CN100589521C - Method for printing and outputting L*a*b* image with high fidelity - Google Patents

Abstract

The invention discloses a method for printing and outputting an L<*>a<*>b<*> image in a high-fidelity manner. The method is carried out according to the following steps: step 1, firstly arranging a CMYK electronic color target, and then measuring the L<*>a<*>b<*> value of each color block aiming at a colored output device and through taking the CMYK electronic color target arranged as an input image after being printed and output, and corresponding and storing the CMYK value and the L<*>a<*>b<*> value of each color block to obtain source data for describing the characteristic of the device; step 2, reading the data of the L<*>a<*>b<*> image and carrying out color gamut compression; and step 3, establishing color conversion relation between L<*>a<*>b<*> and CMYK to convert the L<*>a<*>b<*>image into a CMYK image, and printing and outputting. The invention has the advantages that a CMYK printer is taken as an output device, thereby achieving the highly-accurate conversion from the L<*>a<*>b<*> and the CMYK, and achieving the purpose of printing the L<*>a<*>b<*> image in a high-fidelity manner.

Description

The method of high-fidelity print outputting L * a*b* image

Technical field

The invention belongs to technical field of image processing, relate to a kind of high-fidelity print outputting L ^*a ^*b ^*The method of image.

Background technology

At present, various coloured images are mainly with RGB, CMYK and L ^*a ^*b ^*Three kinds of color spaces carry out record, and RGB and CMYK are the color spaces that depends on equipment, so this class image can directly be exported on equipment such as display and printer; L ^*a ^*b ^*Being a kind of even color space, also be a kind of device-independent color space, so this class image can not directly be exported by color devices.Because L ^*a ^*b ^*The space is non-device color spaces, therefore when this class image of output, must convert thereof into the device color spaces value earlier.But be output equipment with the CMYK printer at present, with L ^*a ^*b ^*Conversion method complexity to CMYK is time-consuming, precision is low and the color difference is big, is difficult to realize high-fidelity printing L ^*a ^*b ^*The order ground of image.

Summary of the invention

The purpose of this invention is to provide a kind of high-fidelity print outputting L ^*a ^*b ^*The method of image, solved existing method with image from L ^*a ^*b ^*Be transformed into the problem that complexity is time-consuming in the CMYK process, precision is low and the color difference is big.

The technical solution adopted in the present invention is a kind of high-fidelity print outputting L ^*a ^*b ^*The method of image, this method is implemented according to following steps,

Step 1, at first CMYK electronics look target being set, then at the color-output device that will use, is input picture with the CMYK electronics look target that is provided with, and after its printout, measures the L of each color lump on the image of printout ^*a ^*b ^*Value is with the CMYK value and the L of each color lump ^*a ^*b ^*Corresponding and the storage of value, the source data of device characteristics is described in acquisition;

Step 2, read the L that desire is printed ^*a ^*b ^*Image obtains L ^*a ^*b ^*Three color-values original component of each pixel of image, and utilize following formula (2) to change, the actual color value component of the image after obtaining changing,

$L_2^{*}=L_1^{*}/2.55;$

$a_2^{*}=a_1^{*}-128;---\left(2\right)$

$b_2^{*}=b_1^{*}-128;$

Wherein, L ₁ ^*, a ₁ ^*, b ₁ ^*Represent L respectively ^*a ^*b ^*Three color-values original component of each pixel of image, L ₂ ^*, a ₂ ^*, b ₂ ^*Be the actual color value component of the image after the conversion,

Then, utilize the source data in the step 1, obtain the gamut range of output equipment, and with L ^*a ^*b ^*The color-values L of each pixel of image ₂ ^*, a ₂ ^*, b ₂ ^*Be compressed to output equipment gamut range inside;

Step 3, according to the source data in the step 1, utilize color density conversion and polynomial regression method, set up L ^*a ^*b ^*Color conversion relation with CMYK; Again according to the L of this transformational relation with the needs printing ^*a ^*b ^*Image transitions becomes the CMYK image, prints to get final product on CMYK equipment.

The invention has the beneficial effects as follows that relying on the CMYK printer is output equipment, has realized L ^*a ^*b ^*Change during to the high-precision real of CMYK, realized that high-fidelity prints L ^*a ^*b ^*The order ground of image.

Description of drawings

Fig. 1 is the schematic flow sheet of the inventive method;

Fig. 2 is the gamut compression principle schematic in the inventive method;

Fig. 3 is the color conversion schematic diagram in the inventive method.

