A Method That Uses the Measured Ink Combination Data/Training Set to Compute the Errors That Can Be Universally Applied to Correct the Output of a Prediction Model

Abstract

The present invention relates to a method of generating “expanded color chart” representing various ink combination, for profiling a multi-color printing device or printer, using “reduced set of color chart”, printed using the printer, where a. The expanded color chart is computed by applying “Error Correction” function to the expanded color chart predicted using a theoretical model of color prediction for a given ink combinations in the expanded chart. b. Error Correction function is computed/modelled as function of the variance/difference observed between the color values predicted by the theoretical model and the actual values measured for the ink combinations in the printed “reduced set of color chart”.

Claims

1. A method of generating “expanded color chart” representing various ink combination, for profiling a multi-color printing device or printer, using “reduced set of color chart”, printed using the printer, where a. The expanded color chart is computed by applying “Error Correction” function to the expanded color chart predicted using a theoretical model of color prediction for a given ink combinations in the expanded chart. b. Error Correction function is computed/modelled as function of the variance/difference observed between the color values predicted by the theoretical model and the actual values measured for the ink combinations in the printed “reduced set of color chart”.

2. The color profile generated using the “expanded color chart” of claim 1.

3. The method of generating color profile using the “expanded color chart” of claim 1, when one of more of the printing inks are fluorescent in nature, where a. Firstly, a color is converted into printing ink percentages using combination of inks not involving the fluorescent ink, when unsuccessful then, b. The color is converted into printing ink percentages using the combination of inks involving the fluorescent ink(s).

4. Method of separating the fluorescence factor SRF, from the reflectance data by considering the difference of reflectance values above the substrate reflectance as SRF and 0 in all other cases where it is below the substrate reflectance.

5. An apparatus consisting of a computing device, a color measuring device and a printer, to be profiled with the reduced set of chart printed using the method of claim 2.

6. An apparatus consisting of a computing device, a color measuring device and a printer, to be profiled with the reduced set of chart printed using the method of claim 3.

7. Printer using the using the profiles of claim 2 and articles printed thereof.

8. Printer using the using the profiles of claim 3 and articles printed thereof.

Description

EXAMPLE 1—PREDICTION MODEL BASED ON SINGLE CONSTANT KUBELKA MUNK THEORY

[0022] Single constant Kubelka Munk theory (KM1) describes the coloration of textiles (dyeing) quite well, but isn't accurate enough to model the printing of textiles. This deficiency can be overcome by using our method.

[0023] Based on equation 1, we propose the correcting function to add the error correction to the prediction from “KM1 model” as below—

Actual_Color_Predicted=KM1_Predicted(Ci)+f_Error(Ci)  eqn (2)

Where,

[0024] Ci denotes the concentration of various inks in the combination. [0025] f_Error returns the correction factor in CIE Lab color space. [0026] KM1_Predicted returns the resulting color based on single constant Kubelka Munk theory in CIE Lab space predicted from the “spectral reflectance data” for various inks at their respective concentrations. [0027] The spectral reflectance data for specific ink at respective concentration is computed from that ink primary color data measured at various known concentrations/percentages using an interpolation function.

[0028] The input to “KM1 model” is spectral data. Following is the general implementation of KM1 model for n color ink combination (c1, c2 . . . cn) on a substrate S.

f(a□)=as,+a,1c1_a,2c2_a,ncn  eqn 3.

[0029] Where, [0030] f(a□) is the absorption coefficient of the overprint/mixture, [0031] as, is the absorption coefficient of the substrate, [0032] a□, 1 c1 is the absorption coefficient of ink 1 at concentration C1, and [0033] a□, n cn is the absorption coefficient of ink n at concentration Cn.

[0034] Absorption coefficient is related to the reflectance by following equations—

K/S or a□=(1−R).sup.2/2R.  Eqn 4

And reflectance to absorption coefficient as,

R=1+(K/S)−{(K/S)[(K/S)+2]}.sup.1/2  Eqn 5

[0035] So using equation (4) the reflectance values can be converted to absorption coefficient and equation (3) can be used to model the resulting absorption coefficients for an ink combination. The resulting absorption coefficient can then be converted back to reflectance using equation (5). The resulting reflectance spectrum can be converted into corresponding CIE Lab value using conversion equations well defined in CIE literature.

[0036] So, for each of the known ink combination in the target, KM1_Predicted function can be used to compute the theoretical predicted values. Rearranging the equation (2), the difference between the measured value and this predicted value is the error in CIE Lab space for each of these known combinations that form the nodes of the “ErrorSolid”.

