Swiss Federal Institute of LausanneColor ReproductionLaboratory 1Spring Semester 2012

Report 1

Colorimetry & Color Systems

Bryan Zhi Li - Sciper 186560 - Communication Systems

March 13, 2012

Bryan Zhi Li Color Reproduction - Laboratory 1

Contents1 CRT Display Systems 3

1.1 Question 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Metameric Colors 42.1 Question 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3 Perceptual distances in color space 53.1 Question 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.2 Question 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.3 Question 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.4 Question 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4 Color Prints 114.1 Question 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.2 Question 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.3 Question 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

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Bryan Zhi Li Color Reproduction - Laboratory 1

1 CRT Display Systems

1.1 Question 11. Linear displays are desirable because it is always easy to display colors and thus all

the different displays will be same. There will not be a need for gamma correctionanymore ; displays will be uniform. However, most of the displays are not linearbecause the relationship between the emitted electrons on the phosphors and theapplied voltage is non linear. This non-linearity is not corrected because the conesensitivities of the eye are not linear and displays are meant for humans. Thus,most displays are still not linear.

2. To obtain XYZ tri-stimulus values, we can simply multiply the triplet of RGBcoordinates by the following matrix :XY

Z

=(XY ZRed XY ZGreen XY ZBlue

)·

RGB

(1)

To obtain the triplet RGB from XYZ tri-stimulus, we can do the following :RGB

=(XY ZRed XY ZGreen XY ZBlue

)−1·

XYZ

(2)

For the numerical values, we get :XYZ

=

41.24 35.76 18.0421.27 71.52 7.2171.933 11.919 95.02

·

RGB

(3)

3. From XYZ values, we convert them into RGB linear values (r,g,b) and apply agamma correction to obtain non-linear RGB values (r’,g’,b’) :

r′

g′

b′

=

(XY ZRed XY ZGreen XY ZBlue)−1

·

XYZ

1γ

(4)

From RGB non linear values (r’,g’,b’), we apply a gamma correction to obtain RGBlinear values (r,g,b) to which we concert them back to XYZ tri-stimulus :XY

Z

=(XY ZRed XY ZGreen XY ZBlue

)·

r′

g′

b′

γ

(5)

4. To verify the value of γ, we can save some linear RGB values and their respectiveoutput display values. Then using numerical methods, we check if the result isequal to 2.5. The numerical method can be implemented as follows :

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Bryan Zhi Li Color Reproduction - Laboratory 1

gamma= 1.5; % starting value for fit[x fval] = fminsearch(@(x) diffPowerSRGB(sRGB,x),gamma);disp([x fval]);

function f = diffPowerSRGB(sRGB,gamma)f = sum(((sRGB.^gamma)-sRGBtoLinearRGB(sRGB)).^2);

end

As the name suggests, the function sRGBtoLinearRGB computes linear RGBvalues from sRGB values.

2 Metameric Colors

2.1 Question 21. For small wavelengths - from 380 nm to 630 nm, the reflection spectra of P and Q

look alike but they diverge very quickly for larger wavelengths.

2. Observing the plot tells us that P and Q are metamers because they behave ap-proximatively the same way under the illuminant D65. Computing their CIELABdifference ∆E - which is 1.0248 - confirms this fact since the difference is so smallthat it should not be distinguishable by the human eye.

3. To compute the CIELAB ∆E, we need to insert the following code lines :XYZP = Spectrum2XYZ(rspectrumP,stdIlluminantA);XYZQ = Spectrum2XYZ(rspectrumQ,stdIlluminantA);LabP = XYZ_2_Lab(XYZP);LabQ = XYZ_2_Lab(XYZQ);deltaE = ( (LabP(1)-LabQ(1))^2 + (LabP(2)-LabQ(2))^2 + (LabP(3)-LabQ(3))^2 )^(1/2);fprintf(’The CIELAB delta E difference : ’);disp(deltaE);

Running the script will give us a ∆E of 4.7558, which is larger than the previous∆E. This index indicates that the eye should be able to distinguish two differentcolors ; thus P and Q are not metamers under the artificial light source A.

4. We notice that when the displayed reflection spectra is large only for a certain rangeof wavelengths, the respective color under each of the illuminants is different. Forexample, the illuminant A has a reflection spectra which is larger for the wavelengthsabove 550nm, meaning that the resulting colors would look redder ; P and Q willalso look like two different colors under the illuminant A. As for the illuminantD65, we notice that the reflection spectra is more or less the same for the ”visual”wavelengths, meaning that since P and Qs’ respective XYZ values are the same,they will be perceived as the same color under this illuminant.