Embodiment

The present invention is described in detail below in conjunction with the drawings and specific embodiments.

L ^*a ^*b ^*The color-values of each pixel all is to use L in the image ^*a ^*b ^*Color space represents that the Lab pattern is according to CIE 1976L ^*a ^*b ^*A kind of color mode of creating, the Lab pattern is made up of three passages, and first passage is psychological lightness, i.e. L, its span is 0～100, and numerical value is big more, and the brightness value of color is big more.Two other is a chrominance channel, and a passage is represented the red green reflection of color; The b passage is represented the champac reflection of color.The span of a and b is-128～127, and for a, numerical value is big more, and color is red more, otherwise numerical value is more little, the inclined to one side more green of this color; The b value is big more, and color is yellow more, otherwise numerical value is more little, the inclined to one side more indigo plant of color.When storage, in order effectively to utilize 8 storages, generally-128～127 scope is adjusted to the scope of 0-255, thus when storage lab image, need the actual color value be changed, and when reading, it need be changed again.

To L ^*a ^*b ^*After image read, its pixel value was just represented the color-values of this pixel, and for example the pixel value of certain point of RGB image is (20,30,50), its color-values R=20, G=30, B=50.L herein ^*a ^*b ^*Image and RGB image are very similar, the color space difference (rgb color space and the L that only are to use ^*a ^*b ^*Color space).

Fig. 1 is the schematic flow sheet of the inventive method, and the main effect of whole system is at various color devices, accurately exports L ^*a ^*b ^*Image can be divided into three big steps and implement,

Step 1: CMYK electronics look target at first is set, and the printed colors target is also measured, and obtains to describe the source data of device characteristics.

The set electronics look target of the present invention is made up of three look zones, four look zones and black print zone three parts.CMY by [0 10 20 30 40 50 60 70 80 90 100] totally 11 grades of gradual changes, always has 11 respectively in the three look zones ³I.e. 1331 color lumps; In the four look zones, K is by [10 20 40 60 80 100] totally 6 grades of variations, and CMY is respectively by [0 10 30 50 70 90 100] totally 7 grades of variations, totally 2058 color lumps; The black print zone has 23 color lumps, and its K value is respectively [0 25 10 15 20 25 30 35 40 45 50 55 60 6,570 75 80 85 90 95 98 100].

At the color-output device that will use, be input picture then, after its printout, measure the L of each color lump with the CMYK look target that is provided with ^*a ^*b ^*Value is with the CMYK value and the L of each color lump ^*a ^*b ^*Corresponding and the storage of value is as the source data of describing the output equipment chromatic characteristic.

Step 2: read the L that needs printing ^*a ^*b ^*View data, and the color data of this image carried out gamut compression.

At L ^*a ^*b ^*In the coloured image, the L of each pixel correspondence ^*, a ^*, b ^*The number range of three passages is as follows:

$L^{*}\&SubsetEqual;\left[\begin{array}{cc}0& 100\end{array}\right]$

$a^{*}\&SubsetEqual;\left[\begin{array}{cc}-128& 127\end{array}\right]$

$b^{*}\&SubsetEqual;\left[\begin{array}{cc}-128& 127\end{array}\right]---\left(1\right)$

Yet at storage L ^*a ^*b ^*During image, the L of each pixel value ^*, a ^*, b ^*Three channel value all are adjusted between 0～255, promptly store with 38, are therefore reading L ^*a ^*b ^*During the color value of image, need utilize formula 2 to change,

$L_2^{*}=L_1^{*}/2.55;$

$a_2^{*}=a_1^{*}-128;$

$b_2^{*}=b_1^{*}-128;---\left(2\right)$

Wherein, L ₁ ^*, a ₁ ^*, b ₁ ^*Represent L respectively ^*a ^*b ^*Three color-values components of each pixel of image, L ₂ ^*, a ₂ ^*, b ₂ ^*Actual color value component for the image after the conversion.

Because the restriction of factors such as paper, printing ink, each color-output device all has certain gamut range, that is to say, for equipment such as general printer, printing machines, always has some colors to exceed its gamut range.For the L that will print output ^*a ^*b ^*Image, often the color-values of some pixel exceeds the gamut range of equipment, at this moment just need utilize the gamut compression technology, the color-values of this part pixel is compressed to the gamut range inside of printer.Before the gamut compression, must obtain the gamut range of output equipment, the present invention adopts CIE Commission Internationale De L'Eclairage publish method, utilizes the source data of storage in the step 1, draws the gamut range of output equipment.

