Method for the reproduction of originals which, with respect to their color content, are scanned according to a tristimulus method

• US 4,409,614 A
• Filed: 12/07/1981
• Issued: 10/11/1983
• Est. Priority Date: 10/10/1978
• Status: Expired due to Fees

• Current Assignee: Friedrich W. Vorhagen, Hans M. Hutten, Helmut Eichler
• Original Assignee: Friedrich W. Vorhagen, Hans M. Hutten, Helmut Eichler
• Inventors: Vorhagen, Friedrich W., Eichler, Helmut, Hutten, Hans M.
• Primary Examiner(s): Martin, John C.
• Application Number:
  US06/328,157
• Time in Patent Office: 673 Days
• Field of Search: 358/76, 358/80
• US Class Current: 358/530
• CPC Class Codes: H04N 1/60 Colour correction or control H04N1/54 takes precedence
• CPC Class Codes: H04N 1/6027 Correction or control of colour gradation or colour contrast H04N1/6058 takes precedence
• CPC Class Codes: H04N 1/622 with simulation on a subsidiary picture reproducer

Abstract

The color scanning signals generated by scanning the original are first converted into three primary color signals having actual color values in a predetermined color coordinate system corresponding substantially identically to theoretical color values of the original. It is only after this conversion that the primary signals or signals derived from these signals are converted to another color rendition system, or the gradation is altered, or the color rendition of individual colors in the overall image or in discrete areas is altered, or any other non-linear processing takes place.

Claims

1. Method for reproduction of originals, including originals of non-metameric colour composition, where the original is scanned in each case, with respect to its colour content, according to a tristimulus method and after processing of the scanning signals a reproduction is obtained, via colour mixture, by means of a predetermined colour rendition system, characterized in that the scanning signals (E_R,E_G,E_B) are converted, into three primary colour signals (e.g. X, Y, Z) having actual colour values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of the original, and that adaptation of the primary colour signals or the signals deriving from these to at least one colour rendition system and/or measures to alter the gradation and/or objective measures to alter the colour rendition of individual colours in the overall image or in discrete areas of the image and/or any other further non-linear processing of the primary colour signals or the signals deriving from these are only carried out after said scanning signals have been converted into the primary colour signals having actual colour values in said predetermined colour coordinate system corresponding substantially identically to said theoretical colour values of the original.

2. Method according to claim 1, characterized in that the primary colour signals are stored temporarily before being further processed.

3. Method according to claim 1, characterized in that with colour rendition systems having a mostly subtractive colour mixture, said objective measures are undertaken after the primary colour signals (X,Y,Z) have been converted into colouring material concentration signals or colour separation density signals (D_C,D_M,D_G) adapted to the colour rendition system.

4. Method according to claim 3, characterized in that the colouring material concentration signals or colour separation density signals (D_C,D_M,C_Y), varied by means of an objective alteration measures, give rise to correspondingly varied primary colour signals (X,Y,Z), by means of which, together with the remaining unaltered stored primary colour signals, a monitor image is generated, via additive colour mixture which shows the operator the alterations - effected via the objective alteration measures in the colouring material concentration signals of the colour separation density signals - in the associated reproduction, generated via the mainly subtractive colour mixture of the colour rendition system, of the original.

5. Method according to claim 4, characterized in that the primary colour signals, true-to-colour with respect to the original and having actual colour values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of the original, are stored in unchanged form until the monitor image corresponds to the desired reproduction result.

6. Method for obtaining three primary colour signals having actual colour values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of an original, including an original of non-metameric colour composition, by scanning said original with respect to its colour content in a tristimulus procedure with scanners that are incorrect with respect to visual colour sensitivity and electronically processing the scanning signals thus produced, characterized in that every scanning signal is subjected for purposes of correcting the gray balance to a gradation equalization (γ

_R, γ

_G, γ

_B), and in that, for improving the colour rendition properties of chromatic object colours, a linear transformation is carried out with the scanning signals.