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Bryan Zhi Li Color Reproduction - Laboratory 1

3 Perceptual distances in color space

3.1 Question 31. Running the script quest3Ex.m yields to the following two figures, where we can

the cross bars are identical along the 3 orientations in CIELAB.

(a) RGB space (b) CIELAB space

Figure 1: Different color spaces

2. Here are the crosses in XYZ and in xy :

(a) XYZ space (b) xy space

Figure 2: Different color spaces

The variations along the red green and blue cross segments in xy correspond to thechroma information in the LAB system, which are the axis a and b.

The distances between the extremities of the transformed crosses in xy do not reallycorrespond to the MacAdam ellipses of the course notes. For instance, if we comparethe generated cross bar and the theoretical ellipse of the course notes, we see thatthe generated one is much larger (the axis are longer), meaning that humans willperceive a difference of colors in a larger range, which is not what suggests thetheoretical MacAdam ellipses. Another interesting fact is the we observe only 7crossbars on the generated xy plane and not 8 ; this could be perhaps explained bythe fact two crossbars appear at the exact same position in the xy plane (towardsthe center where there is the color white) because the two colors are both so brightthat they cannot be differentiated anymore in this system.

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Bryan Zhi Li Color Reproduction - Laboratory 1

3.2 Question 41. Running the script quest4Ex.m with the original number of subdivisions yields to

the following results :

Color Plot(1,1) Plot(1,2) Plot(1,3) Plot(2,1) Plot(2,2) Plot(2,3)Red 3 4 5 6 6 7Green 4 4 5 6 6 8Blue 3 4 4 5 5 6Yellow 3 4 5 5 5 6Cyan 3 4 5 5 6 7

Magenta 3 4 4 5 5 5

2. We see clearly that the number of distinctible colors is not the same in all partsof the color space. This can be explained by the fact the cone sensitivities of theeye. In fact, the eye contains many more green and red cones than blue cones ;thus, we can distinguish more variants of a color when it comes to red or green.Theoretically, we should be able to distinguish the color yellow than magenta (orcyan) since the color yellow is a mixture of red and green colors while magenta (orcyan) contains blue and red colors. This is not the case here probably because ofthe laptop display which is not optimal for such experiments ; environment lightingcan also be an influence.

3.3 Question 51. We should not be allowed to add or subtract lightness differences from saturated

display colors to display them because this L component closely matches the humanperception ; modifying the displayed colors would result into generating ”false” orimaginary colors, which are outside the display’s gamut and thus not displayable.However, the resulting colors are still displayed because the display will simply mapthe ”false” colors to the closest displayable color.

2. We know that the human eye is more sensitive of lightness information than chromainformation ; we also know it is more sensitive to red and green colors (especiallygreen) than blue colors due to the more important number of red and green conesin comparison to blue cones. Thus, if we adjust equally the L component for greenand blue, we would see more lightness differences for the green color than the blueone. Thus, the differences are not similar for different colors of the color space.

3. If we modify with differences along the chroma axis, we change the saturation (orpurity) of the color while adjusting values along the lightness axis will affect theperceived lightness of the color. We can see that on the following figure :

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Bryan Zhi Li Color Reproduction - Laboratory 1

Figure 3: Illustration of the changes along chroma (right) or lightness (left) axis

Observing it shows us that we are more sensitive to lightness difference than chromadifference as we can see clearly two different colors on the left image while it is not easyto distinguish two colors on the right one.

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Bryan Zhi Li Color Reproduction - Laboratory 1

3.4 Question 6Starting with saturated colors, we decrease the chroma by the desired color difference, towhich we obtain the following.

(a) Red (b) Green

(c) Blue (d) Cyan

(e) Yellow (f) Magenta

Figure 4: Modifying with a color difference of ∆E94 = 10 along the chroma axis

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Bryan Zhi Li Color Reproduction - Laboratory 1

Then, we modify the resulting color to make it darker by the same color difference.

(a) Red (b) Green

(c) Blue (d) Cyan

(e) Yellow (f) Magenta

Figure 5: Modifying the previous images with a color difference of ∆E94 = 10 along thelightness axis (darker)

By observing the different images, we see that the CIELAB ∆E94 yield to very differentperceptual differences when it is applied along the chroma axis or the lightness axis.These perceptual differences are distinct to the ones generated by the CIELAB ∆E metric,perhaps due to the different way of computing the CIELAB difference. The CIELAB ∆E94matches also perhaps closer the human perception color difference than the CIELAB ∆Emetric.Here is the added script which generated the colors.% Question 6

% reducing chromaLdeltaE94 = 0;CdeltaE94 = -10;ptLabRed2 = Lab1CreateLab2DeltaE94(ptLabRed1,LdeltaE94, CdeltaE94);

