hues s close s possile to the originl colors. In the present contriution, we re interested in exploring vrious gmut reduction techniques. For the ske of simplicity, we consider tht the set of ville sic colors is determined y the set of custom inks C 1,C 2,C 3 (nd C k if lck is ville) s well y the comintions of two inks C ij nd3inksc ijk. For the ske of the present nlysis, we use the Neugeuer eqution for computing the color seprtions nd the oundries of the trget gmut 8. The CIE- spce is used for pplying the proposed gmut reduction lgorithms. 1.1. essons lerned from the reserch on gmut mpping lthough gmut reduction differs significntly from gmut mpping, let us see if methods used for gmut mpping cn lso e used for gmut reduction. In respect to the clipping 9 of out of gmut colors onto the trget gmut oundry, the work y Ktoh & Itoh 1 suggests tht color differences long the CIE- lightness xis ( *) hve visul impct twice s lrge s color differences long the sturtion ( C*) nd hue ( H*) xes. This my suggest tht for gmut reduction, the originl lightness rnge should e mpped in non-liner mnner onto the trget lightness rnge, thus offering the cpility of keeping some of the originl lightness vlues unchnged. However, when the trget gmut hs reltively smll lightness rnge, one my prefer liner mpping of the originl lightness rnge onto the trget lightness rnge. In respect to gmut compression lgorithms, Morovic & uo 5 hve shown tht gmut mpping lgorithms which project out of gmut colors towrds prticulr point inside the gmut (e.g. = in CIE-) 11 re visully superior to lgorithms which seprtely mp the originl gmut lightness xis into the trget gmut lightness xis nd then the sturtion of originl colors into the sturtion of the trget gmut 12,13. However, this superiority my e due to the prticulr shpes of originl (CRT: red, green, lue locted fr from the lightness xis) nd trget (printer: cyn, mgent nd yellow locted fr from the lightness xis) gmut oundries. For this comintion of originl nd trget gmut oundries, out of gmut colors projected rdilly t constnt lightness levels tend to ecome desturted. However, in the cse of custom inks, the trget gmut oundry depends on the selected set of inks. ut since pper white is prt of the trget gmut, the trget gmut lightness rnge my e significntly lrger thn its rnge of sturtion nd hue vlues. This mens tht trget gmuts defined y custom inks tend to e elongted, from pper white to the drkest color formed y the superposition of the ville inks. Therefore, for gmut reduction, it mkes sense to first mp the originl lightness xis onto the trget lightness xis, nd then mp originl hues nd sturtions within the mpped constnt lightness sections. Regrding the mpping of originl sturtion to the trget sturtion, s proposed y Stone & Wllce 14, we crry out this mpping y non-liner compression (lso clled soft compression 15 ), i.e. mpping which tends to preserve some of the originl sturtion vlues.
1.2. Color seprtion nd color gmut The humn visul system perceives three ttriutes of color: lightness, sturtion nd hue. Gmut mpping is usully performed in color spce tht represents these ttriutes. To otin the color gmut description of device, there re two ctegories of method 16,17,18. lrge set of smples spnning the printle rnge is mesured nd empiricl methods re used to estimte the gmut oundries. The second wy to define the color gmut is sed on n nlyticl model of the printer tht reltes color to the mounts of colornts. In the present rticle, the gmut color of severl custom inks cn e theoreticlly represented with two nlyticl models corresponding to two printing processes. The first model is sed on the MultiColorDithering hlftoning method 2,3 where the inks nd their superpositions re plced side y side. In tht cse, the reduced gmut oundry in CIE-XYZ is mde of plnr tringulr fces with vertices representing the inks nd their superpositions. The second model is sed on the Neugeuer eqution 8,wherethe color gmut oundry comprises curved surfces. The Neugeuer eqution trnsforms coverges of inks nd their superpositions onto CIE-XYZ vlues. 2. GMUT REDUCTION FOR CUSTOM INKS INCUDING THE CK INK In this chpter, we ssume tht the sets of inks includes the lck ink. If the pper is white, the originl gry xis is nerly identicl to the gry xis within the reduced trget color gmut. Trget lightness levels re very close to originl lightness levels. 