Modeling the effects of gamma on the colors ... - Semantic Scholar
Modeling the effects of gamma on the colors displayed on cathode ray tube monitors
Journal of Electronic Imaging, vol. 13, no. 4, Oct. 2004 Snjezana Soltic and Andrew N. Chalmers School of Electrical Engineering and Computer Science, Kyungpook National Univ.
Abstract Displayed
colors on a CRT monitor
– Gamma of the display – Display primaries – White point setting Color
difference in CIELAB color space
– 76 color samples • 66 chromatic samples and 10 achromatic samples
– 8 different gamma values Comparison
of CIELAB color difference
– Color shift • 3.58 CIELAB units with a gamma “discrepancy” of 0.1 • 9.90 CIELAB units with a gamma “discrepancy “ of 0.3 2/23
1. Introduction Appearance
of a color image on a CRT display
– Viewing conditions – Characteristics of the display • Different phosphor sets – 18 CIELAB color difference units • White point – less than 10 CIELAB color difference units
– Gamma of the display Purpose
of this investigation
– Applying suitable mathematical models to quantify the reproduction of colors in an image on display having different gamma values
3/23
2. Background
CRT model – nonlinear transformation – Between the luminance and the numerical pixel value – GOG model
L = ( K1 Dn + K 2 )γ • • • • •
(1)
L : luminance of the screen primary Dn : normalized digital pixel value K1 : gain factor K 2 : offset ( K1 + K 2 = 1)
γ
: nonlinearity of the system
– Assumption – representative of desktop computer monitors • Gain and offset values : K1 = 1.15, K 2 = −0.15 (by Motta) • Reference CRT monitor gamma : 2.2 – sRGB color space
4/23
CRT
model – linear transformation
– Between the set of chromaticities of the RGB phosphor and device-independent CIE tristimulus values • White point setting of the monitor • CIE chromaticity coordinates of the RGB phosphor
– In this work • ITU-R BT 709 reference primary • D65 white point (adopted in the sRGB recommendation) Table 1. CIE-1931 chromaticity coordinates (x,y,z) for ITU-R BT 709 reference primaries and D65 white point
5/23
3. Simulation Four
numerical color sets of 76 samples
– 3 chromatic sample sets (66 samples) • Set1 - 24 high-chroma colors – At least one of the primaries has a value of 255 while a second is at zero and the third takes on values from 0 to 255
• Set2 - 18 lower chroma – One primary is held at 128 while the second is at zero and the third covers the range from 0 to 192
• Set3 – a few lower chroma sample, as well as a moderate chroma – All primaries are nonzero
– 1 achromatic sample set (10 samples) • 10 achromatic samples • Range 35-255 with increments of 25 and a final increment of 20 6/23
Table 2. Digital counts of the samples used in the simulation.
7/23
Table 2. Continued.
8/23
Nonlinear
part of the model
– Offset value of D under set of assumption D − 0.15 = 0 if D ≈ 33.26 1.15 × 255
– Assumption • Three channels all follow Eq. (2) • Gamma applies equally to all three channels γ
D D − 0.15 , 1.15 × LD = 100 × 1.15 × − 0.15 ≥ 0 255 255 D LD = 0 , 1.15 × − 0.15 < 0 255
(2)
• LD : pixel’s normalized luminance (0 ≤ LD ≤ 100) • D : pixel’s original R or B or G value (in range 0-255) • γ : 1.4, 1.7, 1.8, 2.1, 2.2, 2.5, 2.7, and 3
9/23
Color
error in the CIELAB space
– Calculated with respect to the reference gamma of 2.2 ∗ ∆Eab =
[ [L
]
(L − L ) + (a ∗
2 ∗ 2.2
∗
) ( 2
− a2∗.2 + b∗ − b2∗.2
)
2
(3)
• L∗ , a ∗ , b∗ : test sample (γ = 1.4,1.7,1.8, 2.1, 2.5, 2.7, 3) •
∗ 2.2
]
, a2∗.2 , b2∗.2 : reference sample with the gamma of 2.2
– Overall root mean square (rms) error ∗ ∆Eab , rms =
∑ ∆Eab∗
2
(4)
Ns
• N s : the number of samples in the set
10/23
4. Discussion and Results Fig.
1, 2, and 3
– Influence of different gammas in term of a * / b* plots in the CIELAB color space – Strong evidence of significant loss of chroma as the values of gamma are increased. Fig.
4
– For D=60…160 • L* is about 25-30 units higher for the smallest gamma than for the largest.
