Simplified Ink Spreading Equations for CMYK Halftone Prints

Transcription

1 Simpliied Ink Spreading Equations or CMYK Haltone Prints Thomas Bugnon, Mathieu Brichon and Roger David Hersch École Polytechnique Fédérale de Lausanne (EPFL, School o Computer and Communication Sciences, Lausanne 1015, Switzerland ABSTRACT The Yule-Nielsen modiied spectral Neugebauer model enables predicting relectance spectra rom surace coverages. In order to provide high prediction accuracy, this model is enhanced with an ink spreading model accounting or physical dot gain. Traditionally, physical dot gain, also called mechanical dot gain, is modeled by one ink spreading curve per ink. An ink spreading curve represents the mapping between nominal to eective dot surace coverages when an ink haltone wedge is printed. In previous publications, we have shown that using one ink spreading curve per ink is not suicient to accurately model physical dot gain, and that the physical dot gain o a speciic ink is modiied by the presence o other inks. We thereore proposed an ink spreading model taking all the ink superposition conditions into account. We now show that not all superposition conditions are useul and necessary when working with cyan, magenta, yellow, and black inks. We thereore study the inluence o ink spreading in dierent superposition conditions on the accuracy o the spectral prediction model. Finally, we propose new, simpliied ink spreading equations that better suit CMYK prints and are more resilient to noise. Keywords: color reproduction, ink spreading model, spectral prediction model, Yule-Nielsen modiied Spectral Neugebauer, haltones, ink spreading curves, dot gain, ink superposition conditions, noise resilience 1. INTRODUCTION The goal o a color reproduction system is to be able to reproduce input colors as accurately as possible. This is not a trivial task since the human visual system is very sensitive to small color dierences. In printing systems, there are many actors inluencing the range o printable colors: the inks, the substrate (paper, plastic, glass, etc., the illumination conditions, and the haltones. Spectral relection prediction models are helpul in studying the inluence o these actors. One o the undamental aspects a spectral relection prediction model has to consider is how the inks spread on the paper, a phenomenon also reerred to as physical or mechanical dot gain. With an ink spreading model accounting or physical dot gain, a spectral relection prediction model is able to accurately predict relectance spectra in unction o ink surace coverages or three or our inks 1, 2, 3. In order to be eective, such an ink spreading model must take into account not only the interaction between an ink haltone and paper, but also the interaction between an ink haltone and superposed inks. One proposed solution is to use multiple ink spreading curves, also called tone reproduction curves, to characterize the physical dot gain o the ink haltones on paper in all solid ink superposition conditions. For CMYK haltone prints, such an approach requires the characterization o 32 ink spreading curves. The aim o this paper is to evaluate the relevance o each ink spreading curve and subsequently simpliy the ink spreading model in order to use ewer curves. The relevance o an ink spreading curve depends on its impact on the spectral prediction model accuracy as well as how it is aected by noise. Section 2 introduces the Yule-Nielsen modiied Spectral Neugebauer model that is used as spectral relection prediction model. The ink spreading model and the characterization o the ink spreading curves are detailed in Section 3. Section 4 evaluates the inluence o each ink spreading curve on the accuracy o the prediction model and Section 5 the inluence o measurement noise on the characterization o the ink spreading curves. In Section 6, a new set o equations that reduces the number o component equations o the ink spreading model is proposed and evaluated against the existing set o equations. We inally draw the conclusions in Section 7.