After drawing the output equipment gamut range, can carry out gamut compression, its key step is as follows:

A, since Color Gamut Mapping generally all be 2 the dimension L ^*C ^*Carry out in the plane, therefore at first will be before the compression with the L after the conversion ^*a ^*b ^*Value converts L to ^*C ^*h ^*Value, as shown in the formula:

L ^*＝L ^*；

$C^{*}=\sqrt{a^{*2}+b^{*2}};$

h ^*＝acr?tan(b ^*/a ^*)； (3)

L wherein ^*Be brightness value, do not change C before and after the conversion ^*Be chroma value, h ^*Be hue angle.

B, at L ^*C ^*Carry out gamut compression in the two dimensional surface.At first according to L ^*a ^*b ^*H after the value conversion ^*Hue angle utilizes the method for J.Morovic to determine the two-dimentional L of output equipment under this hue angle ^*C ^*The colour gamut plane.As shown in Figure 2, be the gamut compression principle schematic in the inventive method, its abscissa is chroma C ^*, ordinate is brightness L ^*, L ^*Axle is represented the gamut range of equipment with the camber line on its right side, in this plane, and L ^*E point coordinates on the axle is (0,50), the mapping point when it is used as compression; The L that the representative of A point is compressed ^*a ^*b ^*Certain pixel value of image if A in the colour gamut outside, illustrates that this pixel color values exceeds the gamut range of output equipment, then utilizes the borderline B point of device color gamut to replace the A point, and this B point is exactly the intersection point of AE line and gamut boundary; If certain pixel value in device color gamut inside, compresses with regard to not needing.Like this, just the image color value that needs are printed has been compressed to printer gamut range inside.

Step 3: with L ^*a ^*b ^*Image transitions becomes the CMYK image, the line output of going forward side by side.

Utilize printer or printing machine output L ^*a ^*b ^*Image must convert its color value to the color value in equipment work space.Therefore, at first utilize the source data in the step 1, set up L ^*a ^*b ^*With the color conversion relation of CMYK, then with L ^*a ^*b ^*Image transitions becomes the CMYK image, just can finish output services.

CMY is the colorant three primary colors, uses these three kinds of colors almost can export all colours, yet during actual the printing, tends to use the 4th color K.The advantage of using CMYK to print is a lot, and as the increase colour gamut, thereby color black consumption minimizing reduces cost, and makes grey balance more stable.

Since in the four-color process, same group of L ^*a ^*b ^*Value can corresponding many group CMYK values.Therefore, when carrying out color separation processing, a kind of scheme is to determine the CMY component earlier, determines K value component then; Another kind of scheme is to determine earlier to calculate CMY again by K value component.The embodiment of the invention uses a kind of scheme in back to carry out L ^*a ^*b ^*Conversion to CMYK.

Fig. 3 is the color conversion schematic diagram in the inventive method, and its operation principle is with L ^*a ^*b ^*The value separated into two parts, a part is corresponding with the K value after the conversion, and another part is corresponding with CMY, because L ^*a ^*b ^*Value does not have additivity, therefore need convert thereof into the color density value when changing.Divide two parts below, describe the whole transfer process among Fig. 3 in detail.

The calculating of a, K value

For the black print amount can be adjusted flexibly, often use GCR or UCR technology in the color separation process, the present invention selects following a kind of GCR method for use, determines black print K value according to different alternative amounts:

$K=p\&CenterDot;{\left(\frac{K_{\max }-K_{\mathrm{start}}}{1-K_{\mathrm{start}}}\right)}^{\mathrm{\&gamma;}}---\left(4\right)$

Wherein K is the black print value that finally will determine, and Kmax is the theoretical maximum black print value after calculating, and the Kstart representative begins to carry out grey and substitutes initial black print value, and γ is used to control the shape (γ 〉=1) of GCR curve, and p is the weight coefficient that substitutes amount, 0≤p≤1.

