Color conversion method and apparatus with a variable gray component replacement ratio

An amount of a black colorant is determined from input color image signals. Then, chromaticity values, for instance, on the L*H*C* color space, of a color that is obtained by subtracting the above black amount from the input color image signals and represented by C, M and Y are determined. Finally, colorant amounts of C, M and Y are determined from the chromaticity values thus determined.

BACKGROUND OF THE INVENTION 
The present invention relates to conversion from color image information to 
colorant signals of, for instance, cyan, magenta, yellow and black in 
digital color copiers, digital color printers, color facsimile machines, 
etc. 
Digital color copiers etc. using colorants of cyan (C), magenta (M), yellow 
(Y) and black (B) are associated with a problem that in outputting a 
high-density black or dark gray image, black reproduced with three 
colorants of C, M and Y (hereinafter called "process black") is not 
perfectly black, i.e., slightly colored. Further, since the process black 
is produced as a superposition of the three colorants of C, M and Y, a 
misregistration of the three colorants causes a color blur around a black 
portion, which is a problem in printing black characters. 
It is a common procedure to avoid the above problem that black is 
reproduced with a single colorant K (hereinafter called "single black") 
instead of process black. This procedure of using single black instead of 
process black to thereby decrease amounts of the colorants C, M and Y is 
called gray component replacement (GCR) or under color removal (UCR). 
FIGS. 4(a) and 4(b) illustrate a conventional GCR technique. FIG. 4(a) 
shows colorant signals of C, M and Y for reproducing a certain color on a 
document in a digital color copier. As shown in FIG. 4(b), respective 
portions of the colorant amounts of C, M and Y, that is, portions 
associated with the minimum of the colorant amounts of C, M and Y, are 
replaced with a colorant amount of K. Those respective portions are 
subtracted from the colorant signals of C, M and Y. 
However, since the above conventional technique is not properly supported 
by colorimetric theories, a desired color is not obtained and the chroma 
is much reduced. Various improvements have been proposed to avoid this 
problem. 
Among those is a technique disclosed by Sayanagi and Tamune in 
"Considerations (I) on Black Addition in Printing," Proceedings of First 
Color Engineering Conference, 1-7, pp. 33-36, 1984. In this under color 
addition (UCA) technique, C, M and Y are added to prevent the chroma 
reduction. 
In Japanese Patent Application Unexamined Publication No. Sho. 64-45642, 
color image signals are represented on the CIE 1976 L*a*b* uniform color 
space and colorant signals of C, M, Y and K are set so that their 
variations are approximately proportional to variations of chromaticity 
values on the L*a*b* uniform color space. With this technique, the 
colorant signals of C, M, Y and K can be determined by simple 
calculations. 
According to the conventional techniques described above, the colorant 
signals of C, M, Y and K can be determined with a relatively high accuracy 
when the ratio of replacing the process black with the single black 
(hereinafter called "GCR ratio") is fixed. However, for the following 
reasons, the GCR ratio needs to be changed, for instance, in digital color 
copiers. In copying a text, it is desired that black characters be 
reproduced without causing color blurs by achromatic printing (GCR=100%) 
in which process black components are fully replaced by single black. On 
the other hand, in copying a natural image, the GCR ratio should be small 
because a large GCR ratio will cause a rough image. 
Since the relationship between the three input image signals and the four 
colorant signals is not clearly defined, the types of conversion 
parameters to be changed and their variations are complex and unclear. 
Therefore, the conversion to the colorant signals of C, M, Y and K cannot 
be performed with a sufficient accuracy, to cause a problem that the color 
of output images varies with a variation of the GCR ratio. 
SUMMARY OF THE INVENTION 
An object of the present invention is to provide a clear relationship 
between input image signals and chromatic colorant signals to thereby 
enable easy determination of respective colorant signals. 
Another object of the invention is to determine, with high accuracy, 
amounts of chromatic colorants which represent a color of chromatic 
components. 
A further object of the invention is to minimize a variation of a printed 
color with respect to a variation of the GCR ratio. 
According to the invention, a color conversion method for converting input 
color signals representing an input image into amounts of a plurality of 
chromatic colorants and at least one achromatic colorant to reproduce the 
input image on an image supporting member with those colorants, comprises 
the steps of: 
determining an amount of the achromatic colorant from the input color 
signals; 
determining chromaticity values of a color of chromatic components obtained 
by subtracting the determined amount of the achromatic colorant from the 
input color signals; and 
determining amounts of the chromatic colorants for representing the color 
of the chromatic components from the determined chromaticity values. 