7. Method for obtaining primary colour signals having actual colour values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of the original, according to claim 6, characterized in that before the gradation equalization, the scanning signals (E_R,E_G,E_B) are subjected to a white balance (K_R,K_G,K_B) and/or that the gradation equalization ensues via exponention of the scanning signals with an exponent (γ

_R, γ

_G, γ

_B) whose reciprocal (β

_R, β

_G, β

_B) is equal to the slope of the transmission characterizing line of the respective uncorrected scanner for achromatic film colours of the original when said transmission characterizing line has a logarithmic dependence upon said scanner'"'"'s reciprocal on the density (D) of the shade of gray to be rendered.

8. Method for obtaining primary colour signals having actual colour values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of the original, according to claim 7, characterized in that an exponent (γ

_R, γ

_G, γ

_B) is calculated from the spectral data of the respective scanner and from the colouring matter of the original.

9. Method for obtaining three primary colour signals having actual colour values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of the original, according to claim 7, characterized in that the values for the exponent (γ

_R, γ

_G, γ

_B) are experimentally determined by means of a wedge filter in the original or attached at its edge.

10. Method for obtaining three primary colour signals having actual colour values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of the original, according to claim 6, characterized in that no negative coefficients greater than about 3 times the value of the main diagonal are present in a matrix (M) effecting the linear transformation.

11. Method for obtaining three primary colour signals having actual colour values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of the original, according to claim 6, characterized in that a matrix (M) is utilized for effecting the linear transformation, matrix coefficients of said matrix for certain given colours being optimized.

12. Method for obtaining three primary colour signals, having actual colour values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of the original, according to claim 11, characterized in that the matrix coefficients are determined such that the spectral sensitivity curves of the scanners are approximated as well as possible to correct visual-sensitivity-based (vsb) colour mixture curves for additive primary valences.

13. Method for obtaining primary colour signals having actual colour values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of the original, according to claim 10, characterized in that optimization of the matrix coefficients is undertaken for at least three subtractive fundamental colours, preferably of equal visual brightness, and three secondary colours of first order formed from them.

14. Method for obtaining three primary colour signals having actual colour values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of the original, according to claim 10, 11 or 13, characterized in that, for the optimization of the matrix coefficients, the mean colour rendition index is determined and optimzied and/or that the optimizatin is carried out by means of an evolution strategy.

15. Device for carrying out the method according to claim 6 or 7 with a tristimulus scanning means, characterized by a correction circuit (γ

_R, γ

_B, γ

_G) being provided in each output lead for the scanning signals (E_R, E_G, E_B) and by a matrix circuit (M) being provided which is connected at the outputs of the correction circuits (γ

_R, γ

_G, γ

_B).

34. Method for obtaining three primary colour signals having actual colour values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of the original, according to any one of claims 6-9 or 12, wherein said scanning signals are gradation-equalized.

35. Method for obtaining three primary colour signals having actual color values in a predetermined color coordinate system corresponding substantially identically to theoretical colour values of the original, according to any one of claims 7, 8 or 9, characterized in that a matrix is utilized for effecting the linear transformation, matrix coefficients of said matrix for certain colours being optimized.

16. Method for determining signals, corresponding to colouring material concentrations, of a colour rendition system comprising three primary colour signals and based mainly or completely on a subtractive colour mixture, especially for synthesizing primary colour signals having actual colour values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of an original, preferably having non-metameric colours, to be reproduced, characterized by the following steps:

conversion of the primary colour signals (X,Y,Z) into colour signals (R_P,G_P,B_P) adapted to the basic colouring materials of the rendition system with replacement of the spectral density distributions of the individual basic colouring materials of the colour rendition system by three optimal colour-like model colouring materials without secondary conversion of the thus-obtained colour signals (R_P,G_P,B_P) into corresponding colour density signals (d_RP,d_GP,d_BP) and conversion of the colour density signals into model colouring material concentration signals (C_CM,C_MM,C_YM) with replacement of the colour densities of the optimal colour-like model colouring materials, without secondary densities, in the individual wavelength ranges by optimal colour-like model colouring materials that each have a main and two secondary densities which are constant over the respective partial wavelength range, and of which one is assigned in each case, by approximation, to the density of the three basic colouring materials.