In the GCR of formula 4 scheme, parameters such as Kstart, γ and p can be set by user's typography as required, therefore only need obtain Kmax and just can calculate actual K value, and concrete steps are as follows:

At first pick out black print data wherein from the source data of storage, these group data comprise the K value and the corresponding L of 23 color lumps ^*a ^*b ^*Value.Because L ^*a ^*b ^*Value does not possess the characteristics of additivity, therefore converts thereof into the color density value.L ^*a ^*b ^*Value converts the color density value to, is divided into for two steps, promptly earlier L ^*a ^*b ^*Convert the XYZ value to, and then convert XYZ to the color density value.Because XYZ and L ^*a ^*b ^*Between conversion be harmless conversion, the normalized form that this patent utilizes CIE to announce is finished L ^*a ^*b ^*To the conversion of XYZ, and utilize formula 5 to calculate the color density value of XYZ correspondence.

D _X＝log ₁₀(X ₀/X)

D _Y＝log ₁₀(Y ₀/Y)

D _Z＝log ₁₀(Z ₀/Z) (5)

Wherein, X ₀, Y ₀, Z ₀Be the blank sheet of paper chromatic value, the method above utilizing can obtain the K value and the XYZ color density value of 23 color lumps, thereby set up an one dimension look-up table K-LUT.

Suppose D _X, D _Y, D _ZBe respectively L ^*a ^*b ^*Three corresponding color density values utilize the density value of 23 color lumps among this density value and the one dimension look-up table K-LUT to compare, and seek the color density value than its little color lump (suc as formula 6), therefrom select that maximum color lump of corresponding K value, and its K value defined is Kmax,

D _X≥D _XK；

D _Y≥D _YK；

D _Z≥D _ZK； (6)

D wherein _X, D _Y, D _ZBe respectively L ^*a ^*b ^*Three color density values after the conversion, D _XK, D _YK, D _ZKColor density value for certain color lump in the look-up table.

Utilize the GCR scheme of formula 4 at last, set Kstart=0, γ=1, p=0.5 obtains final K value.

The calculating of b, CMY value

After solving the K value, utilize formula 7 that the color density value of black print correspondence is removed from total density value, can obtain the color density value of CMY three look correspondences.

D _X(CMY)＝D _X-D _X(K)；

D _Y(CMY)＝D _Y-D _Y(K)；

D _Z(CMY)＝D _Z-D _Z(K)； (7)

D wherein _X, D _Y, D _ZThe L that changes for needs ^*a ^*b ^*The color density value that value is corresponding, D _{X (CMY)}, D _{Y (CMY)}, D _{Z (CMY)}Be respectively the color density value of CMY three look correspondences, D _{X (K)}, D _{Y (K)}, D _{Z (K)}Be the corresponding color density value of K value after calculating, this value can be obtained by the data among the look-up table K-LUT are carried out interpolation calculation.

After the color density that calculates the CMY correspondence, at first transform 5 calculates the XYZ value of this density value correspondence, and the standard handovers method of utilizing CIE1976 to announce then calculates the corresponding L of XYZ value ^*a ^*b ^*Value, this value is the pairing L of CMY component ^*a ^*b ^*Value.

Therefore, obtain the L of CMY correspondence ^*a ^*b ^*After the value, utilize L ^*a ^*b ^*After calculating the CMY value to the transformation model of CMY, just finish whole conversion.

Present L ^*a ^*b ^*Method to CMY conversion is a lot, and commonly used have LUT method, polynomial regression method and a neural net method.Because three look colour generation phenomenons of general printer are more regular, the present invention adopts the polynomial regression method to calculate.The polynomial regression method is utilized the data in two color spaces, conversion front and back mainly based on least square method, sets up multinomial.Present polynomial regression equation has a variety of, and commonly used 6 and 20 multinomials are as follows:

p(x，y，z)＝α ₁x+α ₂y+α ₃z+α ₄xy+α ₅yz+α ₆zx

p(x，y，z)＝α ₀+α ₁x+α ₂y+α ₃z+α ₄xy+α ₅yz+α ₆zx+α ₇x ²+α ₈y ²+α ₉z ²+α ₁₀xyz+α ₁₁x ²y+α ₁₂x ²z+α ₁₃y ²x+α ₁₄y ²z+α ₁₅z ²x+α ₁₆z ²y+α ₁₇x ³+α ₁₈y ³+α ₁₉z ³ (8)

With 6 multinomials is example, and this formula is applied in the finding the solution of CMY, and the expansion form is:

C(L，a，b)＝α ₁L+α ₂a+α ₃b+α ₄La+α ₅Lb+α ₆ab

M(L，a，b)＝β ₁L+β ₂a+α ₃b+β ₄La+β ₅Lb+α ₆ab

Y(L，a，b)＝γ ₁L+γ ₂a+γ ₃b+γ ₄La+γ ₅Lb+γ ₆ab (9)

By following formula we as can be seen, as long as determined coefficients such as the α in the equation, β, γ, just can obtain any one group of L ^*a ^*b ^*The CMY component that value is corresponding.

