CN108280044A - A kind of Neugebauer equation modification method based on halftoning on the spot - Google Patents
A kind of Neugebauer equation modification method based on halftoning on the spot Download PDFInfo
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Abstract
The invention discloses a kind of Neugebauer equation modification methods based on halftoning tristimulus values on the spot, specially:Essential colour member tristimulus values, dot area percentage, on the spot tristimulus values relevant parameter are obtained using test specimen page;Neugebauer equation group is built, by Converse solved equation group, matches different dot area percentages, establishes the halftoning of corresponding dot area percentage tristimulus values parameter on the spot;Halftoning is analyzed tristimulus values result carries out variable on the spot, using different contrast dot area percentages as independent variable, using halftoning, tristimulus values establishes functional relation as dependent variable on the spot, obtains correction model, and the amendment of Neugebauer equation is realized by the correction model.Calculating process of the present invention is simple, and accuracy in computation is high, final to improve equation precision, and the present invention is applied to printing color separation field, can the non-fundamental color of Accurate Prediction, realize that small color target replaces the color separation target of big color target, practical value height in print color separation.
Description
Technical field
The invention belongs to printed matter color separation technology fields, and in particular to a kind of to be repaiied based on the Neugebauer equation of halftoning on the spot
Correction method.
Background technology
With the rapid development of printing technology, high-grade printed matter market is also evolving meet the needs of people, print
The accuracy of repetition of brush product is increasingly becoming focal issue of people's attention, and therewith, the meaning and value for printing color separation technology also embody
Out.Neugebauer equation occupies an important position as a kind of important method in printing algorithm of color separation in print reproduction.
Neugebauer equation is the Color Printing established according to printing net-point model and Jim Glassman color mixing law
Equation.Shown in equation such as formula (1):
Above formula establishes the relationship between original copy color and color separation CMY dot area percentages, wherein XYZ is three thorns of original copy color
Swash value, f is color elemental area rate, and c, m, y are respectively the yellow trichromatic dot area percentage of green product.
In the epoch of current digital plate-making and digital printing, Neugebauer equation has more important practical value, at
One of the most basic formula calculated for printed matter color.In color management software, Neugebauer equation is to establish output equipment color
Color characteristic describes the important means of file.Neugebauer equation not only illustrates the mechanism of Color Printing from the angle of color science,
Also the method for calculating printed matter color value is given from the angle of mathematics, therefore occupies critically important ground in colored printing duplication
Position.The advantages of Neugebauer equation, is that clear principle is illustrated, and only need to measure a small amount of ink swatch can solve.
However, having been found that in practical applications, the calculated site value of Neugebauer equation and practical printing gained are directly used
To site value between there are larger deviation, go printing that printing can be caused prodigious color error occur by direct calculated value.
Therefore, there is the research much about amendment Neugebauer equation, and propose many modification methods.But to being proposed at present
Various modification methods in, some causes equation stability and synthesis precision relatively low, such as《3 kinds based on subregion Neugebauer equation
The error analysis of algorithm of color separation》The linear regression Neugebauer equation of proposition causes equation precision and stability relatively low, and some causes
It calculates complicated and correction factor to be not easy to determine, such as《The theoretical of Neugebauer equation index modification method dissects》And《Knob Jie fort side
The theory value and its limitation Journal of Sex Research of journey》Middle proposition n index modification methods make correction factor be not easy determining or versatility
Difference.These modification methods are still difficult to simply and rapidly correct out the higher Neugebauer equation of precision.
Invention content
The object of the present invention is to provide a kind of Neugebauer equation modification methods based on halftoning on the spot, optimize knob Jie fort
Equation improves Neugebauer equation precision, solves existing Neugebauer equation and corrects the problems such as complicated and precision is not high.
The technical solution adopted in the present invention is a kind of Neugebauer equation modification method based on halftoning on the spot, specifically
Implement according to the following steps:
Step 1, the design of test specimen page and output:
According to printing color standardisation requirements, the design and output of test specimen page are completed, sample is selected in testing specimen page
Test position is trained to obtain Essential colour member tristimulus values, dot area percentage, on the spot tristimulus values relevant parameter;
Step 2, Neugebauer equation halftoning tristimulus values on the spot is built:
Neugebauer equation group is built, by Converse solved equation group, matches different dot area percentages, establishes corresponding dot surface
The halftoning tristimulus values parameter on the spot of product rate;
Step 3, Neugebauer equation is modified:
Halftoning in step 2 is analyzed tristimulus values result carries out variable on the spot, is with different contrast dot area percentages
Independent variable, using halftoning, tristimulus values establishes functional relation as dependent variable on the spot, obtains correction model, passes through correction model reality
The amendment of existing Neugebauer equation.