2.1. One custom ink (C 1 ) nd lck et us ssume tht only one single color C 1 is selected y the designer in order to give to his design monochromtic spect. The proposed gmut mpping method should mp the originl colors onto the gmut surfce White-C 1 -lck. This two-dimensionl gmut mpping modifies hue nd sturtion. The only printle hue is the hue of color C 1.ll input colors re projected onto the tringulr surfce formed with vertices corresponding to White, lck nd C 1 (Fig. 1). Figure 1 shows on the constnt lightness slice =72 (CIE-) the projection of originl colors onto the trget gmut (continuous old line). White (W) lck (K) - Reduced printle color gmut section full color gmut section C 1-1 C 1 () 3D color gmut trget in CIE-. () Section =72, mpping colors into the printle re. Figure 1. Reduced color gmut with ink C 1 nd lck in CIE-. ll the color points, which re not in the hlf-spce contining C 1 (re ) re mpped onto the gry xis y keeping their reltive lightness vlues constnt. The points locted in the other hlf-spce (re ) re orthogonlly projected onto the surfce, possily clipped or compressed in cse their projection does not intersect surfce section W-C 1 -K. Colors with hues fr from the hue of color C 1 will e therefore more desturted, i.e. closer to gry thn colors with hues close to the hue of C 1. 2.2. Two custom inks (C 1,C 2 ) nd lck The designer my wnt to reduce the hue rnge of his design y using only two inks C 1 nd C 2, keeping some of the originl colors unchnged nd mpping other colors onto the limited hue rnge. The originl gry xis remins printle. The only printle hues re locted etween the hue of ink C 1 nd of ink C 2. s shown in Fig. 2, re is the re where the hues re kept s close s possile to the originl. Originl colors with hue locted outside re re mpped onto res t the order of printle re or onto the gry xis. Printle order res re locted etween hue hlf plnes C 1 nd H1, nd C 2 nd H2. H1 nd H2 re hues selected y the designer t the order of printle hues.
re C includes the originl points locted etween the verticl hue hlfplne H perpendiculr to the hue plne contining C 1,ndtheverticl hue hlf-plne HC perpendiculr to the hue plne contining C 2. The originl color points in re C re mpped onto the gry xis. re is defined etween the hlf-plne of hue C 1 nd re C. ikewise, re D is defined etween the hlf plne of hue C 2 nd re C. The originl points in re nd etween the hue hlf plnes of C 1 ndh1remppedlinerly etween the hue hlf plnes of C 1 nd H1 crrying out n orthogonl C 2 projection towrd hlf plne H1. Colors of res D nd etween the hue hlfplnes C 2 nd H2 re linerly mpped into re C 2 H2. Their sturtion is then reduced to provide spce for reproducing originl sturted colors mpped into n re of C 2 H2 situted eyond the trget gmut oundries. s in the cse of one custom ink nd lck, colors in re nd D with hues fr from the trget gmut will e more desturted thn colors close to the trget gmut hues. Figures 13,,c show color reproduction exmples y color gmut reduction with two custom inks nd lck. The originl cyn dress cn not e printed with the chosen sets of custom inks. For the set of inks (), cyn is projected onto the hue C 2. The cyn dress ppers prtly s desturted green, prtly s gry. The lue ckground nd yellow re mpped onto the gry xis. For the set of inks (c), oth the lue ckground nd the cyn dress re mpped onto the gry xis. DuetotheinkC 2, the yellow dress nd the fces re closer to the originl thn when printed with the set of inks (). 2.3. Three custom inks (C 1,C 2,C 3 ) nd lck Severl types of color spce coverges my e otined y three inks nd lck. Three inks nd lck my cover ll hues (Fig. 3) if the inks re well distriuted round the gry xis. In the cse of three inks nd lck covering only prt of the hues, we my pply mpping similr to the one descried for two custom inks nd lck. For set of three inks covering ll the possile hues, the gmut mpping my e crried out ccording to one of the well known gmut mpping methods descried in the literture 5. Reduced printle color gmut section CIE- section White - 1 C 1 lck () 3D color gmut trget in color spce CIE-. Figure 2. Reduced color gmut with two inks (C1, C2) nd lck. C 3 C 23 Figures 13,d,e show color reproduction exmples y color gmut reduction with three custom inks nd the lck ink covering only prt of ll hues. For the set of inks (d) (set of inks () plus C 3 ), lue nd cyn cn not e reproduced nd re projected onto the hue section C 2. Thnks to C 3, the yellow dress nd the fces re closer to the originl thn when printed with the set of inks (). For the set of inks (e) (set of inks (c) plus C 3 ), the cyn dress, the lue ckground nd the green color re projected onto the hue section C 3. White C 2 lck C 12 re C12 H C HC re C1 re D H1 re H2 C2 () Section =72 (CIE-), mpping colors into the printle re. Reduced printle color gmut section CIE- section - C 1 1 () Trget color gmut (CIE-). () Mpping of colors into the printle re. Figure 3. Reduced color gmut with three inks (C1, C2, C3) nd lck.