17. Method for determining signals, corresponding to colouring material concentrations, according to claim 16, characterized in that the transformation of the primary colour signals into colour value signals and the conversion of the colour density signals into model colouring material concentration signals ensues via two linear transformations of these signals, the matrix coefficients of the first linear transformation (M₁) being determined by the choice of wavelength range limits (λ

₂, λ

₃) and the matrix coefficients of the second linear transformation M₂ being determined by the ratio of main and secondary densities of the model colouring material in the individual wavelength ranges for the respective colour rendition system.

18. Method for determining signals, corresponding to colouring material concentrations, according to claim 16 or 17, characterized in that each model colouring material concentration signal (C_CM, C_MM, C_YM) is varied according to a characteristic curve (K_C, K_M, K_Y) which is laid down such that primary colour signals corresponding to gray scale values lead to colouring material concentration signals that generate the same gray scale values in the respective colour rendition system.

19. Method for determining signals, corresponding to colouring material concentrations, according to claim 16 or 17, characterized in that the model colouring material concentration signals or the colouring material concentration signals are converted into corresponding separation density signals.

20. Method for determining signals, corresponding to colouring material concentrations, according to claim 16 or 17, characterized by a linear transformation of the model colouring material concentration signals of the colouring material concentration signals or the colour separation density signals by means of a correction matrix (M₃) whose coefficients are determined such that the fundamental colours laid down by the primary colouring materials of the colour rendition system, and/or secondary colours of first order from these, are rendered true-to-colour.

21. Method for determining signals, corresponding to colouring material concentrations, according to claim 16, characterized in that for the respective colour rendition system the coefficients of the matrices (M₁,M₂ and/or M₃) are determined by means of an optimization strategy for given colours.

22. Method for determining signals, corresponding to colouring material concentrations, according to claim 21, characterized in that an evolution strategy is carried out for the optimization of the matrix coefficients.

23. Method for determining signals, corresponding to colouring material concentrations, according to claim 21 or 22, characterized in that the optimization strategy is carried out at least for three subtractive primary colours, preferably of equal visual brightness, and three secondary colours of first order obtained from these.

24. Method for determining signals, corresponding to colouring material concentrations, according to claim 16, characterized in that the separation density signals obtained are compared with electronically stored separation densities of discrete secondary colours of the colour rendition system (catalogue colours).

25. Method for determining signals, corresponding to colouring material concentrations, according to claim 24, characterized by a linear interpolation between the established separation density signals D_CM,D_MM,D_YM) and the nearest separation densities of the catalogue colours.

26. Device for determining signals, corresponding to colouring material concentrations, of a colour rendition system comprising three primary colour signals and based mainly on a subtractive colour mixture, characterized by a first matrix circuit (M₁) for transforming the primary colour signals (e.g. X,Y,Z) into colour signals (R_P,G_P,B_P) adapted to the primary colouring materials of the colour rendition system, the matrix coefficients of the first matrix circuit (M₁) being determined such that the spectral density distributions of the individual primary colouring materials of the colour rendition system are replaced by three optimal colour-like model colouring materials without secondary densities and assigned to different wavelength ranges, by logarithmizing circuits (-log (E_R), -log (E_G) and -log (E_B)), connected at the outputs for the colour signals of the first matrix circuit, for transforming the colour signals into corresponding colour density signals, (d_RP,d_GP,d_BP), and by a second matrix circuit (M₃) for transforming the colour density signals into model colouring material concentration signals (C_CM,C_MM,C_YM), the matrix coefficients of the second matrix circuit being determined such that the colour densities of the optimal colour-like model colouring material, without secondary densities, of the individual partial wavelength ranges are replaced by optimal colouring like model colouring materials which have a main and secondary densities constant over the respective partial wavelength ranges, the main and the two secondary densities being assigned in approximation to the densities of the three primary colouring materials in the corresponding wavelength range.

27. Device for determining signals, corresponding to colouring material concentrations, according to claim 26, characterized in that the matrix coefficients of the first matrix circuit (M₁) are determined by the choice of limits for the partial wavelength ranges, those of the second matrix circuit (M₂) by the ratio of main to secondary densities of the model colouring materials in the individual partial wavelength ranges for the respective colour rendition system.

28. Device for determining signals, corresponding to colouring material concentrations, according to claim 26 or 27, characterized in that a circuit (K_C,K_M,K_Y) is provided at the outputs for each model colouring material concentration signal of the second matrix circuit (M₂), which varies the incoming signal according to a prescribed characteristic curve that is laid down such that primary colour signals corresponding to gray scale values are converted into colouring material signals which generate gray scale values in the respective colour rendition system.