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Bryan Zhi Li Color Reproduction - Laboratory 1

ptLabGreen2 = Lab1CreateLab2DeltaE94(ptLabGreen1,LdeltaE94, CdeltaE94);ptLabBlue2 = Lab1CreateLab2DeltaE94(ptLabBlue1,LdeltaE94, CdeltaE94);ptLabYellow2 = Lab1CreateLab2DeltaE94(ptLabYellow1,LdeltaE94, CdeltaE94);ptLabCyan2 = Lab1CreateLab2DeltaE94(ptLabCyan1,LdeltaE94, CdeltaE94);ptLabMagenta2 = Lab1CreateLab2DeltaE94(ptLabMagenta1,LdeltaE94, CdeltaE94);

sbPlotR = 2; % nb of subplot rowssbPlotC = 3; % nb of subplot columnsminSubdivWdg = 2; % min nb of subdivisionmaxSubdivWdg = 7; % max nb of subdivisionszX = 200; % size of the patchesszY = 100;

figure(1);DisplayWedgeSet(ptLabRed1, ptLabRed2, sbPlotR, sbPlotC, minSubdivWdg, maxSubdivWdg, szX, szY);figure(2);DisplayWedgeSet(ptLabGreen1, ptLabGreen2, sbPlotR, sbPlotC, minSubdivWdg, maxSubdivWdg, szX, szY);figure(3);DisplayWedgeSet(ptLabBlue1, ptLabBlue2, sbPlotR, sbPlotC, minSubdivWdg, maxSubdivWdg, szX, szY);figure(4);DisplayWedgeSet(ptLabYellow1, ptLabYellow2, sbPlotR, sbPlotC, minSubdivWdg, maxSubdivWdg, szX, szY);figure(5);DisplayWedgeSet(ptLabCyan1, ptLabCyan2, sbPlotR, sbPlotC, minSubdivWdg, maxSubdivWdg, szX, szY);figure(6);DisplayWedgeSet(ptLabMagenta1, ptLabMagenta2, sbPlotR, sbPlotC, minSubdivWdg, maxSubdivWdg, szX, szY);

% reducing lightness - darkerLdeltaE94 = -10;CdeltaE94 = 0;

ptLabRed3 = Lab1CreateLab2DeltaE94(ptLabRed2, LdeltaE94, CdeltaE94);ptLabGreen3 = Lab1CreateLab2DeltaE94(ptLabGreen2, LdeltaE94, CdeltaE94);ptLabBlue3 = Lab1CreateLab2DeltaE94(ptLabBlue2, LdeltaE94, CdeltaE94);ptLabYellow3 = Lab1CreateLab2DeltaE94(ptLabYellow2, LdeltaE94, CdeltaE94);ptLabCyan3 = Lab1CreateLab2DeltaE94(ptLabCyan2, LdeltaE94, CdeltaE94);ptLabMagenta3 = Lab1CreateLab2DeltaE94(ptLabMagenta2, LdeltaE94, CdeltaE94);

sbPlotR = 2; % nb of subplot rowssbPlotC = 3; % nb of subplot columnsminSubdivWdg = 2; % min nb of subdivisionmaxSubdivWdg = 7; % max nb of subdivisionszX = 200; % size of the patchesszY = 100;

figure(7);DisplayWedgeSet(ptLabRed2, ptLabRed3, sbPlotR, sbPlotC, minSubdivWdg, maxSubdivWdg, szX, szY);figure(8);DisplayWedgeSet(ptLabGreen2, ptLabGreen3, sbPlotR, sbPlotC, minSubdivWdg, maxSubdivWdg, szX, szY);figure(9);DisplayWedgeSet(ptLabBlue2, ptLabBlue3, sbPlotR, sbPlotC, minSubdivWdg, maxSubdivWdg, szX, szY);figure(10);DisplayWedgeSet(ptLabYellow2, ptLabYellow3, sbPlotR, sbPlotC, minSubdivWdg, maxSubdivWdg, szX, szY);figure(11);DisplayWedgeSet(ptLabCyan2, ptLabCyan3, sbPlotR, sbPlotC, minSubdivWdg, maxSubdivWdg, szX, szY);figure(12);DisplayWedgeSet(ptLabMagenta2, ptLabMagenta3, sbPlotR, sbPlotC, minSubdivWdg, maxSubdivWdg, szX, szY);

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Bryan Zhi Li Color Reproduction - Laboratory 1

4 Color Prints

4.1 Question 7

Figure 6: Reflection spectra of a magenta wedge

The real halftone magenta reflection spectra reflects still on some level (not a lot) thewavelength of the green spectra, whereas the ideal one does not; the component red isalso not totally reflected when in an ideal it should. Thus, all these parameters will createquite a divergence to the ideal reflection spectrum.