3. GMUT REDUCTION FOR THREE CUSTOM INKS WITHOUT THE CK INK For printing with set of custom inks, which does not includes the lck ink, new pproch needs to e developed. The full color gmut needs to e mpped into reduced color gmut, which does not include the gry xis (Fig. 4). et us distinguish two cses. In the first cse, the reduced trget color gmut does not intersect the gry xis (Fig. 4). In the second cse, the trget gmut contins prt of the originl gry xis (Fig. 4), i.e., t some lightness levels (point G min ), the gry xis is inside the gmut nd t other levels, the gry xis is outside the gmut. 3.1. Mpping the gry xis Since the gry xis cnnot e printed with the chosen set of inks, it needs to e mpped onto the trget gmut s continuous smooth curve ensuring tht continuous originl gry vlues re mpped into continuous vlues of lightness, sturtion nd hue. White White 8 1 1 C 3 C 2 () () C 12 C 123 G min C 123 lck () Trget color gmut tht does not include the gry xis. The desired curve representing the gry xis in the trget gmut connects the pper white to the point with the lowest lightness C 123. smooth curve which y definition remins within the trget gmut is the curve representing equl mounts of inks C 1,C 2 nd C 3. ccording to Neugeuer, for mount XYZ vlues long this curve: of inks C 1,C 2 nd C 3, we otin the CIE- G () = (1-) 3.C pper + (1-) 2.(C 1 +C 2 +C 3 )+ 2 (1-). (C 12 +C 13 +C 23 )+ 3.C 123, where C pper,c 1,C 2,C 3,C 12,C 13,C 23,C 123 re the CIE-XYZ tristimulus vlues of the pper, the inks nd their superpositions. The equl mounts of inks curve G () is not necessrily included in constnt hue plne. The hue of G my progressively chnge ccording to the lightness level (Fig. 5). lck () Trget color gmut includes the gry xis. Figure 4. Two reduced color gmuts sliced following the plne including the gry xis nd C123. C23 C2 C3 C123 C13 1 CIE- originl gmut section Trget gmut section Mpped gry xis G C12 projectedontosection=7 - C1 Figure 5. Projection of the equl mounts of inks curve G () onto section =7 of the CIE- color spce.
3.2. ightness rescling The proposed color gmut reduction method should keep s much s possile the originl colors. Rescling in terms of lightness my e sed on liner mpping function (Fig. 6). However, rescling ccording to non-liner mpping (lso clled soft compression 15 ) my e preferle (Fig. 6). With liner rescling, ll the points move from their initil position. With smooth non-liner rescling, we keep s it is lrge prt of the originl lightness rnge. For non-liner rescling, lightness level 1 is set, ove which the lightness of colors remins unchnged. Points with lightness lower thn 1 re rescled ccording to curve whose tngent t 1 hs the sme orienttion s the liner portion of the mpping. This curve my e qudrtic ézier curve. Color reproductions of the originl gry xis mpped into 4 different trget color gmuts with non-liner nd liner lightness rescling re shown in Fig. 14. (CIE-) 1 output (CIE-) 1 output.6.6 1 C123 =.2 C123 =.2 rescled originl.2.6 1 rescled.2.6 1 input input () originl () Figure 6. iner () nd non-liner () mpping of lightness in hue section. 3.3. Mpping the hues fter mpping of the gry xis nd lightness rescling, hue nd sturtion need to e mpped. We keep s much s possile the originl hues in the printle trget color gmut nd distriute colors whose hue cnnot e printed on the desturted side of the mpped gry xis G (Fig. 7). Originl Trget Section of full CIE- color gmut for =72. () The trget color gmut includes ll printle hues. Printle hues Section of the reduced color gmut trget for =72. Rendered gry vlue =72 in trget gmut. () The trget color gmut does not include ll printle hues. Figure 7. Color gmut reduction with two types of reduced trget gmuts. In order to keep the continuity etween hues, mpped hue lines on given lightness section hve to gther to the corresponding point of the mpped gry xis G. We define two res for the mpping (Fig. 7). re of the originl color gmut is mpped onto the re of the trget color gmut. In this re, we keep s much s possile the originl hues