29. Device for determining signals, corresponding to colour material concentrations, according to claim 26 or 27 characterized by circuits for transforming the model colouring material concentration signals or colouring material concentration signals into corresponding separation density signals.

30. Device for determining signals, corresponding to colouring material concentrations according to claim 26, characterized by a third matrix circuit (M₃) to which the separation density signals can be supplied, the matrix coefficients of the third matrix circuit being determined such that the fundamental colours laid down by each basic colouring material are rendered as true-to-colour as possible.

31. Device according to claim 30, characterized in that for colour rendition systems with purely subtractive colour mixture the second matrix circuit (M₂) and the third matrix circuit (M₃) are combined as a common matrix circuit.

32. Device for determining signals, corresponding to colouring material concentrations, according to claim 26, characterized by a memory (Sp) in which the separation densities of catalogue colours for the respective colour rendition system are stored, by a comparator circuit which compares the determined model densities (D_CM,D_MM,D_YM) with the catalogue colours, and by an interpolation circuit which carries out an interpolation between the nearest catalogue colour and the determined separation densities.

33. Print simulator, characterized by a device according to any one of claims 26, 27, or 30-32 and a monitor working according to the principle of additive colour mixture, which is connected at the inputs for the primary colour signals (X,Y,Z) of the first matrix circuit (M₁) via corresponding adaptation networks.

36. Method for reproduction of originals, including originals of non-metameric colour composition, wherein the original is scanned in each case, with respect to its colour content, according to a tristimulus method and after processing of the scanning signals a reproduction is obtained, via a colour mixture, by means of a predetermined colour rendition system, characterized in that the scanning signals (E_R,E_G,E_B) are converted, into three primary colour signals (e.g. X,Y,Z) having actual colour values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of the original, in that adaptation of the primary colour signals or the signals deriving from these to at least one colour rendition system and/or measures to alter the gradation and/or objective measures to alter the colour rendition of individual colours in the overall image or in discrete areas of the imaage and/or any other further non-linear processing of the primary colour signals or the signals deriving from these are only carried out after said scanning signals have been converted into the primary colour signals (e.g. X,Y,Z) having actual coloru values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of the original, in that every scanning signal is subjected for purposes of correcting the gray balance to a gradation equalization (γ

_R, γ

_G, γ

_B), and in that, for improving the colour rendition properties of chromatics object colours, a linear transformation is carried out with the scanning signals.

37. Method according to claim 36, characterized in that before the gradation equalization the scanning signals (E_R,E_G,E_B) are subjected to a white balance (K_R,K_G,K_B) and/or that the gradation equalization ensues via exponention of the scanning signals with an exponent (γ

_R,γ

_G,γ

_B) whose reciprocal (β

_R,β

_G,β

_B) is equal to the slope of the transmission characterizing line of the respective uncorrected scanner for achromatic film colours of the original when said transmission characterizing line has a logarithmic dependence upon said scanner'"'"'s reciprocal on the density (D) of the shade of gray to be rendered.

38. Method according to claim 37, characterized in that an exponent (γ

_R,γ

_G,γ

_B) is calculated from the spectral data of the respective scanner and from the colouring matter of the original.

39. Method according to claim 37, characterized in that the values for said exponent (γ

_R,γ

_G,γ

_B) are experimentally determined by means of a wedge filter in the original or attached at its edge.

40. Method according to claim 36, characterized in that no negative coefficients greater than about 3 times the value of the main diagonal are present in a matrix (M) effecting the linear transformation.

41. Method according to claim 36, characterized in that a matrix (M) is utilized for effecting the linear transformation, matrix coefficients of said matrix for certain given colours being optimized.

42. Method according to claim 41, characterized in that the matrix coefficients are determined such that the spectral sensitivity curves of the scanners are approximated as well as possible to correct visual-sensitivity based (vsb) colour mixture curves for additive primary valences.

43. Method according to claim 40, characterized in that optimization of the matrix coefficients is undertaken for at least three subtractive fundamental colours, preferably of equal visual brightness, and three secondary colours of first order formed from them.