2 2. SPECTRAL PREDICTION MODELS AND RELATED APPROACHES Many dierent phenomena inluence the relection spectrum o a color haltone patch printed on a diusely relecting substrate (e.g. paper. These phenomena comprise the surace (Fresnel relection at the interace between the air and the paper, light scattering and relection within the substrate (i.e. the paper bulk, and the internal (Fresnel relections at the interace between the paper and the air. The lateral scattering o light within the paper substrate and the internal relections at the interace between the paper and the air are responsible or what is generally called optical dot gain, also known as the Yule-Nielsen eect. In addition, due to the printing process, deposited ink surace coverages are generally larger than nominal coverages, yielding a physical dot gain also reerred to as mechanical dot gain. Such eective ink surace coverages depend on the inks, the paper, and also the speciic ink superposition conditions, i.e. the superposition o ink haltones and solid inks. At the present time and according to the literature 4, 5, 6, mainly the well-known Yule-Nielsen modiied Spectral Neugebauer model 7, 8 seems to be used in practice. 2.1 The Yule-Nielsen modiied Spectral Neugebauer model (YNSN One o the irst spectral models is the Neugebauer model 9. In its original orm, it predicts the CIE-XYZ tri-stimulus values o a color haltone patch as the sum o the tri-stimulus values o their individual colorants weighted by their ractional area coverages a i. By considering the relection spectra R i o colorants instead o their respective tri-stimulus values, one obtains the spectral Neugebauer equations 8. They predict the relection spectrum o a printed color haltone patch as a unction o the relection spectra o its individual colorants (also called Neugebauer primaries: ( λ * ( λ R = a R (1 i With k inks, there are 2 k colorants: white, the k single ink colorants and all the dierent superpositions o solid inks. For example, the red colorant is the superposition o the magenta and yellow inks. When the ink layers are printed independently one rom another, the ractional area coverages o the individual colorants are closely approximated rom the ink surace coverages by the Demichel equations 10. These equations are shown in Figure 1 or the case o 2 inks, but can be extended to accommodate any number o inks 4. i i Figure 1. Demichel equations or 2 inks: cyan (c and magenta (m. The Neugebauer model is a generalization o the Murray-Davis model 11 whose colorants are ormed by only one ink and the paper white. Since the Neugebauer model neither takes explicitly into account the lateral propagation o light within the paper bulk nor the internal relections (Fresnel relections at the paper-air interace, its predictions are not accurate 12. Yule and Nielsen 7 modeled the non-linear relationship between the relectance o paper, single ink haltones, and solid inks by a power unction whose exponent n can be optimized according to the relectance o a limited set o color patches. Viggiano 8 applied the Yule-Nielsen relationship to the spectral Neugebauer equations, yielding the Yule- Nielsen modiied Spectral Neugebauer model (YNSN: ( ( 1 λ = * n i i λ i R a R n (2 This YNSN model has been used by many researchers or the characterization o printing systems 5, 8, 12, 13, 14, 15, 16, 17. This model thereore plays a signiicant role in building color management systems.

3 2.2 The Ink Spreading Enhanced Yule-Nielsen modiied Spectral Neugebauer model (EYNSN One o the latest models is the Yule-Nielsen modiied Spectral Neugebauer model enhanced with an ink spreading model (EYNSN 1, 2. The ink spreading model is used to account or physical dot gain, i.e. the act that the inks spread out on the paper, resulting in eective ink surace coverages usually larger than the intended nominal ink surace coverages. Figure 2. The Ink Spreading enhanced Yule-Nielsen modiied Spectral Neugebauer model with nominal ink surace coverages c, m, y, and k; eective single ink haltone surace coverage o ink i superposed with solid inks j and k ijk ; eective ink surace coverages c, m, y, and k ; and eective colorant surace coverages a 1 to a 16. Spectral predictions using the EYNSN are perormed according to Figure 2. First, the eective single ink haltone surace coverages or the contributing superposition conditions are determined rom nominal surace coverages by using the tone reproduction curves established during model calibration. There is one curve or each ink haltone in each superposition condition, i.e. an ink haltone superposed with paper only, and with one, two, or three given solid inks. In order to obtain the eective surace coverages o the inks orming a color haltone, the previously stored eective single ink haltone surace coverages are weighted according to the surace coverages o the colorants contributing to that color haltone. With the Demichel equations, we can then compute the corresponding eective surace coverages o the colorants orming that color haltone. Finally, rom these eective colorant coverages, the YNSN model computes the predicted relection spectrum. Note that it is possible to replace the Yule-Nielsen modiied Spectral Neugebauer model (Equation 2 by a Clapper-Yule model 1 extended to account or middle and low screen requencies. 