# Patent

## Title
Methods and apparatus for colorimetrically characterizing color deviation in color imaging devices

## Abstract

Methods and apparatus are provided that print a set of similar color patches using a color output device, determine colorimetric values for each color patch, calculate a standard deviation value for each of the colorimetric values, and calculate a numerical value that is a function of the standard deviation values and that represents the colorimetric deviation of the set.

## Background
REFERENCE TO RELATED APPLICATIONS
This application is a continuation of U.S. patent application Ser. No. 10/744,207, filed 22 December 2003, now U.S. Pat. No. 7,233,397.


BACKGROUND
This invention relates to color imaging devices. More particularly, this invention pertains to methods and apparatus for calorimetrically characterizing color deviation in color imaging devices.
Color imaging devices, such as color copiers, color printers, color printing presses and other similar color imaging devices often exhibit visible color variations in their printed output. These visible variations may occur within a single page (spatial page variations), and also from page to page (page-to-page variations), even though the input to the imaging device is identical for each page. This phenomenon is often referred to as “engine drift,” or “engine instability,” and may result from variations in manufacturing tolerances or aging of the imaging device, time-dependent variations in the colorants used to form the image (e.g., toner or ink), and variations in the ambient environment of the device.
Although engine drift and engine instability have been recognized for some time, there has not been an objective technique to characterize this phenomenon that correlates well with the visually perceived phenomenon. Indeed, previously known techniques for characterizing engine drift have often been based on density measurements. In one such previously known technique, a color imaging device is used to print a test pattern that includes test patches, which are then measured using a densitometer or other similar device that provides measurements of reflected density. After obtaining a large number of measurements (i.e., from multiple locations within a page and from multiple pages) the measured density values are averaged, and a standard deviation measurement is calculated from the measured data.
Although such previously known density-based techniques may be used to characterize engine drift, the techniques are not useful indicators of human perception of engine drift. In particular, density measurements do not correlate well with human perception of color, and density-based indicators of color variation do not correlate well with human perception of color differences. As a result, previously known density-based techniques for characterizing engine drift do not bear a close relationship to how a human observer would perceive such engine drift.
It therefore would be desirable to provide methods and apparatus for objectively characterizing color variations in a color output device.
It further would be desirable to provide methods and apparatus for characterizing color variations in a color output device in a manner that corresponds to human perception of such variations.
SUMMARY
Methods and apparatus in accordance with this invention print a set of similar color patches using a color output device, determine calorimetric values for each color patch, calculate a standard deviation value for each of the calorimetric values, and calculate a numerical value that is a function of the standard deviation values and that represents the colorimetric deviation of the set.



BRIEF DESCRIPTION OF THE DRAWINGS
The above-mentioned objects and features of the present invention can be more clearly understood from the following detailed description considered in conjunction with the following drawings, in which the same reference numerals denote the same elements throughout, and in which:
FIG. 1 is a block diagram of an exemplary system in accordance with this invention;
FIG. 2 is a flowchart of an exemplary method in accordance with this invention;
FIG. 3 is a diagram of an exemplary test pattern for use with systems and methods in accordance with this invention;
FIG. 4 is a diagram of exemplary output pages for use with systems and methods in accordance with this invention; and
FIG. 5 is a diagram of an alternative exemplary test pattern for use with systems and methods in accordance with this invention.



