Generating Spectra from Tristimulus Values

Abstract

To bring color, described by Lab values only, back into the spectral domain the invention discloses a method for automatically generating reflectance spectrum values from tristimulus values using a computer system administrating a database with data matrices of reflectance spectra of different colors differentiated by at least the process parameters print technology, substrate and print order of inks, wherein a) given tristimulus values of a color are classified with regard to the process parameters, b) in the database the data matrices of reflectance spectra of the respective color with the most matching process parameters are identified and c) the identified data matrix is used to define the reflectance spectrum values for the respective color.

Claims

1. Method for automatically generating reflectance spectrum values from tristimulus values using a computer system administrating a database with data matrices of reflectance spectra of different colors differentiated by at least the process parameters print technology, substrate and print order of inks, comprising: a) classifying given tristimulus values of a color with regard to the process parameters, b) identifying in the database the data matrix of reflectance spectra of the respective color with the most matching process parameters, and c) using the identified data matrix to define the reflectance spectrum values for the respective color; wherein the data matrices of reflectance spectra are reduced to basis vector data within a PCA process to yield correct tristimulus values of the reflectance spectra, based on the equation
r=μ+(x−μC.sup.T)*(BC.sup.T).sup.−1B.

2. (canceled)

3. Method according to claim 1, further comprising: d) using the identified data matrix as reference spectrum to calculate resulting tristimulus values, e) comparing the calculated tristimulus values to the given tristimulus values to define differences, f) using the differences to adjust the reference spectrum resulting in a synthesized spectrum.

4. Method according to claim 3, wherein the adjustment of the reference spectrum is based on the equation
r=r.sub.o+(x−r.sub.oC.sup.T)*(BC.sup.T).sup.−1B wherein r be a spectral reflectance, C be the color matching functions, weighted by a given illuminant, x be the vector of tristimulus values CIEXYZ, B be the matrix of 3 chosen basis vectors, r.sub.o be the reference spectrum.

5. Method according to claim 4, wherein B represents the matrix of the first 3 basis vectors resulting from a PCA reduction with the dimension (3×36).

6. Method according to claim 3, wherein the synthesized spectrum is investigated for negative fractions and, if negative fractions exist, further comprising: i) clipping all spectral samples that are below a given threshold t to the threshold t, ii) applying a smoothing filter to the entire clipped spectrum, as the clipping may have introduced edges, and iii) using the clipped spectrum as the reference spectrum.

7. Method according to claim 6, wherein the threshold is t>0.

8. Method according to claim 1, further comprising transforming tristimulus values and reference spectra into a non-linear domain by applying a non-linear transfer function r′=f(r), and reducing the tristimulus values and reference spectra within a PCA process to produce revised basis vector data of reflectance spectra.

9. Method according to claim 1, further comprising using a database with generic basis vector data of reflectance spectra of different colors and a data base with process related data matrices of reference spectra of different colors so that the specific properties of the process are then taken from the reference spectra, while a correction shift is performed by using the generic basis vectors.

10. Method according to claim 1, further comprising producing a number of different reflectance spectra sets and evaluating a quality of the different reflectance spectra sets with regard to the success of the spectral synthesis to decide for the best result.

Description

[0099] These and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of preferred embodiments with the accompanying drawings which show

[0100] FIG. 1 is a flow chart using a typical computer system in which the present invention may be embodied according to a first aspect;

[0101] FIG. 2 is a flow chart using a typical computer system in which the present invention may be embodied according to a second aspect;

[0102] FIG. 3 is a flow chart using a typical computer system in which the present invention may be embodied according to a third aspect;

[0103] FIG. 4 is a flow chart using a typical computer system in which the present invention may be embodied according to a forth aspect and

[0104] FIG. 5 is a flow chart using a typical computer system in which the present invention may be embodied according to a fifth aspect.

[0105] FIG. 1 shows the use of a reference spectra. The required input is:

[0106] A color, described by its Lab values and by the device values (e.g. CMYK) that have been used to print the color, and some metadata describing the type of print process used (e.g. Offset on coated paper). The Lab values are based on a selected illuminant/observer combination (e.g. D50/2°).

[0107] The process includes: [0108] 1. Select a set of reference spectra, based on the given metadata. E.g. for the case of an input color printed by an offset press on coated paper, select a respective reference spectra set. Such a set may be the measured spectra of a printed ECI2002 target (as shown in Figure A8). [0109] 2. Apply the PCA to the entire set of reference spectra, resulting in the mean spectrum μ and three basis spectra B3 (3×36). [0110] 3. Set the mean spectrum μ to a zero spectrum. [0111] 4. Based on the input device combination (e.g. CMYK), select a suitable reference spectrum from the reference spectra set selected before. [0112] 5. Convert the reference spectrum to XYZRef. [0113] 6. Convert the Lab values to XYZ. [0114] 7. Subtract the XYZRef from XYZ, which yields ΔXYZ. [0115] 8. Calculate a difference spectrum Δr=ΔXYZ.Math.M.Math.B3, where M=(B CT)−1 according to equation (6). [0116] 9. Add the difference spectrum Δr and the reference spectrum, which yields the desired synthesized spectrum. [0117] 10. Repeat steps 4-9 for any given input color.