3. THE INK SPREADING MODEL AND ITS DIRECTIVES In contrast to ink spreading models proposed in the literature, the proposed ink spreading model does not consider the dot gain o each ink separately, but takes the ink superposition conditions into consideration. The amount o dot gain o an ink depends on whether the ink haltone is printed alone on paper or in superposition with one or more other inks. The inluence o the superposition with other inks is modeled by using more than one ink spreading curve per ink. The eective ink surace coverages are then computed using a set o equations weighting the mapping perormed by the ink

4 spreading curves. There are dierent possible sets o equations depending on the assumptions made on how the inks inluence each other. Each set o equation is urther reerred to as an ink spreading directive used by the ink spreading model. We irst present the available ink spreading curves and how they are created during the calibration o the spectral prediction model. We then describe three dierent ink spreading directives. 3.1 Available ink spreading curves and their calibration An ink spreading curve maps the nominal surace coverages o an ink into its eective surace coverages, i.e. to the surace that the ink eectively covers once printed on paper. Using the proposed ink spreading model, the amount by which an ink spreads out depends on the presence o other superposed inks. There are thereore several ink spreading curves or each ink haltone. For example, cyan may be printed alone, superposed to solid magenta, or superposed to solid yellow and solid black. In total, or our inks, there are 8 dierent superposition conditions or each ink, yielding 8 dierent ink spreading curves or each ink and a total o 32 ink spreading curves. The possible ink spreading curves are listed in Table 1. Note that the ink spreading curves used or calibrating the spectral prediction model are deined or superposition conditions composed o solid inks only. There is or example a cyan ink spreading curve over solid magenta, but no cyan ink spreading curve over 50% magenta. The ollowing notation is used or the ink spreading curves: ink haltonesuperposed inks. For example, cm reers to the cyan haltone over solid magenta ink spreading curve, cmy reers to cyan over solid magenta and solid yellow, and c reers to the ink spreading curve o a cyan haltone printed alone. These ink spreading curves can be seen as unctions that take a nominal coverage as input and return the corresponding eective coverage as output. Within equations, the letter identiies such a unction. For example, the unction corresponding to the cyan over magenta ink spreading curve is cm (c, where c is the cyan nominal coverage. Table 1. List o the available ink spreading curves Cyan Magenta Yellow Black c ck m mk y yk k ky cm cmk mc mck yc yck kc kcy cy cyk my myk ym ymk km kmy cmy cmyk mcy mcyk ycm ycmk kcm kcmy An ink spreading curve characterizes how a given ink haltone behaves in a given superposition condition, i.e. it characterizes the color wedge printed with a given ink haltone varying between 0% and 100% surace coverage superposed with given solid inks. Such an ink spreading curve is calibrated with spectral measurements o one or more color patches orming that wedge. The spectral measurements must span the visible wavelength range ( nm, and may be extended to the inrared wavelength range ( nm 3. In this paper, we use spectral measurements comprising both the visible and the inrared wavelength ranges ( nm. The black ink is pigment-based and absorbs light in the near inrared range. The other inks are dye-based and do not absorb in the near inrared range. For each measured patch, we ind the eective surace coverage that minimizes the sum o square dierences between the measured spectrum and the spectrum predicted by the YNSN model. Each measured patch provides one point o the ink spreading curve, i.e. it maps a given nominal surace coverage to an eective surace coverage. The entire unction is computed by interpolating linearly between the available points. Each ink spreading curve is independent rom the other ink spreading curves and can be calibrated using a dierent number o patches. In the present work, we calibrate all the ink spreading curves using a single patch whose nominal surace coverage is 50%. We thereore require 32 patches to calibrate all the ink spreading curves. 3.2 Ink spreading directives When using more than one ink spreading curve per ink, there are many possible combinations to compute the eective ink coverages. Each directive o the ink spreading model speciies a dierent combination based on certain assumptions. Below, we describe the three directives presented by Hersch et. al. 1, 2.