– Above D=160 • Converging to common maximum of L*=100 units at D=255
– Shapes of curves • Cube-root transformation in the definition of L* • Luminance response of the display
11/23
Fig. 1
Fig. 2
Fig. 3 Fig. 4 Fig. 1. Predicted influence of gamma on reproduced colors : Set 1 samples (high chroma colors) (Symbols for samples S1-1, S1-9, and S1-17 are obscured by others in the vicinity of the “apices”). Fig. 2. Predicted influence of gamma on reproduced colors : Set 2 samples (mid chroma colors) Fig. 3. Predicted influence of gamma on reproduced colors : Set 3 samples (low chroma colors) Fig. 4. Predicted L* (gray scale response) for different gamma values : Set 4 samples (achromatic gray scale) 12/23
4.1
Sample Set 1
– Error vector magnified by a factor of x2.5
Fig. 5
Fig. 6 Simultaneous reduction in both lightness and chroma
: maximal primary colors
9 Reduction in lightness
9Independent of gamma
9 Increase in chroma
Fig. 5. Predicted vector diagram for Set 1 samples (high chroma colors) in a*/b* plane for relative to
γ = 2.2
γ = 2.1 and γ = 2.5
Fig. 6. Predicted vector diagram for Set 1 samples (high chroma colors) in L*/C* plane : color errors for γ and γ
= 2.5 relative to γ = 2.2
= 2.1 13/23
Table 3. (a) Set 1 Colorimetric Errors for γ = 2.1 and γ = 2.5 relative to γ = 2.2 . (b) Summary of Set 1 rms colorimetric errors for various
γ
, relative to γ = 2.2
Sample 15 The highest error R=0%, G=50%, and B=100% small deviations in gamma -> significant colorimetric error
: the highest error * : individual error ∆Eab ≥ 4 CELAB units : zero colorimetric error * * : ∆Eab > ∆Eab , rms
14/23
4.2
Sample Set 2
Fig. 8
Fig. 7 Loss of chroma (with almost no change in hue) 5 samples : change in hue with little or no change of chroma 4 samples : combination of these effects
Set 2 and 3 Drop in L* value, order of 5-10 CIELAB units Loss of L* to be accompanied by a decrease in chroma[2(6) exception in Set2(3)]
Fig. 7. Predicted vector diagram for Set 2 samples (mid chroma colors) in a*/b* plane for γ = 2.1 and γ = 2.5 Relative to γ = 2.2 Fig. 8. Predicted vector diagram for Set 2 samples (mid chroma colors) in L*/C* plane for γ = 2.1 and γ = 2.5 Relative to γ = 2.2 15/23
Table 4. (a) Set 2 Colorimetric Errors for γ = 2.1 and γ = 2.5 relative to γ = 2.2 . (b) Summary of Set 2 rms colorimetric errors for various
γ
, relative to
γ = 2.2
Set 2 and 3 9For gamma = 2.1 * Fairly consistent in the vicinity of ∆Eab = 2 CIELAB units
9For gamma = 2.5 * Close to ∆Eab = 5 CIELAB units
16/23
4.2
Sample Set 3
Fig. 9
Fig. 10
Much more consistent loss of chroma Chroma difference is small in some samples Evidence of a noticeable hue difference accompanied by almost no chroma change Fig. 9. Predicted vector diagram for Set 3 samples (low chroma colors) in a*/b* plane for γ = 2.1and γ = 2.5 Relative to γ = 2.2 Fig. 10. Predicted vector diagram for Set 3 samples (low chroma colors) in L*/C* plane forγ = 2.1 andγ = 2.5 Relative to γ = 2.2 17/23
Table 5. (a) Set 3 Colorimetric Errors for γ = 2.1 and γ = 2.5 relative to γ = 2.2 . (b) Summary of Set 3 rms colorimetric errors for various
γ
, relative to
γ = 2.2
18/23
4.3
Sample Set 4
Fig. 11. Predicted effect of gamma on L* for 11 gray scale samples : Set 4 samples (achromatic gray scale).
Compared with Fig. 4
Decline in lightness for each sample (exception for D=255)
19/23
Table 6. (a) Set 4 lightness errors for γ = 2.1 and γ = 2.5 relative to γ = 2.2 . (b) Summary of Set 4 average lightness errors for various
γ
, relative to γ = 2.2
20/23
4.4
Summary Table 7. Summary of rms colorimetric errors for Sets 1, 2, and 3.
Set 2 : the highest errors
Set 1 : the lowest (roughtly 30% lower than Set 2) Set 3 : intermediate errors (about 12% lower than Set 2)
21/23
Fig. 12. Predicted colorimetric error resulting from deviations in gamma.
Errors increased almost linearly as gamma deviate from its reference value Slightly different rates of change for positive and negative gamma deviation
22/23
5. Conclusions Simulation Analysis
of influence of monitor gamma
of color error in the CIELAB color space
– Computation of rms colorimetric error (gamma = 1.4…3.0) For
gamma deviation of ± 0.5
– 8 unit of
* ∆Eab ,rms for
chromatic samples (Fig. 12)
– 6 CIELAB units for neutrals Importance
of monitor gamma
– For transmission of color images across the internet – For accurate color image interchange
23/23
Journal of Electronic Imaging, vol. 13, no. 4, Oct. 2004 Snjezana Soltic and Andrew N. Chalmers School of Electrical Engineering and Computer Science, Kyungpook National Univ.