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Bryan Zhi Li Color Reproduction - Laboratory 1

4.2 Question 8

Figure 7: Surface coverage of a 50% nominal coverage magenta patch (in orange)

1. Observing the figure tells us that the surface coverage is not constant at all wave-lengths. The wavelengths with lengths smaller than 600 nm can be deduced withhigh confidence because it looks constant. However, the rest of the wavelengthsshould be discarded because it looks more like an error perhaps due to computa-tional values.

This wavelength range might be deduced from the reflection spectrum of the solidmagenta print because the solid magenta print’s reflection spectrum does not reallyvary much for wavelengths smaller than 600 nm while it increases drastically after600 nm to stabilize itself around 680 nm.Here is the code1 - which is added at the end of the script quest7Ex.m - whichproduced the previous figure% plot the surface coverage - 50%hold on;magenta50 = magentaLevels(6,:);magenta100 = magentaLevels(11,:);white = magentaLevels(1,:);aMagenta50 = (white - magenta50)./ (white - magenta100) ;plot(freq, aMagenta50,’-’,’Marker’,’.’,’Color’,[232, 118, 0]./255);legend(’white’, ’30% mag’, ’50% mag’, ’100% mag’,’ideal mag’,’50% surface coverage’);figNb=figNb+1;

1The piece of code was added below the original script quest7Ex.m.

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Bryan Zhi Li Color Reproduction - Laboratory 1

Figure 8: Surface coverage of a 70% nominal coverage magenta patch (in orange)

2. We see that the proposed range - wavelengths smaller than 600 nm - is also validfor the 70% nominal coverage magenta patch.

3. We simply build a machine which measures the reflection spectrum at 600 nm forexample. Then, for all wavelengths below 600 nm - that is from 380 nm to 600nm for the visual spectrum - where we have a high confidence, we draw a constant(line) at that value. This could be also applied to other inks but probably we wouldprobably change the set up since the others inks have different reflection spectraand thickness.

4.3 Question 91. Here are the two generated graphs in XYZ and xy systems.

(a) XYZ space (b) xy space

Figure 9: Polyline in two color spaces

The figure shows that it is not neither a straight line in the XYZ space nor inthe xy axis. For the xy space, we can even observe that it follows like a 1

xcurve

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Bryan Zhi Li Color Reproduction - Laboratory 1

which concurs with the different magenta levels when we superimpose it with thexy chromaticity diagram.

In both cases, we see that there are chrominance deviations for successive nominalcoverages.

2. If we observe closely, we that on the first image the distances between the pointsare not the same but increases non-linearly. This is because of the dot gain char-acteristic ; the printed point must not relly correspond exactly to a square pixelsurface.

3. Here is how the effective coverages are computed by making use of the Y values2 :XYZMagentaPatches = Spectrum2XYZ(magentaLevels,D65);% Only the second column - Y valuessolidMagenta = XYZMagentaPatches(11,2);white = XYZMagentaPatches(1,2);a = cell(1,size(XYZMagentaPatches,1));for i=1:size(XYZMagentaPatches,1)

a{i} = (white - XYZMagentaPatches(i,2)) ./ (white - solidMagenta);endfprintf(’The effective coverages with Y values are : ’);disp(a);

The output display shows the following :The effective coverages with Y values are : Columns 1 through 7

[0] [0.2604] [0.3902] [0.5226] [0.6440] [0.7379] [0.8113]

Columns 8 through 11

[0.8816] [0.9381] [0.9756] [1]

4. Here is how the dot gain is computed3 :% Filling in the effective coverages in a vector form for the substraction% operation to go fastereffective = zeros(size(a,2),1);nominal = zeros(size(a,2),1);for i=1:size(a,2)

effective(i,1) = a{i};nominal(i,1) = (i-1)/10;

end

dotGain = (effective - nominal).*100;plot(0:10:100,dotGain,’-r’,’Marker’,’.’);grid on;xlabel(’X’,’FontSize’,12);ylabel(’Y’,’FontSize’,12);title(’Dot gain for the considered magenta patches’,’FontWeight’,’bold’);

2The piece of code was added below the original script quest7Ex.m.3The piece of code was added at the end of the original script quest7Ex.m.

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Bryan Zhi Li Color Reproduction - Laboratory 1

The output display shows the following :

Figure 10: Dot gain for the magenta patches

We can use the function of the form −(ax2 + bx+ c) to approximate the dot gain.

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