Several models have been proposed for the colorimetric calibration of CRT monitors. These models use different mathematical functions to approximate the ...
Accurate colorimetric calibration of CRT monitors P. Bodrogi University of Veszprém, Hungary, and University of Karlsruhe, Germany K. Muray Institute for Photometry and Radiometry and California State University, Chico, CA J. Schanda University of Veszprém, Hungary, and CIE Central Bureau, Vienna, Austria
Abstract Several models have been proposed for the colorimetric calibration of CRT monitors. These models use different mathematical functions to approximate the relationship between the digital frame buffer values driving a color channel and the phosphor emission of that channel. Here we present an evaluation of colorimetric errors in terms of CIELAB lightness, hue, and chroma deviations caused by insufficient fit of such functions. A simple new function with few parameters minimizing these deviations is introduced. An analysis of the effect of monitor state and screen position on the accuracy of calibration has also been carried out.
Introduction Several different models have been described in the literature for the colorimetric calibration of CRT monitors (1-5). A useful review of the basic concepts of calibration can be found e.g. in (4). These models usually consist of two stages. The first stage is the approximation of the actual relationship (called "measured CRT curve", designated by f(d)) between the digital frame buffer (DAC) values d driving a single color channel and the relative phosphor radiance of that channel (taking usually 100 for the maximal radiance). This approximation is represented by a mathematical function called "CRT function" and designated by T(d). The insufficient fit of the CRT function T(d) to the measured CRT curve f(d) causes lightness, hue, and chroma differences between the predicted colors and those actually appearing on the screen. In this work attention will be focused on the analysis of these differences appearing in the first stage of the calibration model. The second stage describes the additive mixture of the light emitted by the red, green, and blue phosphors using a three times three matrix (called matrix P) consisting of the CIE X, Y, Z tristimulus values of the red, green, and blue peak primary colors (colors produced by maximum DAC values) of the monitor(5).
The use of matrix P presumes spatial and channel independence (6,8). In this work matrix P was used in all calculations. The violation of the condition of spatial and channel independence causes further lightness, hue, and chroma differences in addition to those caused by the insufficient fit of T(d) to f(d). These differences arising in the second stage will be discussed in a separate paper(10). The optimal CRT function must fulfill the following conditions: 1.) It has to fit the measured CRT curve f(d) and predict accurately the colors; 2.) The determination of the parameters from f(d) has to be simple; 3.) The function and its inverse should be simple to calculate. The following CRT functions will be analysed: Ti ,1 = E i di γi (1 ) γ i
d Ti,2 = N i 2 − 1 see (4), and
(2 ) γ
d i Ti ,3 = kgi N i + koi (3 ) 2 − 1 see (5,7). i: r, g, or b, corresponding to the red, green, or blue channels, respectively; d: DAC value; T: monitor tristimulus value; N: number of bits per color channel; kg , ko : normalized system gain and offset; and
E , γ: further CRT function parameters. None of these equations fulfills condition 1.) The parameters kg , ko , E , γ have to be determined
from the measured CRT curves. The γ values are usually different in Eq. (1), (2), and (3) and also for the red, green and blue channels. A fourth CRT function will be introduced in order to fulfill condition 1.). The influence of monitor state and screen position(6) on the accuracy of the calibration will also be investigated.