DETAILED DESCRIPTION
Referring to FIG. 1, an exemplary system for characterizing color variations in a color output device in accordance with this invention is described. System 10 includes image source 12, color imaging device 14, output pages 16, measurement device 22 and processor 24. Image source 12 includes image file 26, which includes digital data representing a test pattern 18 to be printed by color imaging device 14. Image source 12 may be a personal computer, laptop computer, handheld computer, computer workstation, print server, personal digital assistant, or any other similar device that may be used to provide image files for printing by color imaging devices.
Image source 12 may include a software application (not shown) used to generate image file 26. For example, image source 12 may be a personal computer that includes Adobe PageMaker software that may be used to generate image file 26. Image file 26 may be a digital data file that describes test pattern 18 in a page description language, such as PostScript, PCL, or other similar page description language, or may simply be a raster image, such as a TIFF image, RAW image, or other similar raster image. Color imaging device 14 may be a color printer, color copier, printing press, or other similar color imaging device that uses one or more colorants to provide output pages 16 including test pattern 18. For example, color imaging device 14 may be a color printer that uses cyan (“C”), magenta (“M”), yellow (“Y”) and black (“K”) colorants. Test pattern 18 includes one or more color patches 20.
Measurement device 22 may be any conventional measurement device that may be used to provide calorimetric data that describes a printed sample, such as a calorimeter, spectrophotometer, spectrocolorimeter, or other similar device. For example, measurement device 22 may be a Spectrolino spectrophotometer manufactured by GretagMacbeth LLC, New Windsor, N.Y. Measurement device 22 provides colorimetric data, such as CIE LAB data (referred to herein as “LAB data”) CIE XYZ data (referred to herein as “XYZ data”), CIE LUV data (referred to herein as “LUV data”), CIE LCH data (referred to herein as “LCH data”), or other similar calorimetric data that describes printed samples, such as color patches 20. Processor 24 may be a personal computer, laptop computer, handheld computer, computer workstation, print server, personal digital assistant, or any other similar device that may be used to receive colorimetric data, such as LAB data (i.e., L, a and b values), LUV data (i.e., L, u and v values), LCH data (i.e., L, C and H values), or other similar colorimetric data from measurement device 22 and generate therefrom numerical values that characterize color variations in a color output device in accordance with this invention. Persons of ordinary skill in the art will understand that the functions of processor 24 may be implemented by image source 12.
Referring now to FIGS. 1 and 2, an exemplary method 30 for characterizing color variations in a color output device in accordance with this invention is described. At step 32, color imaging device 14 is used to print test pattern 18 of one or more color patches 20 on one or more output pages 16. For example, a user of image source 12 may issue a print command to print multiple copies of image file 26 on color imaging device 14. At step 34, colorimetric values are determined for each color patch 20. For example, measurement device 22 may be used to determine LAB data for each color patch 20 on each of the output pages 16.
Referring now to FIG. 3, an exemplary output page 16 including exemplary test pattern 18 is described. Test pattern 18 includes one or more regions 40, with each region including one or more color patches 20. As shown in FIG. 3, test pattern 18 includes four regions 40a-40d, with each region including fifteen color patches 20. Persons of ordinary skill in the art will understand that test pattern 18 may include more or less than four regions 40, and each region may include more or less than 15 color patches 20. Each color patch 20 is comprised of a corresponding specified percentage of the colorants used by color imaging device 14 (e.g., C, M, Y and K). For example, color patches 20aa, 20ab, 20ac and 20ad may be comprised of 100% C. and 0% M, 0% Y and 0% K, color patches 20ba, 20bb, 20bc and 20bd may be comprised of 0% C, 100% M, 0% Y and 100% K, and color patches 20ca, 20cb, 20cc and 20cd may be comprised of 100% C, 0% M, 100% Y and 100% K. Persons of ordinary skill in the art will understand that other percentages of colorants also may be used for color patches 20.
Each output page 16 may include multiple similar color patches 20 distributed throughout test pattern 18. For example, color patches 20aa, 20ab, 20ac and 20ad in regions 40a-40d are similar to one another, and are appear at four different locations throughout test pattern 18. Similarly, color patches 20ba, 20bb, 20bc and 20bd in regions 40a-40d are similar to one another, and are appear at four different locations throughout test pattern 18, and color patches 20ca, 20cb, 20cc and 20cd in regions 40a-40d are similar to one another, and are appear at four different locations throughout test pattern 18. Persons of ordinary skill in the art will understand that the specific location of each color patch 20 is not important, but similar color patches preferably should be distributed over various parts of output page 16. As described below, similar color patches 20 located within an individual output page 16 are used to determine spatial page color variations.
Referring now to FIG. 4, an exemplary set of output pages 16 are described. Each of output pages 161-165 includes test pattern 18 including color patches 20. In particular, output page 161, includes color patches 20aa1 and 20ba1, output page 162 includes color patches 20aa2 and 20ba2, output page 163 includes color patches 20aa3 and 20ba3, output page 164 includes color patches 20aa4 and 20ba4, and output page 165 includes color patches 20aa5 and 20ba5. Across the five output pages 161-165, color patches 20aa1, 20aa2, 20aa3, 20aa4 and 20aa5 are similar to one another, and color patches 20ba1, 20ba2, 20ba3, 20ba4 and 20ba5 are similar to one another. As described below, similar color patches 20aa1-20aa5 and 20ba1-20ba5 located across multiple output pages 161-165 are used to determine page-to-page color variations.
Referring again to FIGS. 1 and 2, at step 34, colorimetric values are determined for each color patch 20 on each output page 16. Thus, for example, measurement device 22 may be used to determine LAB data for each color patch 20 on each of output pages 161-165 illustrated in FIGS. 3 and 4, for a total of three hundred sets of LAB data (i.e., sixty color patches 20 on each of the five output pages 161-165). At step 36, the standard deviation of each of the L, a and b values may be determined for sets of similar color patches 20. In particular, for each output page 16, the spatial standard deviation σLspatial, σaspatial, and σbspatial, of each of the L, a and b values, respectively, may be determined for similar color patches 20 within the page:




  
    
      
        
          σ
          ⁢
          
            
          
          ⁢
          
            L
            spatial
          
        
        =
        
          
            
              ∑
              
                
                  (
                  
                    L
                    -
                    
                      L
                      _
                    
                  
                  )
                
                2
              
            
            
              N
              -
              1
            
          
        
      
    
    
      
        (
        1
        )
      
    
  
  
    
      
        
          σ
          ⁢
          
            
          
          ⁢
          
            a
            spatial
          
        
        =
        
          
            
              ∑
              
                
                  (
                  
                    a
                    -
                    
                      a
                      _
                    
                  
                  )
                
                2
              
            
            
              N
              -
              1
            
          
        
      
    
    
      
        (
        2
        )
      
    
  
  
    
      
        
          σ
          ⁢
          
            
          
          ⁢
          
            b
            spatial
          
        
        =
        
          
            
              ∑
              
                
                  (
                  
                    b
                    -
                    
                      b
                      _
                    
                  
                  )
                
                2
              
            
            
              N
              -
              1
            
          
        
      
    
    
      
        (
        3
        )
      
    
  




where L, ā and b are the average L, a and b values, respectively, in each set, and N is the number of samples per set. For example, referring again to FIG. 3, the spatial standard deviation of each of the L, a and b values may be determined for the set of color patches 20aa-20ad, the set of color patches 20ba-20bd, the set of color patches 20ca-20cd, and so on.

In addition, for output pages 161-165, the page-to-page standard deviation σLP-P, σaP-P, and σbP-P, of each of the L, a and b values, respectively, may be determined for similar color patches 20 across the pages:




  
    
      
        
          σ
          ⁢
          
            
          
          ⁢
          
            L
            
              P
              -
              P
            
          
        
        =
        
          
            
              ∑
              
                
                  (
                  
                    L
                    -
                    
                      L
                      _
                    
                  
                  )
                
                2
              
            
            
              N
              -
              1
            
          
        
      
    
    
      
        (
        4
        )
      
    
  
  
    
      
        
          σ
          ⁢
          
            
          
          ⁢
          
            a
            
              P
              -
              P
            
          
        
        =
        
          
            
              ∑
              
                
                  (
                  
                    a
                    -
                    
                      a
                      _
                    
                  
                  )
                
                2
              
            
            
              N
              -
              1
            
          
        
      
    
    
      
        (
        5
        )
      
    
  
  
    
      
        
          σ
          ⁢
          
            
          
          ⁢
          
            b
            
              P
              -
              P
            
          
        
        =
        
          
            
              ∑
              
                
                  (
                  
                    b
                    -
                    
                      b
                      _
                    
                  
                  )
                
                2
              
            
            
              N
              -
              1
            
          
        
      
    
    
      
        (
        6
        )
      
    
  




where L, ā and b are the average L, a and b values, respectively, in each set, and N is the number of samples per set. For example, referring again to FIG. 4, the page-to-page standard deviation of each of the L, a and b values may be determined for the set of color patches 20aa1-20aa5, the set of color patches 20ba1-20ba5, and so on.