Abstract Displayed
colors on a CRT monitor
– Gamma of the display – Display primaries – White point setting Color
difference in CIELAB color space
– 76 color samples • 66 chromatic samples and 10 achromatic samples
– 8 different gamma values Comparison
of CIELAB color difference
– Color shift • 3.58 CIELAB units with a gamma “discrepancy” of 0.1 • 9.90 CIELAB units with a gamma “discrepancy “ of 0.3 2/23
1. Introduction Appearance
of a color image on a CRT display
– Viewing conditions – Characteristics of the display • Different phosphor sets – 18 CIELAB color difference units • White point – less than 10 CIELAB color difference units
– Gamma of the display Purpose
of this investigation
– Applying suitable mathematical models to quantify the reproduction of colors in an image on display having different gamma values
3/23
2. Background
CRT model – nonlinear transformation – Between the luminance and the numerical pixel value – GOG model
L = ( K1 Dn + K 2 )γ • • • • •
(1)
L : luminance of the screen primary Dn : normalized digital pixel value K1 : gain factor K 2 : offset ( K1 + K 2 = 1)
γ
: nonlinearity of the system
– Assumption – representative of desktop computer monitors • Gain and offset values : K1 = 1.15, K 2 = −0.15 (by Motta) • Reference CRT monitor gamma : 2.2 – sRGB color space
4/23
CRT
model – linear transformation
– Between the set of chromaticities of the RGB phosphor and device-independent CIE tristimulus values • White point setting of the monitor • CIE chromaticity coordinates of the RGB phosphor
– In this work • ITU-R BT 709 reference primary • D65 white point (adopted in the sRGB recommendation) Table 1. CIE-1931 chromaticity coordinates (x,y,z) for ITU-R BT 709 reference primaries and D65 white point
5/23
3. Simulation Four
numerical color sets of 76 samples
– 3 chromatic sample sets (66 samples) • Set1 - 24 high-chroma colors – At least one of the primaries has a value of 255 while a second is at zero and the third takes on values from 0 to 255
• Set2 - 18 lower chroma – One primary is held at 128 while the second is at zero and the third covers the range from 0 to 192
• Set3 – a few lower chroma sample, as well as a moderate chroma – All primaries are nonzero
– 1 achromatic sample set (10 samples) • 10 achromatic samples • Range 35-255 with increments of 25 and a final increment of 20 6/23
Table 2. Digital counts of the samples used in the simulation.
7/23
Table 2. Continued.
8/23
Nonlinear
part of the model
– Offset value of D under set of assumption D − 0.15 = 0 if D ≈ 33.26 1.15 × 255
– Assumption • Three channels all follow Eq. (2) • Gamma applies equally to all three channels γ
D D − 0.15 , 1.15 × LD = 100 × 1.15 × − 0.15 ≥ 0 255 255 D LD = 0 , 1.15 × − 0.15 < 0 255
(2)
• LD : pixel’s normalized luminance (0 ≤ LD ≤ 100) • D : pixel’s original R or B or G value (in range 0-255) • γ : 1.4, 1.7, 1.8, 2.1, 2.2, 2.5, 2.7, and 3
9/23
Color
error in the CIELAB space
– Calculated with respect to the reference gamma of 2.2 ∗ ∆Eab =
[ [L
]
(L − L ) + (a ∗
2 ∗ 2.2
∗
) ( 2
− a2∗.2 + b∗ − b2∗.2
)
2
(3)
• L∗ , a ∗ , b∗ : test sample (γ = 1.4,1.7,1.8, 2.1, 2.5, 2.7, 3) •
∗ 2.2
]
, a2∗.2 , b2∗.2 : reference sample with the gamma of 2.2
– Overall root mean square (rms) error ∗ ∆Eab , rms =
∑ ∆Eab∗
2
(4)
Ns
• N s : the number of samples in the set
10/23
4. Discussion and Results Fig.
1, 2, and 3
– Influence of different gammas in term of a * / b* plots in the CIELAB color space – Strong evidence of significant loss of chroma as the values of gamma are increased. Fig.
4
– For D=60…160 • L* is about 25-30 units higher for the smallest gamma than for the largest.