5 In the ollowing equations, the cyan, magenta, yellow, and black nominal coverages are designated using the variables c, m, y, and k, respectively, whereas the eective coverages are designated using the variables c, m, y, and k. a Single ink dot gain In the literature, ink spreading is oten characterized by one ink spreading curve per ink and does not take superposition conditions into account 5. In that case, the eective coverage o an ink depends only on the nominal coverage o the ink and is computed rom the ink spreading curve o the ink alone. This ink spreading directive is urther reerred to as the single directive and is expressed by the ollowing equations: ( ( ( ( c = c m = m y = y k = k k (3 c m y The problem with the single directive is that it does not take superposition conditions into consideration. b Ink spreading o an ink haltone printed on top o ink layers The next directive, urther reerred to as the top directive, assumes that an ink haltone is inluenced by the inks that are already printed. It is inluenced by the underlying inks, but not by new ink layers printed on top o it. The eective coverages are computed in the order in which they are printed. Assuming that the inks are printed in the order cyan, magenta, yellow, and black, we irst compute the eective coverage o cyan. As no other ink is present when cyan is printed, the eective coverage o cyan is computed using the ink spreading curve o cyan alone, as in the single directive. Then, we compute the eective coverage o magenta. Since the cyan ink covers a percentage c o the surace, a percentage c o magenta is printed over solid cyan and a percentage (1-c o magenta is printed alone on paper. We thereore use these percentages to weight the eective coverages returned by the ink spreading curve o magenta over solid cyan and o magenta alone. For yellow, we weight the ink spreading curves o yellow alone, yellow on cyan, yellow on magenta, and yellow on cyan and magenta according to the percentages o surace covered respectively by paper, (1-c (1-m ; cyan only, c (1-m ; magenta only, (1-c m ; and cyan and magenta, c m. We apply the same logic or the black ink haltone. We obtain a total o 15 ink spreading curves weighted according to the ollowing equations: c' = ( c k' = ( 1 c' ( 1 m' ( 1 y' ( k c k + c' ( 1 m' ( 1 y' ( k k c m' = ( 1 c' ( m m + ( 1 c' m' ( 1 y' ( k k m + c' ( m mc + c' m' ( 1 y' ( k k cm y' = ( 1 c' ( 1 m' ( y ( 1 ' ( 1 ' ' ( (4 y c m y k k y + c' ( 1 m' yc ( y + c' ( 1 m' y' k cy( k + ( 1 c' m' y m( y + ( 1 c' m' y' k my( k + c' m' y + c' m' y' k ( ycm k cmy The top directive improves the predictions, but due to the speed o printing devices, ink haltones that are already printed are not dry when the next layer is printed and may thereore be inluenced by the newly printed ink haltone layer. c Ink spreading o an ink haltone printed on top or below other ink layers Each ink haltone is inluenced both by the inks already printed and by the inks that are printed on top o it. The ink spreading directive corresponding to this assumption is urther reerred to as the top or below directive. As the top directive, the top or below directive weights the eective coverages returned by the dierent ink spreading curves according to the colorant surace coverages in the dierent superposition conditions. However, instead o considering only the inks already printed in the possible superposition conditions, the top or below directive accounts or all possible superposition conditions. Since, or 4 inks, there are 8 possible superposition conditions or each ink haltone, the eective coverage o an ink is the weighted average o 8 dierent ink spreading curves. For example, i a patch with 50% cyan, 50% magenta, and 50% yellow is printed, the superposition dependent colorant surace coverages weighting the ink spreading curves o magenta are 25% unprinted paper, 25% cyan, 25% yellow, 25% green and 0% or the 4 superposition conditions containing solid black. For our inks, 32 ink spreading curves are required. (