Referring again to FIG. 2, at step 38, a numerical value is calculated that is a function of the standard deviation values and that represents a colorimetric characterization of the color deviation of a set of similar color values. For example, a formula based on Euclidean distance calculations may be used. In particular, for each output page 16, a numerical value Espatial that represents the spatial color deviation within the page may be determined for similar color patches 20 based on the corresponding standard deviation values calculated in step 36:




  
    
      
        
          E
          spatial
        
        =
        
          
            
              σ
              ⁢
              
                
              
              ⁢
              
                
                  L
                  spatial
                
                2
              
            
            +
            
              σ
              ⁢
              
                
              
              ⁢
              
                
                  a
                  spatial
                
                2
              
            
            +
            
              σ
              ⁢
              
                
              
              ⁢
              
                
                  b
                  spatial
                
                2
              
            
          
        
      
    
    
      
        (
        7
        )
      
    
  




In addition, for output pages 161-165, a numerical value EP-P that represents the page-to-page color deviation across the pages may be determined for similar color patches 20 across the pages based on the corresponding standard deviation values calculated in step 36:

EP-P=√{square root over (σLP-P2+σaP-P2+σbP-P2)}  (8)

The following table illustrates exemplary Espatial and EP-P values for four color patches 20a per output page 16, across five output pages 161-165, where each sample patch 20a has colorant values 100% C, 0% M, 0% Y and 0% K:














Page
Sample
L
a
b



















1
20aa1
47.53
−31.07
−55.4


1
20ab1
48.12
−31.09
−55.3


1
20ac1
44.17
−27.24
−57.09


1
20ad1
47.72
−31.19
−55.33


2
20aa2
47.72
−30.5
−54.84


2
20ab2
47.56
−30.58
−55.37


2
20ac2
43.17
−25.81
−57.34


2
20ad2
45.98
−29.76
−55.97


3
20aa3
46.95
−29.95
−55.35


3
20ab3
47.41
−29.8
−55.49


3
20ac3
43.57
−25.67
−57.11


3
20ad3
45.24
−28.43
−56.51


4
20aa4
48.21
−30.2
−55.13


4
20ab4
48.31
−29.73
−55.32


4
20ac4
44.38
−25.8
−56.86


4
20ad4
46.82
−29.12
−55.82


5
20aa5
47.19
−32.07
−55.07


5
20ab5
48.02
−32.27
−55.28


5
20ac5
43.66
−27.39
−57.24


5
20ad5
45.03
−29.38
−56.64









Based on these exemplary values, and using equations (1)-(3) and (7), the spatial color deviation Espatial for each page is:














Page
Espatial



















1
2.971285



2
3.24904



3
2.735232



4
2.808842



5
3.169704










In addition, using equations (4)-(6) and (8), the page-to-page color deviation EP-P for each patch location is:














Patch Location
EP-P



















a
1.00057



b
1.117555



c
0.999795



d
1.609404










Persons of ordinary skill in the art will understand that the spatial color deviation Espatial values determined across multiple pages may be averaged to provide an average spatial color deviation, and that the page-to-page color deviation EP-P values determined across multiple patch locations may be averaged to provide an average page-to-page color deviation. Persons of ordinary skill in the art also will understand that other functions of may be used to characterize the color deviation of a set of similar color values. For example, functions based on CMC color deviation formulae or other similar color difference formulae may be used.
In addition, persons of ordinary skill in the art will understand that test pattern 18 may include more than four regions 40a-40d, and each region may include more than fifteen color patches 20. For example, FIG. 5 illustrates an alternative exemplary test pattern 18 that each includes four regions 40a-40d, with each region including sixty color patches P1-P60. Exemplary colorant values (specified in percent) for each patch are illustrated in the following table:

