Further, according to the invention, a color conversion apparatus for 
converting input color signals representing an input image into amounts of 
a plurality of chromatic colorants and at least one achromatic colorant to 
reproduce the input image on an image supporting member with those 
colorants, comprises: 
means for determining an amount of the achromatic colorant from the input 
color signals; 
means for determining chromaticity values of a color of chromatic 
components obtained by subtracting the determined amount of the achromatic 
colorant from the input color signals; and 
means for determining amounts of the chromatic colorants for representing 
the color of the chromatic components from the determined chromaticity 
values.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
The present invention has been made based on the considerations and 
elucidations described below. 
First, the characteristics of the C, M, Y and K colorants are discussed 
from the colorimetric viewpoint, which has not been done much 
conventionally. To simplify the subject, the printer is discussed, which 
works based on an ideal subtractive color mixture system. 
Since commonly used K colorants, for instance, a carbon black, have a 
reflectance that has almost no dependence on the wavelength, the 
reflectance of a solid pattern of a K colorant can be approximated by 
.rho..sub.K. Since the Lambert-Beer's low holds in the ideal subtractive 
color mixture system, the following relationship is established between an 
amount k of the K colorant and a reflectance .rho.(k): 
EQU .rho.(k)=.rho..sub.K.sup.k (1) 
The following equations hold for a first color expressed by certain three 
colorants C, M and Y and a second color obtained by adding to the first 
color the K colorant of the amount k and expressed by the four colorants 
C, M, Y and K: 
EQU X(k)=.rho.(k).multidot.X (2a) 
EQU Y(k)=.rho.(k).multidot.Y (2b) 
EQU Z(k)=.rho.(k).multidot.Z (2c) 
where X, Y and Z are tristimulus values of the first color and X(k), Y(k) 
and Z(k) are tristimulus values of the second color. 
The tristimulus values X, Y and Z are converted to L*, a* and b* such that: 
EQU L*=116(Y/Y.sub.0).sup.1/3 -16 (3a) 
EQU a*=500{(X/X.sub.0).sup.1/3 -(Y/Y.sub.0).sup.1/3 } (3b) 
EQU b*=200{(Y/Y.sub.0).sup.1/3 -(Z/Z.sub.0).sup.1/3 } (3c) 
where X.sub.0, Y.sub.0 and Z.sub.0 are tristimulus values of reference 
white. 
Similarly, L*(k) , a*(k) and b*(k) are calculated from X(k), Y(k) and Z(k) 
such that: 
##EQU1## 
By performing conversion from the L*a*b* color space to a cylindrical 
coordinate system, a hue H*(k) and a chroma C*(k) are obtained such that: 
EQU H*(k)=tan.sup.-1 {b*(k)/a*(k)}=tan.sup.-1 (b*/a*)=H* (5a) 
EQU C*(k)=[{a*(k)}.sup.2 +{b*(k)}.sup.2 ].sup.1/2 =.rho.(k).sup.1/3 C*(5b) 
where H* and C* are a hue and a chroma of the first color, respectively. 
FIGS. 5(a) and 5(b) illustrate the above equations on the a*-b* plane and 
the L*-C* plane, respectively. Vertices of a hexagon drawn by a solid line 
in FIG. 5(a) represent chromaticity values of colors corresponding to the 
maximum densities of C, M, Y, R, G and B, respectively. The inside of the 
hexagon represents a color gamut of the three colors C, M and Y. Hexagons 
drawn by a dashed line and a chain line define color gamuts when the K 
colorant is added by k values of 0.5 and 1 (normalized so as to take 
values of 0 to 1), respectively. A tetragon drawn by a solid line, a 
dashed line and a chain line in FIG. 5(b) also define color gamuts of the 
three colors. From the above equations and FIGS. 5(a) and 5(b), it is 
understood that when the first color represented by the three colors C, M 
and Y changes to the second color by adding the K colorant, 
1) the hue H* does not change, and 
2) the color changes linearly on the L*-C* plane. 
From the discussions described above in detail, it is understood that the 
input color image signals can be converted to the output CMYK signals 
according to the following procedure by determining, in advance, features 
as to how the chromaticity values vary on a proper color space, for 
instance, the L*H*C* space, when the colorant signals C, M, Y and K are 
changed. (The input color signals are regarded as a combination of the 
chromatic components represented by C, M and Y and the achromatic 
component represented by K.) 
1) Determining the amount k of the K colorant from the input color image 
signals by a proper method (which may apparently be a known one). 
2) Determining the chromaticity values of a color (represented by the three 
colors C, M and Y) obtained by subtracting the K colorant of the amount k 
from the input color image signals, based on the features of the 
chromaticity variation. 
3) Determining amounts c, m and y of the respective colorants C, M and Y 
from the chromaticity values obtained in step 2) by a proper method (which 
may apparently be a conventional method such as a linear matrix method). 