6 Equations 5 weight the ink spreading curves o each ink haltone according to the corresponding colorant surace coverages. In these equations, computing the eective coverage o an ink requires the eective coverages o the other inks, which are not available. Because o the non-linearity o the equations, there is no analytical solution to the equation system. The eective coverages must thereore be computed iteratively, starting with the nominal coverages 1. Usually, ive iterations ensure suicient convergence to determine the eective ink haltone coverages. ( ( ( c ( ( ( c m( ( ( c y( ( c my( ( ( c k( m' ( 1 y' k' ( c c mk ( 1 m' y' k' c yk( c m' y' k' c myk( c ( ( ( y ( c' ( 1 m' ( 1 k' ( y yc ( 1 c' m' ( 1 k' ( y y m c' m' ( 1 k' ( y ycm ( 1 c' ( 1 m' k' ( y y k c' ( 1 m' k' yck ( y ( 1 c' m' k' y mk( y c' m' k' ( y ( ( ( m ( ( ( ( m m c ( ( m y( ( ( m m cy ( ( ' ( m mk c' ( 1 y' k' ( m mck ( 1 c' y' k' ( m m yk c' y' k' mcyk ( m ( ( ( k ( c' ( 1 m' ( 1 y' ( k k c ( 1 c' m' ( 1 y' ( k k m c' m' ( 1 y' ( k k cm ( 1 c' ( 1 m' y' k y( k c' ( 1 m' y' k cy( k ( 1 c' m' y' k my( k c' m' y' ( k c' = 1 m' 1 y' 1 k' c m' = 1 c' 1 y' 1 k' m + m' 1 y' 1 k' c + c' 1 y' 1 k' + 1 m' y' 1 k' c + 1 c' y' 1 k' m + m' y' 1 k' c + c' y' 1 k' + 1 m' 1 y' k' c + 1 c' 1 y' k + + y' = 1 c' 1 m' 1 k' y k' = 1 c' 1 m' 1 y' k + + k cmy ycmk 4. RELEVANCE OF THE DIFFERENT INK SPREADING CURVES Using the top or below directive or the ink spreading model requires 32 dierent ink spreading curves. Creating these ink spreading curves requires at least 32 spectral measurements. In order to try to reduce the number o ink spreading curves, we evaluate their relevance. I a speciic ink spreading curve does not improve the accuracy o the spectral prediction model, we try to discard it. We use two dierent measurements set or the experiments. The irst set, urther reerred to as the PIXMA set, is composed o the measurements o 625 patches printed on the Canon Pixma 4000 ink jet printer using classical rotated clustered dot screens at 100 lpi and a resolution o 600 dpi. The 625 patches are composed o all combinations o cyan, magenta, yellow, and black at 0%, 25%, 50%, 75%, and 100% nominal surace coverages. The second set, urther reerred to as the CIEL set, is composed o the measurements o 750 patches printed on a newspaper web-oset press using classical rotated clustered dot screens at 75 lpi and a resolution o 1200 dpi. The 750 patches are composed o all combinations o cyan, magenta, and yellow at 0%, 25%, 50%, 75%, and 100% nominal surace coverages and black at 0%, 10%, 30%, 50%, 80%, and 100%. The ollowing experiment is perormed both on the PIXMA and CIEL sets. It irst calibrates the spectral prediction model, including the 32 ink spreading curves. Then, we successively modiy each ink spreading curve by setting the eective coverage at 50% to a value between 0% and 100%. For each modiication, we predict the spectra o the patches in the measurement set and compute the average ΔE 94 between the measured and predicted spectra 18. Each modiication is thereore associated to an average ΔE 94. The resulting curves are called surace coverage accuracy curves. In Appendix A, Figures 6 and 7 show the surace coverage accuracy curves or the PIXMA set (ink jet and CIEL set (oset, respectively. The circles indicate the calibration points, i.e. prior to modiications, and the crosses indicate the eective coverages at 50% yielding the minimum average ΔE 94. All the surace coverage accuracy curves have the shape o convex parabolas, but not all parabolas have similar curvatures. Some are nearly lat, especially the ink spreading (5

7 curves whose superposition condition includes solid black, i.e. the last our o the irst three lines o the surace coverage accuracy curves. We urther reer to these 12 ink spreading curves as the ink spreading curves on solid black. When observing the surace coverage accuracy o ink spreading curves which do not include solid black, we make the ollowing observations. The eective coverages at 50% chosen during calibration (circles agree well with the minima (crosses. Moreover, the surace coverage accuracy curves are highly relevant to the accuracy o the prediction model because o their curvature. I the eective coverage at 50% o one o these ink spreading curves is set too ar o the minimum, the average ΔE 94 becomes large. Finally, we can see that the eective coverage at 50% o a given ink haltone yielding the minimum ΔE 94 is dierent depending on the superposition condition. This emphasizes the act that the ink spreading o an ink haltone depends on the presence o other inks. The opposite analysis is true or the ink spreading curves on solid black. The calibrated eective surace coverages do not agree well with the computed minima. They are not relevant or the accuracy o the prediction model because the curvature o the parabolas is low, i.e. a modiication o an eective haltone surace coverage at 50% nominal coverage on solid black does not deteriorate the accuracy o the prediction model. The system is underdetermined 3 and it seems preerable to discard the ink spreading curves on solid black. 