An optimal CRT function We define a new CRT function in the following way:
Ti ,41( di ) = ai di + bi
0 ≤di ≤t1i
Ti ,42 ( di ) = ti di + ui di + vi
t1i < di ≤ t2 i
2
γ i
d Ti ,43 = kgi N i + koi 2 − 1
di > t 2i
(4 )
here t1i and t2i are fixed values of di determined from the best visual overall fit of the three part curve; a, b are parameters of the linear approximation in the DAC interval [0, t1 ]; t, u, v are parameters of the quadratic approximation in the DAC interval [ t1 , t2 ]. For DAC values greater than t2 Eq. (3) is applies. As can be seen, conditions 2.) and 3.) are fulfilled. This function predicts the CIE X, Y, Z tristimulus values of the displayed colors with higher accuracy than Eqs. (1), (2), and (3), as it will be shown in the following sections. Experimental method The measurements were conducted in a dark room. The monitor was switched on well before the measurement for stabilisation. The functions f i ( d i ) (i = r, g, or b) were determined by measuring luminances in the center of a 214 pixel x 160 pixel color bar displayed in the middle of the screen. This bar represents 11% of the whole addressable display area. The rest of the screen was left black. The red, green, and blue channels were driven always separately by all possible DAC values N between 0 and 2 − 1 . Matrix P was determined under similar conditions. An INPHORA TRI 4 tristimulus colorimeter was used for the measurements with its 1 degree measuring field positioned to the center of the screen. This position will be referred to as primary position. The distance between the screen and the entrance lens of the colorimeter was 55 cm. The monitor and the colorimeter were controlled by the same PC, all measurements were carried out automatically using our program package for monitor calibration PPMC (9). Two monitors were examined: 1. A general purpose inexpensive 14" minitor with a maximum resolution of 640 x 480 pixels (termed H); and 2. a medium quality 20'' monitor (termed E) with a maximum resolution of 1280 x 1024 pixels. Both monitors were driven with VGA
graphics cards, using 640 X 480 pixel resolution graphics mode, N=6 bits per color channel, and with nested gain/offset control(5). The monitor state used in the experiments is defined as follows: First the gain/offset control knobs were set to maximum and then the offset control knob was decreased until the full-screen peak white luminance 2 measured in the middle of the screen was 70 cd/m for 2 monitor H and 75 cd/m for monitor E. This monitor state will be referred to as primary state. Computational method The parameters of the CRT functions in Eqs. (1)-(4) were determined from the measured CRT curves f i ( d i ) by using the method of least square errors in PPMC(9). In Eq. (4) the following DAC interval limits were used for all channels: t1 =5 and t2 =17. 125 possible combinations of the following red, green, and blue DAC values: 0, 15, 31, 47, 63 were selected. This set of display colours will be called sample. The CIELAB L*, a*, b* values of the sample colors were calculated in five different ways, first (j=1, 2, 3, and 4) using the CRT functions of Eqs. (1), (2), (3), and (4), respectively, and finally (j=5) using the measured CRT curves f i ( d i ) . The peak white calculated from matrix P was considered as reference white. The CIELAB lightness, chroma, hue angle and color differences arising due to the insufficient fit of the CRT functions were calculated for each sample color and for each CRT function j=1..4:
∆L* j = L* j − L*5 ∆C* j = C* j − C*5 ∆h
*
j
=h
*
j
−
(5 )
h*5
∆E * j = ( L* j − L*5 )2 + ( a* j − a* 5 )2 + ( b* j − b*5 )2
Results The average ∆E * j values and STDs (standard deviations) of the whole sample for the two monitor types are listed in Table 1. As can be seen from Table 1, the first and the second CRT functions cause unacceptably high average color differences between the predicted and the actual color.
Table 1 The average ∆E * j values and STDs of the whole sample calculated using the four CRT functions j=1..4, monitors H and E.
17
C*
12
1 8,48
2 4,59
3 1,39
4 0,39
H: STD E: Aver.
6,38 3,90
2,80 2,44
2,17 1,12
0,21 0,28
E: STD
3,02
1,58
1,88
0,15
The averages of the third CRT function are acceptable, but the STDs in column j = 3 remain still large. This is because Eq. (3) still causes average CIELAB color * * differences of ∆Eab =3.72 (H) and ∆Eab =3.22 (E) if all DAC values are less than half of their maximum value ("region of dark colors"). If accurate calibration is required in the region of dark colors then the CRT function defined by Eq. (4) should be used. In this case * average CIELAB color differences are ∆Eab =0.52 (H) and ∆E (E). The average ∆E value of the whole sample in case of Eq. (4) is insignificant, and the STDs are also very small. * ab =0.74
2 -10
-5
-3 0
∆ L* j
Figure 1. The sample in the ∆h* − ∆C* diagram, using the CRT function defined by Eq. (1).
17 12 7 2 -10
-5
-3 0
j
10
∆ h*
Figure 2. The sample in the ∆h* − ∆C* diagram, using the CRT function defined by Eq. (2).
CIELAB lightness 17 12 7
C*
Table 2 The average ∆ L
5
-8
differences and STDs of the whole sample for the two monitor types. The lightness differences have the same * tendencies as ∆Eab , as can be seen on Table 2. *
10
∆ h*
* ab
Table 2 shows the average
5
-8
C*
j H: Aver.
7
2
values and STDs of the -10
-5
whole sample calculated using the four CRT functions j=1..4 for monitors H and E. 1 3,24
2 1,95
3 0,38
4 0,17
H: STD E: Aver.