nd sturtions. When the trget color gmut incorportes ll printle hues, color points in re my e printed with their originl hue nd possily sturtion close to the originl sturtion s shown in Fig. 7. However when the trget gmut does not contin ll hues t ll lightness levels, some hues cnnot e reproduced (Fig. 7). In order to prtition the trget gmut into res nd, we drw line through G perpendiculr to GG, yielding intersection points nd with the reduced trget gmut (Fig. 8). To ensure the continuity of colors mpped into the nd spces, ll lines linking points in re nd G should intersect segment [G ] or [G ]. For exmple, in Fig. 8, line GC does not intersect segment [G ]. In tht cse, segment [G ] must e replced y [CG ] in order to form the finl oundry of re. The curves (e.g. curve G E) used for the mpping of hue lines from re to re re constructed ccording to Fig. 8. The control points D of qudrtic ézier splines re locted on segments [G ] or [G C]. Hue C C Hue E CIE- originl color spce section Reduced color gmut Originl hue line Mpped hue line G D Hue order of the originl hue line order of the mpped hue line Figure 8. Mpping originl hue lines into curves in the trget gmut. For mpping the most sturted originl colors of ech hue, i.e. the originl color gmut oundry (Fig. 9), we define two projection methods. The first method (Fig. 9) mps ech point of the full color gmut oundry into the nerest trget gmut oundry point (P n ) in term of E (CIE-). The second method (Fig. 9c) mps ll points of the originl color gmut oundry whose hues re printle (externl oundry of ), to the most sturted loctions of the sme hue on the reduced gmut oundry. Other points re distriuted on the externl oundry of (P ) ccording to their originl ngulr distriution within re reltive to G onto similr ngulr distriution within re reltive to G (Fig. 9c). This second mpping method enles ech originl color to e distinguishle when printed with the chosen set of custom inks. However, the first mpping method renders colors closer to the originl colors. - G - - P n - P () () (c) Figure 9. Mpping of the originl color gmut oundry points () onto the reduced trget gmut ccording to () the closest point nd ccording to (c) their ngulr distriution. Figure 1 shows the mpping of re of the originl color spce onto the trget gmut. y using curves (Fig. 1) insted of stright lines (Figs. 1,c), originl colors t high sturtion re rendered more ccurtely. The mpping of re of the originl gmut into re of the reduced trget gmut my e crried out y three different methods. We my mp the originl hue line (1) long ézier curve linking G nd P n (nerest point on trget gmut)
with P (point on trget gmut ccording to ngulr distriution) s control point (Fig. 1), (2) long stright line linking G nd P n (Fig. 1), or (3) long line linking G nd the point P (Fig. 1c). ccording to the second method, severl originl hue line re possily mpped into single hue line. Mpping hue lines long curves (first method) llows to distinguish etween neighoring hues. P n P n P P - -25-25 25 25 () () (c) Figure 1. Mpping of hue lines () with curves in oth res nd, () with lines linking the nerest trget oundry color nd, nd (c) with lines distriuted ccording to n ngulr distriution. 3.4. Sturtion mpping fter estlishing the mpping of hue lines etween originl nd reduced trget gmut, let us propose oth liner nd non-liner sturtion mpping method. 3.4.1 iner sturtion mpping The definition of re ensures tht for ech hue, point exists on the reduced trget gmut oundry. However, re is defined differently, depending if liner or non-liner mpping is chosen. For liner mpping, re is defined s explined in Sec. 3.3 (Fig. 8). Sturtion vlues re mpped long successive positions of the curve representing the mpped hue line. 3.4.2 Non-liner sturtion mpping For pplying non-liner sturtion mpping, re must ensure tht ech of its color points hs lrger sturtion thn the sturtion of G (Fig. 12). The sturtion of G corresponds to MinSt (Fig. 11) nd the sturtion of the most sturted mpped point E corresponds to MxSt. With non-liner sturtion mpping, we would like to keep the rendered points s close s possile to the originl points. We define three different sturtion rescling segments. t high sturtion, non-liner mpping etween input sturtion nd output sturtion preserves s much s possile high sturtion levels (Fig. 11). t intermedite sturtion levels, liner sturtion mpping is pplied. ow sturtions re compressed into limited rnge y non-liner mpping. Non-liner sturtion mpping cn e pplied to colors in re (Fig. 12). In re, it is not possile to remin close to the originl sturtion vlues. However, in order to ensure continuity t the oundries of res nd, we lso pply non-liner sturtion mpping in re (Fig. 12). This tends to mp sturted colors locted outside the trget gmut hues to colors closer to gry. Stoutput 1 MxSt evel2 evel1 MinSt Stinput.2.6 1 Figure 11. Sturtion rescling. G () D E () Non-liner sturtion mpping Figure 12. Exmple of trget color gmut division for non-liner sturtion mpping.