5. RESILIENCE OF THE INK SPREADING CURVES TO NOISE The ink spreading curves on black do not improve the accuracy o the spectral prediction model. Let us urther show that they are not only irrelevant, but also highly subject to noise. There are indeed several possible origins o noise in the measured spectra. Noise comes rom the printing device itsel, rom dirty patches, rom variations in the intrinsic relectance o the substrate, rom variations in the printing conditions, etc. These dierent sources produce each a dierent kind o noise, making them diicult to separate and model. We thereore use Gaussian noise and analyze its impact on the calibration o the ink spreading curves. In the ollowing experiment, we observe how stable the calibration o the ink spreading curves is in the presence o Gaussian noise added to each wavelength o the measured relectance with both average and standard deviation between 0 and For each ink spreading curve and each noise average, we calibrate 500 times the eective coverage o the 50% patch as ollows: We irst choose randomly the standard deviation o the noise between 0 and We generate the noise independently or each wavelength and add it to the measured spectrum o the 50% patch. The ink spreading curve is established using this measured noise augmented relectance spectrum. For each ink spreading curve and each noise average, we have 500 dierent itted eective coverages. The results are shown in Appendix B. Figures 8 and 9 show the results or the PIXMA (ink jet and CIEL (oset measurement sets, respectively. Both igures present the same behavior: The eective surace coverages superposed with solid black are very sensitive to noise, i.e. the same noise induces very large eective surace coverage calibration variations. On the other hand, the other eective surace coverages are mainly subject to the mean value o the Gaussian noise. As expected, when adding noise with a positive mean, the predicted relection spectra become higher. This positive dierence is compensated by lower eective surace coverages. Figure 3. Spectra o solid cyan supposed with solid black (continuous line and o solid cyan superposed with solid magenta and black (dashed line rom the CIEL measurement set. Figure 4. Spectra o solid black (continuous line and o solid magenta superposed with solid black (dashed line rom the PIXMA measurement set. The problem caused by the ink spreading curves on solid black is underlined in Figures 3 and 4. In Figure 3, we ocus on the magenta ink spreading curve over solid cyan and solid black or the CIEL measurement set. The relection spectrum without magenta corresponds to the beginning o the ink spreading curve (0% coverage o magenta. The spectrum with

8 solid magenta corresponds to the end o the ink spreading curve (100% coverage o magenta. We see that the dierence between the two spectra is negligible. Thereore, the ink spreading curve o magenta over solid cyan and black has a negligible inluence when predicting relection spectra. Moreover, noise has a large impact on the calibration o the ink spreading curve because small variations in the 50% magenta coverage spectrum must be compensated by large variations in the ink spreading curve. The same reasoning applies to Figure 4 when considering the ink spreading curve o magenta over solid black (PIXMA set. The result o the calibration o the ink spreading curves or the PIXMA measurement set is shown in Figure 5. Figure 5 shows the dot gain curves, deined as eective minus nominal surace coverage in unction o nominal surace coverage. All the dot gain curves except those on solid black show a consistent behavior. Conversely, we can see the eect o measurement noise on the dot gain curves superposed with solid black: The curves suddenly behave randomly. Figure 5. Dot gain curves, derived rom the corresponding ink spreading curves, calibrated at 25%, 50%, and 75% nominal coverage on the PIXMA measurement set. The horizontal axis corresponds to the nominal surace coverage o the ink haltone and the vertical axis to the dot gain. 6. REMOVING THE INK SPREADING CURVES ON SOLID BLACK In the previous two sections, we have shown that the ink spreading curves on solid black are not resilient to noise and do not improve the accuracy o the spectral prediction model. We thereore propose a new directive or the ink spreading model called haltone black that discards these 12 ink spreading curves, yielding the ollowing set o equations: c' = ( 1 m' ( 1 y' ( c m' = ( 1 c' ( 1 y' ( m c m + m' ( 1 y' ( c + c' ( 1 y' ( m cm mc + ( 1 m' y' ( c + ( 1 c' y' ( m c y m y + m' y' ( c + c' y' ( m cmy mcy y' = ( 1 c' ( 1 m' ( y k' = ( 1 c' ( 1 m' ( 1 y' y k ( k + c' ( 1 m' ( y + c' ( 1 m' ( 1 y' ( k yc k c (6 + ( 1 c' m' ( y + ( 1 c' m' ( 1 y' ( k y m k m + c' m' ( y + c ' m' ( 1 y' ( k k cm ycm + ( 1 c' ( 1 m' y' ( k k y + c' ( 1 m' y' k cy( k + ( 1 c' m' y' k my( k + c' m' y' ( k k cmy