The Neugebauer equation modification method of the present invention both can be used for correcting green product Huang three primary colours Neugebauer equation, can also
Color Neugebauer equation is folded for correcting RGB three.
When correcting green product Huang three primary colours Neugebauer equation, what is established in above-mentioned steps 2 is the blueness of corresponding dot area percentage
Product Huang three primary colours halftoning tristimulus values parameter on the spot, using different contrast dot area percentages as independent variable in step 3, with green product Huang
Tristimulus values is that dependent variable establishes functional relation, and then completes green product Huang three primary colours Neugebauer equation to three primary colours halftoning on the spot
It corrects.
Shown in three primary colours Neugebauer equation group such as formula (2):
XYZ is primary colours standard sample tristimulus values, [X in formulaw, Yw, Zw] indicate paper tristimulus values on the spot in vain, [Xi, Yi, Zi]
Indicate the tristimulus values on the spot of certain primary colours.fiIndicate primary colours dot area percentage.
Three primary colours halftoning is on the spot shown in tristimulus values parameters relationship such as formula (3):
When amendment RGB three folds color Neugebauer equation, what is established in above-mentioned steps 2 is the red of corresponding dot area percentage
Turquoise three folded color halftoning tristimulus values parameter on the spot, using different contrast dot area percentages as independent variable in step 3, with RGB
Tristimulus values is that dependent variable establishes functional relation, and then completes RGB three and fold color Neugebauer equation to three folded color halftonings on the spot
It corrects.
RGB three is folded shown in color Neugebauer equation group such as formula (4):
[X in formulai, Yi, Zi], [Xj, Yj, Zj] indicate the halftoning tristimulus values on the spot of two primary colours to be superimposed, [Xij,
Yij, Zij] indicate that RGB folds the tristimulus values on the spot of color, fiIndicate primary colours dot area percentage, fijIt indicates to fold color dot area
Rate.
RGB three folds color halftoning, and tristimulus values parameters relationship such as formula (5) is shown on the spot:
The features of the present invention also characterized in that
It is described that sample training test position is selected to obtain Essential colour member tristimulus values in testing specimen page in step 1
Specific method is:It is that 5%-15% chooses as step-length using dot area percentage difference in dot area percentage is 5%-100% ranges
Sample training test position obtains Essential colour member tristimulus values, dot area percentage, on the spot tristimulus values phase using Spectrodensiotometer
Related parameter.
It is analyzed in step 3, between variable and is specially:Using the curve matching in functional approaching, the principle of least square is utilized
Halftoning is analyzed tristimulus values result carries out variable on the spot.
The present invention is realized based on the halftoning target that tristimulus values is modified Neugebauer equation on the spot, of the invention
Advantageous effect is, on the basis of being studied printing technology and being tested, it is proposed that one kind being based on halftoning tristimulus on the spot
The modification method of value simplifies calculating process, and obtains higher accuracy in computation, and practical value is high, has to actual production huge
Directive significance, can the non-fundamental color of Accurate Prediction, realized in printing color separation small color target replace big color target.
Description of the drawings
Fig. 1 is the idiographic flow schematic diagram that the present invention corrects Neugebauer equation;
Fig. 2 is halftoning area schematic on the spot at different dot area percentages in the present invention;
Fig. 3 is the standard testing specimen page that output is designed in the present invention;
Fig. 4 is the sample training test position for selecting to use in testing specimen page in the present invention.
Specific implementation mode
Present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.
The present invention is based on the Neugebauer equation modification methods of halftoning tristimulus values on the spot, and it is yellow both to can be used for correcting green product
Three primary colours Neugebauer equation can be used for amendment RGB three and fold color Neugebauer equation, as shown in Figure 1.
(1) yellow product blueness three primary colours Neugebauer equation is corrected to be specifically implemented according to the following steps:
Step 1, the design and output of specimen page are tested:
According to《G7 printing colors standardize》It is required that the qualified normative document of the output for printing.Design output is surveyed
Sample using dot area percentage difference be 5%-15% is step-length in test specimens in dot area percentage is 5%-100% ranges
Sample training test position is chosen in, using 528 Spectrodensiotometers of X-RITE respectively in D50 light sources, 2 ° of viewing conditions
Under, D50 light sources, under 10 ° of viewing conditions, D65 light sources under 2 ° of viewing conditions and D65 light sources, under 10 ° of viewing conditions, are measured and are obtained
Each Essential colour member tristimulus values of sample training test position, dot area percentage, on the spot tristimulus values relevant parameter.