[0037] Assuming that we are dealing with a CMYK printing ink solid, the input to the KM1 model used by above KM1_Predicted function will be printed color wedges of CMYK inks at various percentages between 0 to 100% (eg, at a spacing of 10%). The test target could be division K=3 of the ink colorspace, totalling 81 patches. The error function can be a linear interpolation function in 4 dimensional CMYK color space interpolating between the values of the known errors from the measured data. From this chart and the prediction model described, highly accurate chart with a division of k=10, can be generated, that can be used as a target for generating color tables. This discussion for CMYK/4 color solid can be extended to color solids using more than 4 colors in a similar manner.

EXAMPLE 2—PREDICTION MODEL BASED ON SINGLE CONSTANT KUBELKA MUNK THEORY AND SPECTRAL RADIANCE FACTOR (SRF) FOR PREDICTING OVERPRINTS WITH FLUORESCENT COLORS

[0038] As can be seen from equation 4, the absorption coefficient are valid for reflectance values less than or equal to value of 1, above which the Kubelka Munk equation fails as we are dealing with fluorescence and not absorption. The key to handle this situation is to separate the reflectance curve into Normal reflectance values Normal(R) that can be used by equation 4 and SRF values that represent fluorescence and can be handled separately. Equation (6) describes this.

R=Normal(R)+SRF  eqn(6)

[0039] In order to determine SRF, a special measuring instrument is required that measures the color sample with and without fluorescence in order to separate the SRF. Such instruments are not common in practice and there are good chances that they may not be available with the user creating the color tables. Hence a good approximation to the equation (6) can be to either consider anything above reflectance value of 1 to be SRF or, assume any reflectance above the reflectance of the substrate to be SRF. We choose the later as this makes sense because normally substrate has the highest reflectance under normal circumstances and this is why we consider the substrate as whitest point of the image. So SRF can be computed using the following modified equation (7).

TABLE-US-00001 If (R > Rs) { Normal (R) = Rs; SRF = R − Rs; } else { Normal (R) = R; SRF = 0; } ------ eqn (7)

[0040] Where, R is the reflectance of the measured sample, Rs is the reflectance of the substrate.

[0041] So for computing the overprint, resulting absorption coefficients f(a□) based on Normal(R) of the ink combination are added together (see eqn (3)) and SRF component of the ink combination is computed as per eqn(8). The resulting SRF is weighed by the factor computed as 1/(1+f(a□)), where f(a□) is the resulting ink absorption coefficients (See eqn (9)).

SRF(Combined)=SRF1c1+SRF2c2+ . . . +SRFncn  eqn 8.

[0042] Where, [0043] SRF(Combined) is the combined SRF of the overprint/mixture, [0044] SRF1 c1 is the SRF of ink 1 at concentration C1, and [0045] SRFn cn is the SRF of ink n at concentration Cn.

SRF(Final)=SRF(Combined)*1/(1+f(a□)).  eqn (9)

Where f(a□), is the resulting absorption coefficient of the ink combination.

[0046] The f(a□) is converted to resulting reflectance values f(R) using equation (5).

[0047] The final reflectance Final(R) for the predicted color thus can be computed by following equation (10).

Final(R)=f(R)+SRF(Final).  eqn (10).

[0048] Final(R) can be converted to resulting color in CIE Lab space using the well known conversions defined in the CIE literature.

[0049] The Error correction function can be modelled as 2 stage correction for this Prediction model. One correction that is applied to SRF(Final) and another to the final color value in CIE Lab space. The correction factor for CIE Lab space can be computed in a manner same as in example 1. For correction of the resulting SRF following equation can be used—

SRF(Final)=SRF(Final)*SRF_correction_factor  eqn (11).

Where, SRF correction factor for known ink combinations from the measured data can be computed as follows—

SRF_correction_factor=SRF(Measured)/SRF(Final).  eqn (12).

[0050] The SRF correction factor for unknown ink combination can be computed in the manner similar to LAB error factors. So, for computing the color values of unknown ink combinations the SRF value from equation (9) is corrected by using equation (11) before adding in equation (10). The final reflectance values from equation(10) is converted to CIE Lab value before adding the final correction factor in CIE Lab space.

[0051] Again, assuming that we are dealing with a 4 color printing ink solid, the input to the above Prediction model will be printed color wedges of 4 color inks at various percentages between 0 to 100% (eg, at a spacing of 10%). The test target could be division K=3 of the ink colorspace, totalling 81 patches. The error function can be a linear interpolation function in 4 dimensional color space interpolating between the values of the known errors from the measured data. From this chart and the prediction model described, highly accurate chart with a division of k=10, can be generated, that can be used as a target for generating color tables. This discussion for CMYK/4 color solid can be extended to color solids using more than 4 colors in a similar manner.

EXAMPLE 3—PREDICTION MODEL BASED ON MULTIPLICATIVE RELATIONSHIP OF INKS IN THE MIXTURE FOR PRINTING ON PAPER COATED/UNCOATED

[0052] The normalized reflectance values of all the inks are multiplied together after accounting for the substrate as per the equation (13). Let's call this “Multiplicative model”.