44. Method according to any one of claims 40, 41 or 43, characterized in that for the optimization of the matrix coefficients the mean colour rendition index is determined and optimized and/or that the optimization is carried out by means of an evolution strategy.

45. Method according to any one of claims 36 or 37, characterized by a γ

correction circuit (γ

_R,γ

_B,γ

_G) being provided in each output lead for the scanning signals (E_R,E_G,E_B) and by a matrix circuit (M) being provided which is connected at the outputs of the correction circuits (γ

_R,γ

_G,γ

_B).

46. Method according to claim 36, characterized in that the primary colour signals are stored temporarily before being further processed.

47. Method according to claim 36, characterized in that with colour rendition systems having mostly subtractive colour mixture, said objective measures are undertaken after the primary colour signals (X,Y,Z) have been converted into colouring materials concentration signals or colour separation density signals (D_C,D_M,D_G) adapted to the colour rendition system.

48. Method according to claim 47, characterized in that the colouring material concentration signals or colour separation density signals (D_C,D_M,D_Y), varied by means of the objective alteration measures, give rise to correspondingly varied primary colour signals (X,Y,Z) by means of which, together with the remaining, unaltered stored primary colour signals, a monitor image is generated, via additive colour mixture, which shows the operator the alterations--effected via the objective alteration measures in the colouring material concentration signals or the colour separation density signals--in the associated reproduction, generated via the mainly substractive colour mixture of the colour rendition system, of the original.

49. Method according to claim 48, characterized in that the primary colour signals, true-to-colour with respect to the original and having actual colour values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of the original, are stored in unchanged form until the monitor image corresponds to the desired reproduction result.

50. Method for determining signals, corresponding to colouring material concentrations, of a colour rendition system comprising three primary colour signals and based mainly or completely on a subtractive colour mixture, especially for synthesizing primary colour signals having actual colour values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of an original, preferably having no metameric colours, to be reproduced, characterized by the following steps:

conversion of the primary colour signals (X,Y,Z) into colour signals (R_P,G_P,B_P) adapted to the basic colouring materials of the rendition system with replacement of the spectral density distributions of the individual basic colouring materials of the colour rendition system by three optimal colour-like model colouring materials without secondary densities and assigned to different wavelengths, conversion of the thus-obtained colour signals (R_P,G_P,B_P) into corresponding colour density signals (d_RP,d_G-P,d_BP) and conversion of the colour density signals into model colouring material concentration signals (C_CM,C_MM,C_YM) with replacement of the colour densities of the optimal colour-like model colouring materials, without secondary densities, in the individual wavelength ranges by optimal colour-like model colouring materials that each have a main and two secondary densities which are constant over the respective partial wavelength range, and of which one is assigned in each case, by approximation, to the density of the three basic colouring materials, wherein any non-linear processing of the primary colour signals or any signals deriving from these is only carried out after said scanning signals have been converted into the primary colour signals having actual colour values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of the original.

51. Method according to claim 50, characterized in that the primary colour signals are stored temporarily before being further processed.

52. Method according to claim 51, characterized in that with colour rendition systems having a mostly subtractive colour mixture, said objective measures are undertaken after the primary colour signals (X,Y,Z) have been converted into colouring materials concentration signals or colour separation density signals (D_C,D_M,D_G) adapted to the colour rendition system.

53. Method according to claim 52, characterized in that the colouring material concentration signals or colour separation density signals (D_C,D_M,D_Y) by means of the objective alteration measures, give rise to correspondingly varied primary colour signals (X,Y,Z) by means of which, together with the remaining unaltered stored primary colour signals a monitor image is generated, via additive colour mixture, which shows the operator the alterations--effected via the objective alteration measures in the colouring material concentration signals or the colour separation density signals--in the associated reproduction, generated via the mainly subtractive colour mixture of the colour rendition system, of the original.

54. Method according to claim 53, characterized in that the primary colour signals, true-to-colour with respect to the original and having actual colour values in a predetermined colour coordinate system corresponding substantially identically to theoretical colour values of the original, are stored in unchanged form until the monitor image corresponds to the desired reproduction results.