Step 2, yellow product blueness three primary colours Neugebauer equation halftoning tristimulus values on the spot is built:
Three primary colours Neugebauer equation group is built first, shown in primary colours Neugebauer equation group such as formula (2).Neugebauer equation group
In, tristimulus values is dot area tristimulus values corresponding when being 100% on the spot.But in actually calculating, different contrast institutes
Corresponding region on the spot and 100% big region on the spot simultaneously differ, therefore the tristimulus values on the spot of different contrasts is not dot surface
Tristimulus values on the spot at product 100%.Such as site at 50% correspond on the spot than 100% at site correspond to it is small on the spot, thus
The region on the spot corresponding to site at this time is should be at 50% on the spot, tristimulus values also should be the site in the region three thorn on the spot at this time
Swash value, as tristimulus values matches the different nets of correspondence to halftoning as shown in Fig. 2, therefore, passing through Converse solved equation group on the spot
The halftoning tristimulus values on the spot of point area.
Then, three primary colours tristimulus values XYZ sample sets are combined with dot area percentage sample set, base is obtained with this
Color halftoning tristimulus values on the spot, obtains primary colours halftoning tristimulus values parameters relationship on the spot, as shown in formula (3).
Step 3, yellow product blueness three primary colours Neugebauer equation is modified:
Using the curve matching in functional approaching, using the principle of least square to primary colours halftoning tristimulus values knot on the spot
Fruit analyzed between variable, specifically using polyfit (x, y, n) function in MATLAB softwares, with different contrast dot area percentages
For independent variable, using halftoning, tristimulus values establishes dot area and halftoning on the spot between tristimulus values as dependent variable on the spot
Functional relation completes the amendment to yellow product blueness three primary colours Neugebauer equation.
(2) amendment RGB three is folded color Neugebauer equation and is specifically implemented according to the following steps:
Step 1, the design and output of specimen page are tested:
According to《G7 printing colors standardize》It is required that the qualified normative document of the output for printing.Design output is surveyed
Sample using dot area percentage difference be 5%-15% is step-length in test specimens in dot area percentage is 5%-100% ranges
Sample training test position is chosen in, using 528 Spectrodensiotometers of X-RITE respectively in D50 light sources, 2 ° of viewing conditions
Under, D50 light sources, under 10 ° of viewing conditions, D65 light sources under 2 ° of viewing conditions and D65 light sources, under 10 ° of viewing conditions, are measured and are obtained
Each Essential colour member tristimulus values of sample training test position, dot area percentage, on the spot tristimulus values relevant parameter.
Step 2, structure RGB three folds color Neugebauer equation halftoning tristimulus values on the spot:
Three folded color Neugebauer equation groups are built first, as shown in formula (4).It is inversely asked by three folded color Neugebauer equation groups
Solution, matches different dot area percentages, three folded color tristimulus values XYZ sample sets is combined with dot area percentage sample set, with
This obtains three folded color halftonings tristimulus values on the spot, obtains three folded color halftonings tristimulus values parameters relationship, such as formula on the spot
(5) shown in.
Step 3, color Neugebauer equation is folded to RGB three to be modified:
Also with MATLAB, to halftoning in step 2, tristimulus values result is fitted on the spot, with different contrast sites
Area occupation ratio is independent variable, and using folded color halftoning, tristimulus values establishes functional relation as dependent variable on the spot, obtains correction model, passes through
The amendment that color Neugebauer equation is folded to RGB three can be completed in the correction model.
The evaluation that horizontal and vertical two dimensions are carried out to the correction model of foundation, to illustrate having for modification method of the present invention
Effect property.
Longitudinal evaluation:It is mainly used for verifying the technical feasibility of modification method of the present invention, that is, passes through aberration result verification sheet
Whether the modification method of invention is feasible.
Lateral appraisement:By longitudinal evaluation verify modification method of the present invention it is feasible after, pass through color using lateral appraisement method
Whether poor result evaluates the Neugebauer equation correction model precision established using the method for the present invention than existing Neugebauer equation mould
Type precision increases.
It is evaluated from laterally and longitudinally two dimensions, is calculated using CIE1976L*a*b* colour difference formulas, aberration is public
Shown in formula such as formula (4):
Embodiment
Now with product monochrome, for red folded color, illustrate that the Neugebauer equation of tristimulus values is repaiied on the spot based on halftoning
Positive process.