Patch
C
M
Y
K






















P1
25
0
0
0



P2
50
0
0
0



P3
75
0
0
0



P4
100
0
0
0



P5
0
25
0
25



P6
0
50
0
50



P7
0
75
0
75



P8
0
100
0
100



P9
25
25
25
0



P10
50
50
50
0



P11
75
75
75
0



P12
100
100
100
0



P13
0
0
25
25



P14
0
0
50
50



P15
0
0
75
75



P16
0
0
100
100



P17
0
25
0
0



P18
0
50
0
0



P19
0
75
0
0



P20
0
100
0
0



P21
25
25
0
25



P22
50
50
0
50



P23
75
75
0
75



P24
100
100
0
100



P25
25
0
25
25



P26
50
0
50
50



P27
75
0
75
75



P28
100
0
100
100



P29
0
0
25
0



P30
0
0
50
0



P31
0
0
75
0



P32
0
0
100
0



P33
0
0
0
25



P34
0
0
0
50



P35
0
0
0
75



P36
0
0
0
100



P37
0
25
25
0



P38
0
50
50
0



P39
0
75
75
0



P40
0
100
100
0



P41
25
0
25
0



P42
50
0
50
0



P43
75
0
75
0



P44
100
0
100
0



P45
25
25
25
25



P46
50
50
50
50



P47
75
75
75
75



P48
100
100
100
100



P49
25
0
0
25



P50
50
0
0
50



P51
75
0
0
75



P52
100
0
0
100



P53
25
25
0
0



P54
50
50
0
0



P55
75
75
0
0



P56
100
100
0
0



P57
0
25
25
25



P58
0
50
50
50



P59
0
75
75
75



P60
0
100
100
100










As previously mentioned, persons of ordinary skill in the art will understand that the specific location of each color patch 20 is not important, but similar color patches preferably should be distributed over various parts of output page 16.

The foregoing merely illustrates the principles of this invention, and various modifications can be made by persons of ordinary skill in the art without departing from the scope and spirit of this invention.

## Claims

1. A method for characterizing a color variation of a color output device, the method comprising:
printing a set of similar color patches using the color output device;
determining colorimetric values for each color patch;
calculating a standard deviation value for each of the colorimetric values;
calculating a numerical value that is a function of the standard deviation values and that represents a colorimetric deviation of the set;
characterizing the color variation of the color output device based on the calculated numerical value; and
outputting a signal representative of the characterized color variation.

2. The method of claim 1, wherein the color output device is a color printer.

3. The method of claim 1, wherein the color output device is a color copier.

4. The method of claim 1, wherein the color output device is a color printing press.

5. The method of claim 1, wherein the color patches comprise predetermined percentages of cyan, magenta, yellow and black colorants.

6. The method of claim 1, wherein printing further comprises printing the set of similar color patches on an output page.

7. The method of claim 1, wherein printing further comprises printing the set of similar color patches on a plurality of output pages.

8. The method of claim 1, wherein the colorimetric values comprise L, a and b values.

9. The method of claim 1, wherein the colorimetric values comprise X, Y and Z values.

10. The method of claim 1, wherein determining further comprises measuring the color patches using a colorimeter.

11. The method of claim 1, wherein determining further comprises measuring the color patches using a spectrophotometer.

12. The method of claim 1, wherein determining further comprises measuring the color patches using a spectrocolorimeter.

13. The method of claim 1, wherein the function comprises a sum of squares of the standard deviation values.

14. The method of claim 1, wherein the function comprises a square root of a sum of squares of the standard deviation values.

15. A system for characterizing color variations in a color output device, the system comprising:
an image file comprising a set of similar color patches, the image file adapted to be printed on the color output device;
a means for determining colorimetric values for each printed color patch; and
a means for calculating a standard deviation value for each of the colorimetric values, and a numerical value that is a function of the standard deviation values and that represents a colorimetric characterization of color deviation of the set.

16. The system of claim 15, wherein the color output device is a color printer.

17. The system of claim 15, wherein the color output device is a color copier.

18. The system of claim 15, wherein the color output device is a color printing press.

19. The system of claim 15, wherein the color patches comprise predetermined percentages of cyan, magenta, yellow and black colorants.

20. The system of claim 15, wherein the set of similar color patches are printed on an output page.

21. The system of claim 15, wherein the set of similar color patches are printed on a plurality of output pages.

22. The system of claim 15, wherein the colorimetric values comprise L, a and b values.

23. The system of claim 15, wherein the colorimetric values comprise X, Y and Z values.

24. The system of claim 15, wherein the measuring device comprises a colorimeter.

25. The system of claim 15, wherein the measuring device comprises a spectrophotometer.

26. The system of claim 15, wherein the measuring device comprises a spectrocolorimeter.

27. The system of claim 15, wherein the function comprises a sum of squares of the standard deviation values.

28. The system of claim 15, wherein the function comprises a square root of a sum of squares of the standard deviation values.