55. Method according to claim 50, wherein every scanning signal is subjected for purposes of correcting the gray balance to a gradation equalization (γ

_R,γ

_G,γ

_B), and in that, for improving the colour rendition properties of chromatic object colours, a linear transformation is carried out with the scanning signals.

56. Method according to claim 55, characterized in that, before the gradation equalization, the scanning signals (E_R,E_G,E_B) are subjected to a white balance (K_R,K_G,K_B) and/or that the gradation equalization ensues via exponention of the scanning signals with an exponent (γ

_R,γ

_G,γ

_B) whose reciprocal (β

_R,β

_G,β

_B) is equal to the slope of the transmission characterizing line of the respective uncorrected scanner for achromatic film colours of the original when said transmission characterizing line has a logarithmic dependence upon said scanner'"'"'s reciprocal on the density (D) of the shade of gray to be rendered.

57. Method according to claim 56, characterized in that an exponent (γ

_R,γ

_G,γ

_B) is calculated from the spectral data of the respective scanner and from the colouring matter of the original.

58. Method according to claim 56, characterized in that the values for an exponent (γ

_R,γ

_G,γ

_B) are experimentally determined by means of a wedge filter in the original or attached at its edge.

59. Method according to claim 55, characterized in that no negative coefficients greater than about 3 times the value of the main diagonal are present in a matrix (M) effecting the linear transformation.

60. Method according to claim 55, characterized in that the matrix (M) is utilized for effecting the linear transformation, matrix coefficients of said matrix for certain given colours being optimized.

61. Method according to claim 60, characterized in that the matrix coefficients are determined such that the spectral sensitivity curves of the scanners are approximated as well as possible to correct visual-sensitivity-based (vsb) colour mixture curves for additive primary valences.

62. Method according to claim 59, characterized in that optimization of the matrix coefficients is undertaken for at least three subtractive fundamental colours, preferably of equal visual brightness, and three secondary colours of first order formed from them.

63. Method according to claim 59, characterized in that, for the optimization of the matrix coefficients, the mean colour rendition index is determined and optimized and/or that the optimization is carried out by means of an evolution strategy.

64. Method according to claim 55, characterized in that the transformation of the primary colour signals into colour value signals and the conversion of the colour density signals into model colouring material concentration signals ensues via two linear transformations of these signals, the matrix coefficients of the first linear transformation (M₁) being determined by the choice of wavelength range limits (λ

₂,λ

₃) and the matrix coefficients of the second linear transformation (M₂) being determined by the ratio of main and secondary densities of the model colouring material in the individual wavelength ranges for the respective colour rendition system.

65. Method according to claim 55, characterized in that each model colouring material concentration signal (C_CM,C_MM,C_YM) is varied according to a characteristic curve (K_C,K_M,K_Y) which is laid down such that primary colour signals corresponding to gray scale values lead to colouring material concentration signals that generate the same gray scale values in the respective colour rendition system.

66. Method according to claim 55, characterized in that the model colouring material concentration signals or the colouring material concentration signals are converted into corresponding separation density signals.

67. Method according to claim 55, characterized by a linear transformation of the model colouring material concentration signals or the colouring material concentration signals or the colour separation density signals by means of a correction matrix (M₃) whose coefficients are determined such that the fundamental colours laid down by the primary colouring materials of the colour rendition system, and/or secondary colours of first order from these, are rendered true-to-colour.

68. Method according to claim 55, corresponding to colouring material concentrations, characterized in that, for the respective colour rendition system, the coefficients of the matrices (M₁,M₂ and/or M₃) are determined by means of an optimization strategy for given colours.

69. Method according to claim 68, characterized in that an evolution strategy is carried out for the optimization of the matrix coefficients.

70. Method according to claim 68, corresponding to colouring material concentrations characterized in that the optimization strategy is carried out at least for three subtractive primary colours, preferably of equal visual brightness, and three secondary colours of first order obtained from these.

71. Method according to claim 55, corresponding to colouring material concentrations characterized in that the separation density signals obtained are compared with electronically stored separation densities of discrete secondary colours of the colour rendition system (catalogue colours).

72. Method according to claim 71, corresponding to colouring material concentrations, characterized by a linear interpolation between the established separation density signals (D_CM,D_MM,D_YM) and the nearest separation densities of the catalogue colours.