(1) basis《G7 printing colors standardize》It is required that the normative document that printing meets, as shown in figure 3, in dot area
Rate is in testing specimen page to choose sample training using dot area percentage difference as shown in Table 1 as step-length in 5%-100% ranges
Test position, sample training test position are as shown in Figure 4.Using 528 Spectrodensiotometers of X-RITE in D50 light sources, 2 ° of visual field items
Under part, the Essential colour member tristimulus values XYZ at the normative document difference dot area, dot area percentage and on the spot three thorns are measured
Swash value.
(2) Converse solved product color Neugebauer equation group, the halftonings of the corresponding different dot areas of matching tristimulus values on the spot.
Product color tristimulus values XYZ sample sets are combined with dot area percentage sample set, product color halftoning on the spot three is obtained with this
Values, the results are shown in Table 1:
1 product primary colours halftoning of table tristimulus values on the spot
Halftonings of the primary colours M at different sampled points tristimulus values group on the spot is listed in table 1, is obtained by result in table, half
Tristimulus values changes tone with the variation of different contrasts on the spot, and when dot area moves closer to 100%, halftoning is on the spot
Tristimulus values is final consistent also close to 100% tristimulus values on the spot.
(3) utilize the method for function approximation that the discrete point of the halftoning that is obtained in (2) tristimulus values on the spot is described,
Then it carries out curve fitting.Using the dot area percentage of different contrasts as independent variable, using halftoning on the spot tristimulus values as dependent variable,
Analyze between variable, final opening relationships.It is programmed using MATLAB softwares, calls polyfit (x, y, n) function
Write programmed algorithm, constructor.Tristimulus algorithm is as follows on the spot for the M primary colours halftoning of structure:
In the above results, X, Y, Z indicate that M primary colours halftoning tristimulus values on the spot, x, y, z indicate dot area percentage.
(4) the Converse solved halftoning for matching corresponding different contrasts of red folded color Neugebauer equation group tristimulus values on the spot is utilized
Group combines red folded color tristimulus values XYZ sample sets with dot area percentage sample set, unlocks halftoning tristimulus values on the spot
Group obtains corresponding halftoning tristimulus values on the spot, and the results are shown in Table 2 for tristimulus values on the spot for red folded color halftoning:
The red folded color halftoning of table 2 tristimulus values on the spot
Halftonings of the folded color R at different sampled points tristimulus values group on the spot is listed in table 2, in table it can be seen from three
Values group result is consistent with monochromatic result, and tristimulus values changes halftoning with the variation of different contrasts on the spot, works as site
When area moves closer to 100%, halftoning on the spot tristimulus values also close to 100% tristimulus values on the spot.
(5) equally the method for function approximation is used to fold color halftoning on the spot using dot area percentage as independent variable with R with (3)
For dependent variable, programmed algorithm is write using MATLAB, structure R folds color halftoning, and tristimulus algorithm is as follows on the spot:
In above-mentioned formula, X, Y, Z indicate that red folded color halftoning tristimulus values on the spot, x, y, z indicate dot area percentage.
(6) product primary colours correction model is verified
A. longitudinal evaluation
It is run using primary colours correction model and calculates halftoning tristimulus values on the spot, result substitution Neugebauer equation is calculated
To sample tristimulus values as a result, the result is relatively sought aberration Δ E with tristimulus values is measured1, the results are shown in Table 3:
The longitudinally evaluation aberration distribution of 3 product primary colours of table
B. lateral appraisement
Neugebauer equation is not corrected into 100% tristimulus values substitution on the spot and obtains sample tristimulus values X1Y1Z1, and will
X1Y1Z1Aberration Δ E is sought with tristimulus values is measured2。
Calculate Δ E1With Δ E2The two difference, and average, the situation of change of value of chromatism between the two is analyzed, as a result such as
Shown in table 4:
4 product primary colours lateral appraisement aberration of table is distributed
Table 3 and table 4 are the M monochromes aberration distribution situations that vertically and horizontally different dimensions are evaluated.
From the results, it was seen that using halftoning model running calculates on the spot when aberration be substantially reduced, wherein aberration difference
Maximum can reduce 1.8NBS, and average color difference difference is 1.6NBS.And with the variation of dot area percentage, when sampled point is gradual
When close to 100%, aberration illustrates that the structure of M primary colours correction models effectively increases the precision of equation close to 0.