2,94 1,27
1,60 0,92
1,24 0,27
0,12 0,14
E: STD
1,28
1,01
0,97
0,06
Figures 1-4 show the whole sample in the ∆h* − ∆C* diagram in case of monitor H. Similar figures have been obtained for the monitor E.
10
∆ h*
Figure 3. The sample in the ∆h* − ∆C* diagram, using the CRT function defined by Eq. (3).
17 12 7 2 -10
As can be seen in Figures 1-2 the predicted colors by the CRT functions Eq. (1) and Eq. (2) exhibit large CIELAB chroma and hue angle errors. Figure 3 shows that these errors can be reduced by Eq. (3). The most accurate prediction of colors appearing on the display is provided by Eq. (4), as can be observed in Figure 4.
5
-8
C*
j H: Aver.
-3 0
-5
-3 0
5
10
-8 ∆ h*
Figure 4. The sample in the ∆h* − ∆C* diagram, using the CRT function defined by Eq. (4).
The effect of monitor state and screen position on the accuracy of the calibration The CRT function parameters in Eqs. (1)-(4) have also been determined based on f(d) functions measured in different monitor states and in different positions on the screen also. The monitor state was changed by choosing different control knob settings. The screen position was changed by displaying the 214 pixel x 160 pixel color bar at different parts of the screen (e.g. the top left corner instead of the middle). The color differences of Eq. (5) were calculated for the case of the monitor H by using the f(d) function measured in the primary state and in the primary position. The CRT function of Eq. (3) was determined for the primary state and top left corner, as well as the primary position and the state of maximal gain/offset setting (peak white 2 luminance: 93 cd/m ). Table 3 contains the average * ∆Eab values and STDs. Table 3 Averages and STDs of colorimetric errors caused by Eq. (3) if its parameters were determined in another position (column A) or in another state * (column B). Row 1: ∆Eab , 2: ∆L* , 3: ∆C* , 4: ∆h* . A 1 2 3 4
Aver. 2,67 1,25 1,71 1,32
B STD 1,78 1,57 1,2 2,38
Aver. 21,69 8,34 15,54 29,43
STD 10,25 6,57 9,3 77,09
As can be seen from Table 3, it is very important to determine the CRT function parameters in the same monitor state where the CRT function is used predicting the colors appearing on the screen. Changing the monitor state without recalibration leads to significant errors. Although changing the screen position does not cause too large errors, it would be desirable to use different CRT function parameters in different regions of the screen.
Summary In this paper the colorimetric differences between the predicted and actual display colors arising due to the imperfect fitting of different mathematical functions widely used to approximate the radiance characteristics of color CRT monitors have been analyzed. The use of the first two functions must be avoided if accurate calibration is required. A new simple function causing
minimal errors was introduced (Eq. (4)). This function is recommended especially if accurate calibration of dark colors is required. In addition, it was pointed out that the monitor has to be recalibrated if the monitor state has been changed. Acknowledgements We gratefully acknowledge the grant of the Miescher foundation for the purchase of the INPHORA colorimeter, the US - Hungarian Joint fund (KM & JS) and the DAAD grant (PB) for partial support of the experimental work and the Institute for Lighting Technology of the University Karlsruhe and the Department of Image Technologies and Neural Computers of the University Veszprém and the OTKA F014485 grant for their support of the research. References 1. W.T. Hartmann, and Th. E. Madden, Journal of Imaging Technology 13, p. 103 (1987). 2. D. H. Brainard, Color Res. Appl. 14, p. 23 (1989). 3. D. L. Post, and Ch. S. Calhoun, Color Res. Appl. 14, p. 172 (1989). 4. D. Travis, Effective Color Displays, Theory and Praxis, Acad. Press (1991). 5. R. S. Berns, R. J. Motta, and M. E. Gorzynski, Color Res. Appl. 18, p. 299 (1993). 6. R. S. Berns, M. E. Gorzynski, and R. J. Motta, Color Res. Appl. 18, p. 315 (1993). 7. CIE TC 2-26 Technical Report, Guide to Characterizing the Colorimetry of Computer-Controlled CRT Displays (1993). 8. R. J. Motta, M.S.Thesis, Rochester Institute of Technology (1991). 9. P. Bodrogi, Program Package for Monitor Calibration (PPMC), University of Veszprém, Dep. of Informatics (1994). 10. P. Bodrogi, and J. Schanda, to be published in Displays (1995).