9 Using the haltone black directive, it is possible to break the computation o the eective coverages into two steps: First, we compute the eective coverages or cyan, magenta, and yellow using the iterative method proposed or the top or below directive. Then, we directly compute the black eective coverage using the eective coverages o the other inks. The accuracy o the dierent ink spreading directives proposed in Section 3.2 and Section 6 are compared in Table 2 or the PIXMA measurement set and in Table 3 or the CIEL measurement set. On the PIXMA measurement set, the haltone black directive yields the best accuracy while the top or below directive suers rom the measurement noise as seen in Figure 5. On the CIEL measurement set, both directives yield similar results. Considering that the patches are printed on newsprint paper, which is non-coated and less uniorm than traditional paper, the achieved accuracy is remarkable. We still recommend using haltone black. It uses only 20 ink spreading curves instead o 32, reduces the calibration eort and decreases the time required to perorm a spectral prediction. Table 2. Accuracy o the spectral prediction model on the PIXMA measurement set. For each o the 625 patches o the measurement set, we compute the ΔE 94 between the predicted and measured spectra. The statistics show the average ΔE 94, the corresponding standard deviation, 95% percentile, and maximum ΔE 94. The Yule-Nielsen actor is n = 10. Average St. Deviation 95% percentile Maximum No ink spreading Single Top Top or below Haltone black Table 3. Accuracy o the spectral prediction model on the CIEL measurement set. For each o the 750 patches o the measurement set, we compute the ΔE 94 between the predicted and measured spectra. The statistics show the average ΔE 94, the corresponding standard deviation, 95% percentile, and maximum ΔE 94. The Yule-Nielsen actor is n = 7.8. Average St. Deviation 95% percentile Maximum No ink spreading Single Top Top or below Haltone black CONCLUSION Ater introducing the Yule-Nielsen modiied Spectral Neugebauer prediction model, we present the ink spreading model and its dierent directives. We then perorm experiments to deduce the ink spreading curves that have a high impact on the accuracy o the spectral prediction model and that are resilient to measurement noise. Based on this in-depth analysis, we show that the ink spreading curves o ink haltones superposed with solid black are neither relevant or the accuracy o t he spectral prediction model nor resilient to measurement noise. We thereore propose an improved ink spreading directive called haltone black relying on a reduced set o ink spreading equations. This new directive is compared with the other ones or two dierent measurement sets, one rom a consumer-grade inkjet printer and the other rom a newspaper web-oset press. In both cases the haltone black directive perorms best on average. Depending on the printing technology, the other directives may sometimes show similar perormances, but since haltone black requires only 20 ink spreading curves instead o 32, we recommend it or CMYK spectral prediction models. ACKNOWLEDGMENT Part o this research was perormed within the ramework o the CTI project supported by the Swiss government agency or the promotion o innovation. The project has also been partially supported by the Swiss National Science Foundation, grant n