ccording to the sturtion mpping shown in Fig. 11, evel 2 nd evel 1 cn e defined s percentges of the full sturtion output rnge. The non-liner high sturtion rnge defined y evel 2 my e useful prmeter for incresing or decresing the overll sturtion of gmut reduced imges. Color reproductions of hue line ccording to liner nd non-liner sturtion mpping re shown in Fig. 15. With non-liner sturtion mpping, the rnge where originl sturtions nd mpped sturtions remin very close cn e controlled y the designer. 3.5 Imge reproduction exmple Figures 16,,c show the sme imge rendered with different sets of 3 custom inks, without lck. The drkest printle color with the first set of inks, C 123, is not lck ut drk rown. The strongly reduced trget gmut does not cover even smll prt of the gry xis. s shown on the top-right wedge, most green nd lue hues cn not e reproduced. Fig. 16 shows the est compromise otined with the presented mpping method. Fces, white, yellow nd rown colors re rendered close to the originl colors. ll other colors re rendered in rown tones which represent the gry xis mpped into the trget gmut. Fig. 16 shows the imge mpped into lrger trget gmut. ll the hues re printle. Fces, yellow nd rown ojects re rendered close to the originl colors wheres other colors tend to e desturted. Originl colors close to lck re rendered with colors close to C 123 (e.g. drk ckground). The third gmut reduced imge (Fig. 16c) is rendered with set of inks whose colors re close to mgent, cyn nd yellow. ll rendered colors re close to the originl colors. 4. CONCUSION ND PERSPECTIVES This pper proposes methods for mpping n originl full color gmut into reduced trget color gmut. Gmut reduction differs from gmut mpping minly y the fct tht the trget color gmut my not include the gry xis. Vrious methods for color gmut reduction hve een proposed. The methods we introduce depend on the choice of the custom inks nd on the presence or sence of the lck ink. In the cse of 3 inks without lck, the originl gry xis is mpped long curve defined y equl mounts of the chosen inks. When the trget gmut does not incorporte the gry xis, we divide it into two volumes, one on the desturted side of the mpped gry xis curve nd the other on the sturted side of the curve. Colors whose hues re not prt of the trget color gmut re mpped to colors locted on the desturted side of the curve. Colors within the set of printle hues remin within the trget color gmut nd retin s much s possile their originl hue nd sturtion. On constnt lightness slices, we mp the originl hue lines locted on the sturted side of the curve long curves connecting the most sturted colors with the mpped gry point. The mpping of originl hue lines onto these curviliner hue trjectories llows to retin s much s possile their originl hues. non-liner sturtion mpping lso llows to retin s much s possile the originl sturtion vlues. Once integrted into n interctive softwre pckge, gmut reduction my ecome vlule tool for creting designs to e printed with limited set of custom inks. In ddition, it my e very useful for designing nknotes where the color of custom ink vries ccording to its horizontl or verticl position. REFERENCES 1. E. J. STONITZ, V.OSTROMOUKHOV ndd.h.sesin, Reproducing Color Imges Using Custom Inks, Proc. of SIGGRPH 98, in Computer Grphics Proc., nnul Conference Series, 267-274, July 1998. 2. V. OSTROMOUKHOV, R.D.HERSCH, Multi-Color nd rtistic Dithering, Proc. of SIGGRPH 99, CM Computer