The above discussions are made using the L*a*b* color space (and the L*H*C* 
color space which is the cylindrical coordinate system corresponding to 
the former). It is apparent that a similar procedure can be obtained for 
each of other various color spaces such as the L*u*v*, YIQ and XYZ color 
spaces by simply switching the parameters of the above equations. 
The above procedure is summarized in FIG. 1. In step S11, the achromatic 
colorant amount is determined from the input color signals. In step S12, 
the chromaticity values of a color obtained by subtracting the 
thus-determined achromatic colorant amount from the input color signals. 
Finally, in step S13, the chromatic colorant amounts to represent that 
color are determined from the chromaticity values determined in step S12. 
An embodiment of the invention is described below in which the three 
chromatic colorants C, M and Y and the one achromatic colorant K are used 
and the L*a*b* color space or the L*H*C* color space which is the 
cylindrical coordinate system of the former is employed. 
As described above, the chromaticity values L*, a* and b* of a first color 
represented by the three colors C, M and Y are correlated on the L*a*b* 
color space with the chromaticity values L*(k), a*(k) and b*(k) of a 
second color obtained by adding the colorant K by the amount k to the 
first color such that: 
EQU L*(k)=.rho.(k).sup.1/3 (L*+16)-16 (6a) 
EQU H*(k)=H* (6b) 
EQU C*(k)=.rho.(k).sup.1/3 C* (6c) 
where .rho.(k) denotes the reflectance of the colorant K of the amount k. 
A description is made below of the case of reproducing input color signals 
O with the K colorant of the maximum amount and the three chromatic 
colorants, i.e., by the achromatic printing (GCR=100%). First, 
substitution of chromaticity values L*.sub.0, H*.sub.0 and C*.sub.0 of the 
input color signals O into L*(k), H*(k) and C*(k) of equations 6a-6c leads 
to the following simultaneous three linear equations for the chromaticity 
values L*, H* and C* of the color (first color) represented by the three 
colors C, M and Y: 
EQU L*=.rho.(k).sup.-1/3 (L*.sub.0 +16)-16 (7a) 
EQU H*=H*.sub.0 (7b) 
EQU C*=.rho.(k).sup.-1/3 C*.sub.0 (7c) 
Dashed lines drawn on the a*-b* plane of FIG. 3(a) and the L*-C* plane of 
FIG. 3(b) represent equations 7a-7c. Point in each of FIGS. 3(a) and 3(b) 
represents the chromaticity values of the input color signals. Vertices of 
a hexagon in FIG. 3(a) represent chromaticity values of the maximum 
density colors of C, M, Y, R, G and B. The inside of the hexagon 
represents a color gamut of the three colors C, Y and Y. A tetragon in 
FIG. 3(b) also defines the color gamut of the three colors. Point S in 
each of FIGS. 3(a) and 3(b) represents chromaticity values of a color 
associated with the maximum chroma on a plane of H*=H*.sub.0. 
An intersecting point A of the dashed line and the outline of the three 
color gamut in FIG. 3(b) represents the chromaticity values of the color 
represented by the three colors C, M and Y. Therefore, .rho.(k) is 
obtained by substituting a chromaticity value L*.sub.A of point A into 
equation 7a or by substituting a chromaticity value C*.sub.A of point A 
into equation 7c. From the Lambert-Beer's law, the amount k is expressed 
such that: 
EQU k=log .rho.(k)/log .rho..sub.K. (8) 
Finally, the amount k of the K colorant in the case of the achromatic 
printing is determined if .rho..sub.K is measured in advance. A look-up 
table (LUT) corresponding to the above equation may be prepared. 
Next, a description is made of a case where the GCR ratio is less than 
100%, i.e., part of the achromatic component is not replaced with single 
black. In this case, an amount k' of the K colorant takes a value larger 
than 0 and smaller than k. From the amount k obtained above, the amount k' 
is expressed by: 
EQU k'=f(k) (9) 
where f(k) is a function suitable for the input color signals and 
determined in advance. A LUT may be prepared for the function f(k). 
Chromaticity values L*.sub.A', C*.sub.A' and H*.sub.A' (=H*) of a color A' 
represented by the three colors C, M and Y are determined by calculating 
.rho.(k') from the amount k' obtained above, and then substituting 
.rho.(k') into equations 7a-7c. 
To determine the colorant amounts of C, M and Y from the above-obtained 
L*.sub.A, H*.sub.A and C*.sub.A or L*.sub.A', H*.sub.A' and C*.sub.A', the 
known techniques using the linear matrix operation, nonlinear matrix 
operation or direct mapping may be used. 
With the above-described procedure, highly accurate color conversion can be 
realized in which the output color does not vary with respect to a 
variation of the GCR ratio and has only a small color difference from the 
input color signals. 