Final(R)=Rs*R1c1*R2c2* . . . *Rncn  eqn (13)

Where,

[0053] Final(R) is the reflectance of the overprint,

[0054] Rs is the reflectance of the substrate

[0055] R1 c1 is the reflectance of ink 1 at concentration C1 divided by reflectance of substrate Rs,

[0056] R2 c2 is the reflectance of ink 2 at concentration C2 divided by reflectance of substrate Rs, and

[0057] Rn cn is the reflectance of ink n at concentration C2 divided by reflectance of substrate Rs.

[0058] Final(R) can be converted to resulting color in CIE Lab space using the well known conversions defined in the CIE literature.

[0059] Similar to example 1, we propose the correcting function to add the error correction to the prediction from “Multiplicative model” as below—

Actual_Color_Predicted=Multiplicative model(Ci)+f_Error(Ci)  eqn (14)

Where,

[0060] Ci denotes the concentration of various inks in the combination. [0061] f_Error returns the correction factor in CIE Lab color space. [0062] “Multiplicative model” returns the resulting color based on equation (13) above in CIE Lab space predicted from the “spectral reflectance data” for various inks at their respective concentrations. [0063] The spectral reflectance data for specific ink at respective concentration is computed from that ink primary color data measured at various known concentrations/percentages using an interpolation function.

[0064] So, for each of the known ink combination in the target, “Multiplicative model” can be used to compute the theoretical predicted values. Rearranging the equation (14), the difference between the measured value and this predicted value is the error in CIE Lab space for each of these known combinations that form the nodes of the “ErrorSolid”.

[0065] Assuming that we are dealing with a CMYK printing ink solid, the input to the “Multiplicative model” will be printed color wedges of CMYK inks at various percentages between 0 to 100% (eg, at a spacing of 10%). The test target could be division K=3 of the ink colorspace, totalling 81 patches. The error function can be a linear interpolation function in 4 dimensional CMYK color space interpolating between the values of the known errors from the measured data. From this chart and the prediction model described, highly accurate chart with a division of k=10, can be generated, that can be used as a target for generating color tables. This discussion for CMYK/4 color solid can be extended to color solids using more than 4 colors in a similar manner. Fluorescent ink primaries can be handled using the same method of separating the SRF as in case of Single constant K/S.

Generation of Color Profiles/Color Tables.

[0066] The resulting test charts with higher divisions that are generated from small number of measured data as a result of the method disclosed here can be used to create color tables using methods well known in the literature. The difficulty may arise in case of fluorescent colors as they need to be handled differently than normal inks due to their fluorescence. The fluorescent inks loose their fluorescence very fast as the concentration of color is increased or more color is added to the mixture. Also, since the fluorescent inks are not as light fast as the normal inks, they must be used carefully in the color mixture so that, the reduction in the overall light fastness of the printed image is minimum.

[0067] We propose that the color gamut boundary without (Gamut A) and with fluorescent inks (Gamut B) is computed. The gamut mapping is to be performed on Gamut B. When computing the color table, the color corresponding to the node in the color table is first determined to lie where? Is it inside Gamut A or outside? Only when a color is outside of the bounds of Gamut A, the fluorescent inks are used in computing the color percentages of the mixture. There are several ways to achieve this. One of the way is to consider the normal ink color solid first in computing the ink concentration for the color. Only when no solution is found the ink color solid with fluorescent inks is used. This way computing Gamut A can be avoided.

[0068] The various steps of computing a color table are well defined in literature including the methods to compute the color gamut, color gamut mapping and finding the ink combination for a given color in order to populate the various nodes of the color table. So, we will not describe these here but it is understood for anybody skilled in art to be able to implement the methods efficiently.

[0069] The apparatus (FIG. 2) for generating color profiles using the correction and profile generation methods described above consists of a computing device, color measuring device and a printer that is to be profiled. The patches generated by the printer are read using the color measuring device and corresponding color tables are generated by the computing device using the method described in the present invention (FIG. 1).

CITED REFERENCES

[0070] [1] Kiran Deshpande and Phil Green—A simplified method of predicting the colorimetry of spot color overprints. [0071] [2] ICC_white_paper_43_Draft2kd.doc—Recommendations for predicting spot colour overprints. [0072] [3] Data-driven Spectral Model for Color Gamut Simulation—Pau Soler, Ján Morovi and Howard Doumaux. [0073] [4] Colour Physics for Industry (Second Edition)—Edited by Roderick McDonald. ISBN 0 901956 70 8. [0074] [5] Computational color technology by Henry R. Kang. ISBN 0-8194-6119-9. [0075] [6] Fabrice Rousselle, Thomas Bugnon, Roger D. Hersch—Spectral prediction model for variable dot-size printers.