Grphics, nnul Conference Series, 425-432, 1999. 3. S. M. CHOSSON, R. D. HERSCH, Visully-sed color spce tetrhedriztions for printing with custom inks, in Color Imging: Device-Independent Color, Color Hrdcopy, nd Grphic rts VI, SPIE Vol. 43, 81-92, Jn. 1. 4 http://www.colour.org/tc8-3/ 5 J.MOROVIC,M.R.UO, Developing lgorithms for universl color gmut mpping, in. W. MCDOND, M.R. UO, Color Imging: Vision nd Technology, John Wiley & Sons, 253-282, 1999. 6. S. J. HRRINGTON, Principles for mpping from full color to highlight color, Xerox Wester Reserch Center, IS&T's Eighth Interntionl Congress on dvnces in Non-Impct Printing Technologies, 459-462, Oct. 1992. 7. J.. POWER,.S.WEST, E.J.STONITZ, Reproducing Color Imges s Duotones, Proc. of SIGGRPH 96, in Computer Grphics Proc., nnul Conference Series, 237-248, ug. 1996. 8. M. MHY, Clcultion of color gmuts sed on the Neugeuer Model, Color Reserch nd ppliction,vol.22, No. 6, 365-374, http://www.interscience.wiley.com/, Dec. 1997. 9. E. D. MONTG,M.D.FIRCHID, Gmut Mpping: Evlution of Chrom Clipping Techniques for Three Destintion Gmuts, The Sixth Color Imging Conference: Color Science, Systems, nd pplictions, 57-61, Nov. 1998. 1. N. KTOH, M.ITO, Gmut mpping for computer generted imges, IS&T/SID, The Fourth Color Imging Conference, 126-129, 1996. 11. P. IHNEN Colour reproduction theory sed on the principles of colour science, IRIGI Conf. Proc. PST, Vol. 19, 1-36, 1987. 12.. J. JOHNSON (1979) Perceptul Requirements of Digitl Picture Processing, Pper presented t IRIGI symposium nd printed in prt in Printing World, Fe. 198. see http://www.colour.org/tc8-3/survey/s_79j.html 13.. MCDOND, Gmut mpping in Perceptul Colour Spce, IS&T/SID, First Color Imging Conference: Trnsforms nd Trnsportility of Color, 193-196, 1993. 14. M. C. STONE,W.E.WCE, Gmut mpping computer generted imgery, Grphics Interfce'91, 32-39, 1991. 15. T. HOSHINO, R.S.ERNS, Color mpping techniques for color hrd copy imges, in Device Independent Color Imging nd Imging Systems Integrtion, Proc. of SPIE Vol. 199, 152-164, 1993. 16. N. KTOH, M.ITO, Three-dimensionl gmut mpping using vrious color difference formule nd color spces, J. of Electronic Imging, Vol. 8, No. 4, 365-379, Oct. 1999. 17. P. G. HERZOG, M.MÜER, Gmut Mpping using n nlyticl Color Gmut Representtion, in Color Imging: Device-Independent Color, Color Hrdcopy, nd Grphic rts II, Proc. of SPIE Vol. 318, 117-128, 1997. 18. J. MOROVIC,M.R.UO, Clculting Medium nd Imge Gmut oundries for Gmut Mpping, Color Reserch nd ppliction,vol.25, No. 6, 394-41, http://www.interscience.wiley.com/, Dec.. PPENDIX Originl nd gmut reduced imges re given t: http://diwww.epfl.ch/w3lsp/pulictions/colour/ dditionl informtion such s the CIE-XYZ vlues of the custom inks nd their comintions is lso given in order to llow other reserchers to compre their gmut reduction lgorithms with our methods.
() (d) C1 C2 K C3 C1 C2 K (e) (c) C1 C2 K C3 C1 C2 K () () (d) (c) (e) n (f) l (g) n l (h) n l (i) Figure 13. Originl imge () mpped into 4 different trget color gmuts: two custom Figure 14. Gry xis (f) inks nd lck (),(c); three custom inks nd lck (d),(e). mpped into 3 different trget gmuts ccording to (n) non-liner nd (l) liner lightness rescling. () (g) () Figure 15. Originl hue line (within the disks) otined y () liner sturtion mpping, () non-liner sturtion mpping. (i) (h) C1 C3 C123 C1 C2 C3 C123 Cc1 Cc2 C2 () () (c) Figure 16. Originl imge (outside the disks) mpped onto 3 different reduced trget gmuts (inside the disks). Cc3 Cc123