10 REFERENCES R. D. Hersch, P. Emmel, F. Collaud, F. Crété, Spectral relection and dot surace prediction models or color haltone prints, Journal o Electronic Imaging, Vol. 14, No. 3, (2005 R. D. Hersch, F. Crété, Improving the Yule-Nielsen modiied spectral Neugebauer model by dot surace coverages depending on the ink superposition conditions, Color Imaging X: Processing, Hardcopy, and Applications, SPIE Vol. 5667, (2005 Th. Bugnon, M. Brichon and R.D. Hersch, Model-Based Deduction o CMYK Surace Coverages rom Visible and Inrared Spectral Measurements o Haltone Prints, Color Imaging XII: Processing, Hardcopy, and Applications, SPIE Vol. 6493, to (2007; D.R.Wyble, R.S. Berns, A Critical Revie w o Spectral Models Applied to Binary Color Printing, Journal o Color Research and Application, Vol. 25, No. 1, 4-19 (2000 R. Balasubramanian, Optimization o the spectral Neugebauer model or printer characterization, Journal o Electronic Imaging, Vol. 8, No. 2, (1999 T. Ogasahara, Veriication o the Predicting Model and Characteristics o Dye-Based Ink Jet Printer, Journal o Imaging Science and Technology, Vol. 48, No. 2, (2004 J.A.C. Yule, W.J. Nielsen, The penetration o light into paper and its eect on haltone reproductions, Proc. TAGA Vol. 3, (1951 J.A.S Viggiano, Modeling the Color o Multi-Colored Haltones, Proc. TAGA, (1990 H.E.J. Neugebauer, Die theoretischen Grundlagen des Mehrarbendrucks, Zeitschrit uer wissenschatliche Photographie, Vol. 36, (1937, reprinted in Neugebauer Seminar on Color Reproduction, SPIE Vol. 1184, (1989 M.E. Demichel, Procédé, Vol. 26, (1924 A. Murray, Monochrome reproduction in photoengraving, J. Franklin Institute, Vol. 221, (1936 H.R. Kang, Applications o color mixing models to electronic printing, Journal o Electronic Imaging, Vol. 3, No. 3, (1994 R.D. Hersch, F. Collaud, P. Emmel, Reproducing color images with embedded metallic patterns, Proc. SIGGRAPH 2003, ACM Trans. on Graphics, Vol. 22, No. 3, (2003 K. Iino, R.S. Berns, Building color management modules using linear optimization I. Desktop, Journal o Imaging Science and Technology, Vol. 42, No. 1, (1998 K. Iino, R.S. Berns, Building color management modules using linear optimization II. Prepress system or oset printing, Journal o Imaging Science and Technology, Vol. 42, No. 2, (1998 A. U. Agar and J. P. Allebach, An Iterative Cellular YNSN Method or Color Printer Calibration, Proc. o the 6th IS&TSID Color Imaging Conerence, Scottsdale AZ, (1998 S. Zui, R. Schettini, An innovative method or spectral-based printer characterization, Color Imaging: Device- Independent Color, Color Hardcopy, and Applications VII (R. Eschbach, G.G. Marcu eds., SPIE Vol. 4663, 1-7 (2002 G. Sharma, Digital Color Imaging Handbook, Chapter 1, 35-36, CRC Press, 2003

11 APPENDIX A The ollowing two igures show the impact o the ink spreading curves on the prediction accuracy o the EYNSN model. For each ink spreading curve, we modiy the eective coverage at 50% nominal coverage and compute the average ΔE 94 between the measured and predicted spectra. The circle indicates the eective coverage at 50% nominal coverage deduced during calibration. The cross indicates the eective coverage that minimizes the average ΔE 94. The experiment is perormed once or an inkjet printer and once or an oset press. Figure 6. Surace coverage accuracy curves showing the impact o dot gain variations computed or the PIXMA measurement set (inkjet, 100 lpi, Yule-Nielsen actor n = 10. The horizontal axis denotes the eective surace coverage at 50% nominal surace coverage and the vertical axis the prediction accuracy in terms o average ΔE 94 between measured and predicted spectra. Figure 7. Surace coverage accuracy curves showing the impact o dot gain variations computed on the CIEL measurement set (oset, 150 lpi, Yule-Nielsen actor n = 7.8. The horizontal axis denotes the eective surace coverage at 50% nominal surace coverage and the vertical axis the prediction accuracy in terms o average ΔE 94 between measured and predicted spectra.

12 APPENDIX B The ollowing two igures show the impact o noise on the calibration o the ink spreading curves. For each ink spreading curve and each noise average, we calibrate 500 times the 50% patch as ollows: We irst choose randomly the standard deviation o the noise between 0 and Then, we generate the noise independently or each wavelength and add it to the measured spectrum o the 50% patch. Finally, we calibrate the ink spreading curve using this noisy spectrum. For each ink spreading curve and each noise average, we thereore have 500 dierent itted eective coverages. In the igures, we plot the average and standard deviations o the itted eective coverages. The dotted line represents the calibration without noise. The Yule-Nielsen actor is n=7.8 or the CIEL set and n=10 or the PIXMA set. Figure 8. Impact o noise on the calibration o the ink spreading curves computed or the PIXMA measurement set. Figure 9. Impact o noise on the calibration o the ink spreading curves computed or the CIEL measurement set.