(7) red folded colour correction model verification
A. longitudinal evaluation
Halftoning tristimulus values on the spot is calculated using the folded colour correction model running of the present invention, result is substituted into Neugebauer equation
Sample tristimulus values is obtained as a result, the result is relatively sought aberration Δ E with tristimulus values is measured3, the results are shown in Table 5:
The longitudinally evaluation aberration distribution of the red folded color of table 5
B. lateral appraisement
Neugebauer equation is not corrected into 100% tristimulus values substitution on the spot and obtains sample tristimulus values X2Y2Z2, and will
X2Y2Z2Aberration Δ E is sought with tristimulus values is measured4。
Calculate Δ E3With Δ E4The two difference, and average, the situation of change of value of chromatism between the two is analyzed, as a result such as
Shown in table 6:
The red folded color lateral appraisement aberration distribution of table 6
Table 5 and table 6 are that R folds the color aberration distribution situation that vertically and horizontally different dimensions are evaluated.
From the results, it was seen that using halftoning model running calculates on the spot when aberration be substantially reduced, wherein aberration difference
Maximum can reduce 2.2NBS, and average color difference difference is 1.0NBS.And with the variation of dot area percentage, when sampled point is gradual
When close to 100%, aberration illustrates that the structure of the folded colour correction models of R effectively increases the precision of equation close to 0.
It completes to amendment of the Neugebauer equation based on halftoning tristimulus values on the spot by above-mentioned steps, demonstrates simultaneously
The feasibility and validity of modification method of the present invention.
Claims (5)
1. a kind of Neugebauer equation modification method based on halftoning on the spot, which is characterized in that include the following steps:
Step 1, the design of test specimen page and output:
According to printing color standardisation requirements, the design and output of test specimen page are completed, sample training is selected using test specimen page
Position obtains Essential colour member tristimulus values, dot area percentage, on the spot tristimulus values relevant parameter;
Step 2, Neugebauer equation halftoning tristimulus values on the spot is built:
Neugebauer equation group is built, by Converse solved equation group, matches different dot area percentages, establishes corresponding dot area percentage
Halftoning tristimulus values parameter on the spot;
Step 3, Neugebauer equation is modified:
Halftoning in step 2 is analyzed tristimulus values result carries out variable on the spot, is from change with different contrast dot area percentages
Amount, using halftoning, tristimulus values establishes functional relation as dependent variable on the spot, obtains correction model, and knob is realized by the correction model
The amendment of Jie fort equation.
2. the Neugebauer equation modification method according to claim 1 based on halftoning on the spot, which is characterized in that described to repair
When correction method is used to correct three primary colours Neugebauer equation, what is established in the step 2 is the three primary colours half of corresponding dot area percentage
Tone tristimulus values parameter on the spot, using different contrast dot area percentages as independent variable when the functional relation established in step 3, with three
Primary colours halftoning on the spot for dependent variable establish by tristimulus values;
The three primary colours Neugebauer equation group is:
Tristimulus values parameter is the three primary colours halftoning on the spot:
3. the Neugebauer equation modification method according to claim 1 based on halftoning on the spot, which is characterized in that described to repair
When correction method is used for three folded color Neugebauer equations, what is established in the step 2 is three folded color halftonings of corresponding dot area percentage
Tristimulus values parameter on the spot, the functional relation established in step 3 is using different contrast dot area percentages as independent variable, with three folded colors
Halftoning on the spot for dependent variable establish by tristimulus values;
Three folded color Neugebauer equation groups are:
Tristimulus values parameters relationship is three folded color halftonings on the spot:
4. the Neugebauer equation modification method according to claim 1 based on halftoning on the spot, which is characterized in that step 1
Described in using test specimen page select sample training position obtain the specific method of Essential colour member tristimulus values for:In dot surface
Product rate is in 5%-100% ranges, is that 5%-15% chooses sample training test position, profit as step-length using dot area percentage difference
Essential colour member tristimulus values, dot area percentage, on the spot tristimulus values relevant parameter are obtained with Spectrodensiotometer.
5. the Neugebauer equation modification method according to claim 1 based on halftoning on the spot, which is characterized in that step 3
Described between variable analysis be specially:Using the curve matching in functional approaching, using the principle of least square to halftoning reality
Ground tristimulus values result analyzed between variable.
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CN112003993A (en) * | 2020-09-03 | 2020-11-27 | 北京印刷学院 | Printing color reproduction method and device and electronic equipment |
CN114211874A (en) * | 2021-11-23 | 2022-03-22 | 杭州电子科技大学温州研究院有限公司 | Method for detecting large-area color uniformity of printing |
CN114211874B (en) * | 2021-11-23 | 2023-09-29 | 杭州电子科技大学温州研究院有限公司 | Detection method for printing large-area color uniformity |
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