– Above D=160 • Converging to common maximum of L*=100 units at D=255
– Shapes of curves • Cube-root transformation in the definition of L* • Luminance response of the display
11/23
Fig. 1
Fig. 2
Fig. 3 Fig. 4 Fig. 1. Predicted influence of gamma on reproduced colors : Set 1 samples (high chroma colors) (Symbols for samples S1-1, S1-9, and S1-17 are obscured by others in the vicinity of the “apices”). Fig. 2. Predicted influence of gamma on reproduced colors : Set 2 samples (mid chroma colors) Fig. 3. Predicted influence of gamma on reproduced colors : Set 3 samples (low chroma colors) Fig. 4. Predicted L* (gray scale response) for different gamma values : Set 4 samples (achromatic gray scale) 12/23
4.1
Sample Set 1
– Error vector magnified by a factor of x2.5
Fig. 5
Fig. 6 Simultaneous reduction in both lightness and chroma
: maximal primary colors
9 Reduction in lightness
9Independent of gamma
9 Increase in chroma
Fig. 5. Predicted vector diagram for Set 1 samples (high chroma colors) in a*/b* plane for relative to
γ = 2.2
γ = 2.1 and γ = 2.5
Fig. 6. Predicted vector diagram for Set 1 samples (high chroma colors) in L*/C* plane : color errors for γ and γ
= 2.5 relative to γ = 2.2
= 2.1 13/23
Table 3. (a) Set 1 Colorimetric Errors for γ = 2.1 and γ = 2.5 relative to γ = 2.2 . (b) Summary of Set 1 rms colorimetric errors for various
γ
, relative to γ = 2.2
Sample 15 The highest error R=0%, G=50%, and B=100% small deviations in gamma -> significant colorimetric error
: the highest error * : individual error ∆Eab ≥ 4 CELAB units : zero colorimetric error * * : ∆Eab > ∆Eab , rms
14/23
4.2
Sample Set 2
Fig. 8
Fig. 7 Loss of chroma (with almost no change in hue) 5 samples : change in hue with little or no change of chroma 4 samples : combination of these effects
Set 2 and 3 Drop in L* value, order of 5-10 CIELAB units Loss of L* to be accompanied by a decrease in chroma[2(6) exception in Set2(3)]
Fig. 7. Predicted vector diagram for Set 2 samples (mid chroma colors) in a*/b* plane for γ = 2.1 and γ = 2.5 Relative to γ = 2.2 Fig. 8. Predicted vector diagram for Set 2 samples (mid chroma colors) in L*/C* plane for γ = 2.1 and γ = 2.5 Relative to γ = 2.2 15/23
Table 4. (a) Set 2 Colorimetric Errors for γ = 2.1 and γ = 2.5 relative to γ = 2.2 . (b) Summary of Set 2 rms colorimetric errors for various
γ
, relative to
γ = 2.2
Set 2 and 3 9For gamma = 2.1 * Fairly consistent in the vicinity of ∆Eab = 2 CIELAB units
9For gamma = 2.5 * Close to ∆Eab = 5 CIELAB units
16/23
4.2
Sample Set 3
Fig. 9
Fig. 10
Much more consistent loss of chroma Chroma difference is small in some samples Evidence of a noticeable hue difference accompanied by almost no chroma change Fig. 9. Predicted vector diagram for Set 3 samples (low chroma colors) in a*/b* plane for γ = 2.1and γ = 2.5 Relative to γ = 2.2 Fig. 10. Predicted vector diagram for Set 3 samples (low chroma colors) in L*/C* plane forγ = 2.1 andγ = 2.5 Relative to γ = 2.2 17/23
Table 5. (a) Set 3 Colorimetric Errors for γ = 2.1 and γ = 2.5 relative to γ = 2.2 . (b) Summary of Set 3 rms colorimetric errors for various
γ
, relative to
γ = 2.2
18/23
4.3
Sample Set 4
Fig. 11. Predicted effect of gamma on L* for 11 gray scale samples : Set 4 samples (achromatic gray scale).
Compared with Fig. 4
Decline in lightness for each sample (exception for D=255)
19/23
Table 6. (a) Set 4 lightness errors for γ = 2.1 and γ = 2.5 relative to γ = 2.2 . (b) Summary of Set 4 average lightness errors for various
γ
, relative to γ = 2.2
20/23
4.4
Summary Table 7. Summary of rms colorimetric errors for Sets 1, 2, and 3.
Set 2 : the highest errors
Set 1 : the lowest (roughtly 30% lower than Set 2) Set 3 : intermediate errors (about 12% lower than Set 2)
21/23
Fig. 12. Predicted colorimetric error resulting from deviations in gamma.
Errors increased almost linearly as gamma deviate from its reference value Slightly different rates of change for positive and negative gamma deviation
22/23
5. Conclusions Simulation Analysis
of influence of monitor gamma
of color error in the CIELAB color space
– Computation of rms colorimetric error (gamma = 1.4…3.0) For
gamma deviation of ± 0.5
– 8 unit of
* ∆Eab ,rms for
chromatic samples (Fig. 12)
– 6 CIELAB units for neutrals Importance
of monitor gamma
– For transmission of color images across the internet – For accurate color image interchange
23/23