Utilize 1331 groups of data in the three look look targets, set up matrix model, coefficient that can solving equation.Suppose:

$\begin{array}{cc}V=\left[\begin{array}{ccccc}{L}_1& L_2& L_3& ...& L_8\\ a_1& a_2& a_3& ...& a_8\\ b_1& b_2& b_3& ...& b_8\\ L_1{a}_1& L_2{a}_2& L_3{a}_3& ...& L_8{a}_8\\ L_1{b}_1& L_2{b}_2& L_3{b}_3& ...& L_8{b}_8\\ a_1{b}_1& a_2{b}_2& a_3{b}_3& ...& a_8{b}_8\end{array}\right]& \begin{array}{c}C={\left[\begin{array}{ccccc}{c}_1& c_2& c_3& ...& c_n\end{array}\right]}^T\\ M={\left[\begin{array}{ccccc}{m}_1& m_2& m_3& ...& m_n\end{array}\right]}^T\\ Y={\left[\begin{array}{ccccc}{y}_1& y_2& y_3& ...& y_n\end{array}\right]}^T\\ \mathrm{\&alpha;}={\left[\begin{array}{ccccc}{\mathrm{\&alpha;}}_1& {\mathrm{\&alpha;}}_2& {\mathrm{\&alpha;}}_3& ...& {\mathrm{\&alpha;}}_n\end{array}\right]}^T---\left(10\right)\\ \mathrm{\&beta;}={\left[\begin{array}{ccccc}{\mathrm{\&beta;}}_1& {\mathrm{\&beta;}}_2& {\mathrm{\&beta;}}_3& ...& {\mathrm{\&beta;}}_n\end{array}\right]}^T\\ \mathrm{\&gamma;}={\left[\begin{array}{ccccc}{\mathrm{\&gamma;}}_1& {\mathrm{\&gamma;}}_2& {\mathrm{\&gamma;}}_3& ...& {\mathrm{\&gamma;}}_n\end{array}\right]}^T\end{array}\end{array}$

Each is organized coefficient and can be solved to:

α＝(VV ^T) ^-1VC

β＝(VV ^T) ^-1VM

γ＝(VV ^T) ^-1VY (11)

Because along with increasing of the degree of polynomial, the precision of color space conversion can increase, therefore often use the multinomial of more multinomial number to find the solution in actual use, as use 20 multinomials to calculate CMY.

Claims (1)

1, a kind of method of high-fidelity print outputting L * a*b* image, it is characterized in that: this method is implemented according to following steps,

Step 1, at first CMYK electronics look target is set, then at the CMYK equipment that will use, CMYK electronics look target with setting is an input picture, after its printout, the L*a*b* value of each color lump on the image of measurement printout, with the CMYK value and the corresponding also storage of L*a*b* value of each color lump, obtain to describe the source data of CMYK device characteristics;

Step 2, read the L*a*b* image that desire is printed, obtain three color-values original component of each pixel of L*a*b* image, and utilize following formula (2) to change, the actual color value component of the image after obtaining changing,

$L_2^{*}=L_1^{*}/2.55;$

$a_2^{*}=a_1^{*}-128;---\left(2\right)$

$b_2^{*}=b_1^{*}-128;$

Wherein, L ₁ ^*, a ₁ ^*, b ₁ ^*Represent three color-values original component of each pixel of L*a*b* image respectively, L ₂ ^*, a ₂ ^*, b ₂ ^*Be the actual color value component of the image after the conversion,

Then, utilize the source data in the step 1, obtain the gamut range of CMYK equipment, and with the color-values L of each pixel of L*a*b* image ₂ ^*, a ₂ ^*, b ₂ ^*Be compressed to CMYK device color gamut scope inside,

In the described step 2 to the color-values L of each pixel of L*a*b* image ₂ ^*, a ₂ ^*, b ₂ ^*Carrying out gamut compression is to utilize a kind of cutting method to carry out gamut compression, and concrete steps are as follows:

At first the L*a*b* value to be converted to the L*C*h* value before a, the compression, as shown in the formula (3):

L ^*＝L ^*；

$C^{*}=\sqrt{a^{*2}+b^{*2}};$

h ^*＝acr?tan(b ^*/a ^*)； (3)

L wherein ^*Be brightness value, C ^*Be chroma value, h ^*Be hue angle;

B, in the L*C* two dimensional surface, carry out gamut compression, at first, utilize the method for J.Morovic to determine the two-dimentional L*C* colour gamut plane of CMYK equipment under this hue angle according to the h* hue angle after the conversion of L*a*b* value, in this plane, L ^*Mapping point when the E point representative on the axle is compressed; A pixel value of the L*a*b* image that the representative of A point is compressed, if A in the colour gamut outside, illustrates that this pixel value exceeds the gamut range of CMYK equipment, with the more borderline A point that replaces of device color gamut, this point is exactly the intersection points B of AE and gamut boundary; If certain pixel value in device color gamut inside, compresses with regard to not needing;

Step 3, according to the source data in the step 1, utilize color density conversion and polynomial regression method, the color conversion of setting up L*a*b* and CMYK concerns that concrete steps are:

Determine the K component that every group of L*a*b* value is corresponding earlier, determine again to obtain the CMYK value at last by its corresponding CMY component,

The calculating of a, K value

Select following a kind of GCR method for use, determine black print K value according to different alternative amounts,

$K=p\&CenterDot;{\left(\frac{K_{\max }-K_{\mathrm{start}}}{1-K_{\mathrm{start}}}\right)}^{\mathrm{\&gamma;}}---\left(4\right)$

Wherein K is the black print value that finally will determine, and Kmax is the theoretical maximum black print value after calculating, and the Kstart representative begins to carry out grey and substitutes initial black print value, and γ is used to control the shape of GCR curve, γ 〉=1 wherein, and p is for substituting the weight coefficient of amount, 0≤p≤1,

In the GCR scheme of formula (4), parameters such as Kstart, γ and p are all set by user's typography as required, and concrete steps are:

At first from the source data of storage, pick out black print data wherein, these group data comprise the K value and the corresponding L*a*b* value of 23 color lumps, convert thereof into the color density value, utilize the K value and the XYZ color density value of 23 color lumps, set up an one dimension look-up table K-LUT, when the L*a*b* value converts the color density value to, at first utilize the standard handovers algorithm among the CIE1976 to convert thereof into the XYZ value, utilize formula (5) to convert XYZ color density value to then

D _X＝log ₁₀(X ₀/X)

D _Y＝log ₁₀(Y ₀/Y)

D _Z＝log ₁₀(Z ₀/Z) (5)

X wherein ₀, Y ₀, Z ₀Be the blank sheet of paper chromatic value;

Again the L*a*b* pixel value is converted to color density value D _X, D _Y, D _Z, from look-up table K-LUT, seek the color density value then than its little color lump, suc as formula (6), therefrom select that maximum color lump of K value, its K value defined is Kmax,

D _X≥D _XK；

D _Y≥D _YK；

D _Z≥D _ZK； (6)

D wherein _X, D _Y, D _ZBe respectively three color density values after L*a*b* changes, D _XK, D _YK, D _ZKBe the color density value of certain color lump in the look-up table,

Utilize the GCR scheme of formula (4) at last, set Kstart=0, γ=1, p=0.5 calculates final K value;

The calculating of b, CMY value

After solving the K value, utilize formula (7) that the color density value of black print correspondence is removed from total density value, obtain the color density value of CMY three look correspondences, so just can utilize the XYZ of CIE standard to calculate its corresponding L*a*b* value to the L*a*b* conversion method,

D _X(CMY)＝D _X-D _X(K)；

D _Y(CMY)＝D _Y-D _Y(K)；

D _Z(CMY)＝D _Z-D _Z(K)； (7)

D in the formula (7) _{X (CMY)}, D _{Y (CMY)}, D _{Z (CMY)}Be respectively the color density value of CMY three look correspondences, D _{X (K)}, D _{Y (K)}, D _{Z (K)}Be the corresponding color density value of K value after calculating, this value is obtained by the data among the look-up table K-LUT are carried out interpolation calculation, selects for use the polynomial regression method to carry out the calculating of CMY in this step;

The L*a*b* image transitions of needs being printed according to this transformational relation becomes the CMYK image again, can print on CMYK equipment.

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