[0118] Note that using the given device values for the selection of the reference spectrum is a typical example. Other criteria for the selection may be used as well. Examples are to use the recipe for mixing the pigments of the ink, or selecting the ref. spectrum based on the smallest color difference ΔE from the input Lab.

[0119] FIG. 2 shows the use of a method for iterative clipping of negative fractions. The required input identical as describes with regard to FIG. 1. The process includes the steps 1 to 9 as describes with regard to FIG. 1 and the following steps: [0120] 10. Check the synthesized spectrum for values below zero or above the (possibly OBA-corrected) 100% limit. If no limit violations occur, use the synthesized spectrum. [0121] 11. If at least one of the zero and 100% limits are violated, clip the values of the synthesized spectrum as described and smooth it. [0122] 12. Use the clipped spectrum as the new reference spectrum and continue with step 5. [0123] 13. Repeat steps 4-12 for any given input color.

[0124] FIG. 3 shows the use of a method by applying the PCA in a non-linear domain. The required input identical as describes with regard to FIG. 1. The process includes the steps as follows: [0125] 1. Select a set of reference spectra, based on the given metadata. E.g. for the case of an input color printed by an offset press on coated paper, select a respective reference spectra set. Such a set may be the measured spectra of a printed ECI2002 target (figure on the right). [0126] 2. Transform all spectra of the selected set into the nonlinear domain using a non-linear mapping function (e.g. a root function). [0127] 3. Apply the PCA to the entire set of reference spectra, resulting in the mean spectrum μ and three basis spectra B3 (3×36). [0128] 4. Set the mean spectrum μ to a zero spectrum. [0129] 5. Based on the input device combination (e.g. CMYK), select a suitable reference spectrum from the reference spectra set selected before. [0130] 6. Convert the reference spectrum to XYZ.sub.Ref in the nonlinear domain. [0131] 7. Convert the input Lab values to XYZ. [0132] 8. Map the XYZ values into the nonlinear domain using the same or a similar mapping function as used for the spectra. [0133] 9. Subtract the XYZ.sub.Ref from XYZ, which yields ΔXYZ. [0134] 10. Calculate a difference spectrum Δr=ΔXYZ.Math.M.Math.B3, where M=(B C.sup.T).sup.−1 according to equation (6). [0135] 11. Add the difference spectrum Δr and the reference spectrum, which yields the desired synthesized spectrum in the nonlinear domain. [0136] 12. Transform the synthesized spectrum back into the linear domain using an inverse mapping function. [0137] 13. Calculate XYZ values from the synthesized linear spectrum and subtract the input XYZ values from it, which yields dXYZ. [0138] 14. If the difference dXYZ is greater than a given threshold, multiply it by a constant a and subtract it from the input XYZ values. Continue with step 8. [0139] 15. If the difference dXYZ is smaller than the threshold, it can be processed further by checking for violation of the limits. [0140] 16. If limits are violated, clipping and smoothing is applied to the synthesized spectrum. [0141] 17. The clipped and smoothed spectrum is mapped into the linear domain and used to replace the reference spectrum. Continue with step 9. [0142] 18. If no limits are violated, the synthesized spectrum is final. [0143] 19. Repeat steps 5-18 for any given input color.

[0144] FIG. 4 shows the use of different sets of spectra for analysis and reference. In this example, the spectral data set used for analysis of the PCA is different from the spectral data set used for selecting the reference spectrum. Other than that, the process steps are identical with the methods described before.

[0145] The figure shows how to use a separate data matrix exemplarily for the case checking and correcting for limit violations. However, it can be applied to the other methods as well.

[0146] FIG. 5 shows the method of measuring the success of spectral synthesis. The required input is:

[0147] A set of colors, described by their Lab values and by the device values (e.g. CMYK) that have been used to print the colors, and some metadata describing the type of print process used (e.g. Offset on coated paper). The Lab values are based on a selected illuminant/observer combination (e.g. D50/2°).

[0148] The process includes the steps: [0149] 1. Select a set of reference spectra, based on the given metadata. E.g. for the case of an input color printed by an offset press on coated paper, select a respective reference spectra set. Such a set may be the measured spectra of a printed ECI2002 target. [0150] 2. Apply one of the methods described above, but excluding any clipping, to synthesize a spectrum. [0151] 3. Repeat the synthesis for all of the given input colors, so that an entire set of synthesized spectra is generated. [0152] 4. Store the set of synthesized spectra [0153] 5. Calculate the quality metric Q.sub.syn using one of the described formulae. [0154] 6. Store the quality metric associated with the set of synthesized spectra. [0155] 7. Select another reference spectra set and repeat steps 2-6. [0156] 8. Repeat step 7 N times. [0157] 9. From the storage, select the synthesized set of spectra, which has the lowest associated quality metric.

[0158] Although this invention has been described with respect to preferred embodiments, those embodiments are illustrative only. No limitation with respect to the preferred embodiments is intended or should be inferred. It will be observed that numerous variations and modifications may be effected without departing from the scope of the invention as defined by the claims appended hereto.