FIG. 2 shows an example of an apparatus for performing the procedure 
described above. 
The color conversion apparatus of FIG. 2 consists of the following units. A 
first achromatic component reflectance calculating unit 11 calculates the 
achromatic component reflectance .rho.(k) for the GCR ratio of 100%. An 
achromatic colorant amount calculating unit 12 calculates the achromatic 
colorant amount k based on the achromatic component reflectance calculated 
by the unit 11. An achromatic colorant amount conversion unit 13 converts 
the achromatic colorant amount k to the achromatic colorant amount k' 
corresponding to a specified GCR ratio. A second achromatic color 
component reflectance calculating unit 21 calculates .rho.(k') 
corresponding to the specified GCR ratio based on the achromatic colorant 
amount k' calculated by the unit 13. A chromaticity values determining 
unit 22 calculates the chromaticity values of a color of the chromatic 
components obtained by subtracting colorant amounts corresponding to the 
achromatic colorant amount k' from the input color signals. A color signal 
conversion unit 3 calculates the chromatic colorant amounts for 
representing the color of the chromatic components from the chromaticity 
values determined by the unit 22. 
The first achromatic component reflectance calculating unit 11 calculates 
the achromatic component reflectance .rho.(k) for the GCR ratio of 100% by 
substituting into equation 7c the chromaticity value C*.sub.0 of the input 
color signals and the chromaticity value C*.sub.A of the intersecting 
point A in FIG. 3(a). Alternatively, the achromatic component reflectance 
.rho.(k) may be calculated using equation 7a. 
The achromatic colorant amount calculating unit 12 determines the 
achromatic colorant amount k for the GCR ratio of 100% by substituting the 
achromatic component reflectance .rho.(k) calculated by the unit 11 into 
equation 8. The reflectance .rho..sub.K is measured in advance and stored 
in a proper memory means, and is read from the memory means when it is 
substituted into equation 8. The achromatic colorant amount calculating 
unit 12 may be so constructed as to reference a LUT representing equation 
8. 
The achromatic colorant amount conversion unit 13 calculates the achromatic 
colorant amount k' using equation 9. The function f(k) is determined in 
advance as a function suitable for the input color signals, and can be set 
properly by an operator in accordance with the input color signals. The 
unit 13 may be so constructed as to reference a LUT representing equation 
9. 
The second achromatic component reflectance calculating unit 21 calculates 
.rho.(k') from the above-determined amount k' using equation 8. The unit 
21 may be so constructed as to reference a LUT representing equation 8. 
The chromaticity values determining unit 22 determines the chromaticity 
values L*.sub.A', C*.sub.A' and H*.sub.A' (=H*) of the color A' 
represented by the three colors C, M and Y by substituting .rho.(k') into 
equations 7a-7c. 
The color signal conversion unit 3 determines the colorant amounts of C, M 
and Y from L*.sub.A', C*.sub.A' and H*.sub.A'. The unit 3 can be 
constructed easily by employing the conventional techniques based on the 
linear matrix operation, nonlinear matrix operation or direct mapping. 
While in the above embodiment the L*a*b* color space (and the L*H*C* color 
space which is the cylindrical coordinate system of the former) is used, 
other various color spaces such as the L*u*v*, YIQ and XYZ color spaces 
can also be used simply by switching the parameters of the equations. 
While in the above embodiment the amount k is calculated according to the 
Lambert-Beer's law, it may be calculated according to the Yule-Nielsen's 
equation or other equations. Alternatively, the amount k may be obtained 
by other various methods, for instance, by referencing a LUT provided by 
measuring .rho.(k) in advance. While in the above embodiment k' is given 
as a function of k, it may be given as a function of the lightness L* or 
chroma C* of the input color signals, or a function of both. 
In the above example, in some cases, for instance, when the input color 
signals are outside the color gamut of an output device, a color needs to 
be mapped to a point inside the color gamut of the output device. The 
color conversion apparatus can easily be adapted to perform mapping of the 
color A or A' to a color inside the color gamut of the output device in 
addition to the determination of the chromaticity values of the color A or 
A' that is represented by the three colors C, M and Y. 
As described above, according to the invention, the input color signals are 
separated into the color of the chromatic components and the color of the 
achromatic component, and then the chromaticity values of the color of the 
chromatic components are determined. The chromatic colorant amounts are 
determined from the chromaticity values thus determined. Therefore, the 
colorant amounts can be determined easily, and the color conversion can be 
performed with high accuracy and with only a small color difference from 
the input color signals. Further, even if the achromatic colorant amount 
is changed, the output color can be kept approximately equal to the input 
color signals, i.e., almost no variation occurs in the output color.