[argyllcms] Re: perceptual black too light

Graeme Gill wrote:
I wasn't really aiming for a perfect simulation, and the uniform randomness made some things a little easier to calculate. The next level of refinement would be to try and characterize real world error distributions (ie. are they uniform and gaussian when measured in XYZ ?), and to taylor the smoothing factors appropriately in the L*a*b* colorspace (ie. translate it into sample point weightings).
Some time ago I had measured a data set of 53 CMYK colors, where each color was printed 10 times (530 measurements total), in order to get a clue of the repeatability of my printer + measurements. Please find them attached.

A sample size of 10 for each color is however not enough to test whether the sample follows a particular distribution, but it permits to compute a mean Lab value for each of the 53 colors, and to compute the deviation (error) of each of the 530 samples from its corresponding mean value (though of course the expected value of the distribution is predicted by the sample mean only with some uncertainty, given only a small sample size of only 10).

As said above, drawing a histogram from only 10 samples is rather useless. So I have only created overall histograms for the L*, a* and b* deviation of all 530 measurements from their corresponding mean, and also a histogram for dE.

The histograms for the L*, a* and b* errors look indeed bell-shaped and the L* and a* samples are not rejected as non-normal by a Kolmogorov Smirnov null hypothesis test at 5% confidence level, only the samples of b* seems to deviate a bit stonger from normal, here it needs a 1% confidence level, in order that K-S test does not reject the samples as non-normal. A hypothesis test for a uniform distribution (with the same mean and standard deviation as the samples) is rejected for all three channels. And the dE histogram looks similar to a chi-square distribution (which is expected, if the L*, a* and b* errors are similar to a normal distribution).

I've also computed the covariance and correlation between the errors of the three channels - and they seem not to be significantly correlated (which actually surprised me).

Sure, the errors of L*, a* and b* are not perfectly normally distributed, they are a bit skewed, a bit fat-tailed (particular b*), and likely also introduce a small offset. Nevertheless I think, assuming a normal distribution is a good first oder approximation for modeling the errors, while a uniform distribution is IMO rather less realistic.

And of course: The errors are not i.i.d. and independent of the color being rendered, but they are heteroscedastic, i.e. the variance is different at each location in the color space. A trend is basically visible in my samples, but one also must not overestimate the different variances of my 53 colors, because the variance estimates themselves are pretty "noisy" as well due to the low sample size of only 10 per color (standard deviation of the estimated variance is about 50% of the estimated variance). I have not yet attempted to explain the heteroscedasticity with a model. I've also no idea, what model might be appropriate - maybe even a non-parametric regression like [std_L, std_a, std_b] = RSPL(CMYK), or [std_L, std_a, std_b] = RSPL(Lab), with a high smoothing factor?

For the profile generation, eventually the point weights need to be proportional to 1/variance, since your rspl weights are weights for the suared error. As you do not support separate weights for each RSPL output dimension, but only a single weight per point, a reasonable compromise is likely to use 1/(variance_L+variance_a+variance_b) as point weight.

I had not done the same exercise in XYZ space, but I'm afraid, the errors are heteroscedastic in XYZ as well. I would really be surprised if the repeatability error of a printer would be homoscedastic in XYZ space.

Regards,
Gerhard

-----------------------------------------------

Output of the attached repeatability.m:


Overall variance [L*,a*,b*]: var_all =

 1.4827  1.0973  1.0379

Overall standard deviation [L*,a*,b*]: std_all =

 1.2177  1.0475  1.0188

Overall average MSE: mse_all = 3.6179
Overall average RMSE (RMS dE): rmse_all = 1.9021

Overall covariance between L*,a*,b* channels: cov_e =

  1.4827068   0.0012555  -0.0221001
  0.0012555   1.0972627  -0.0059687
 -0.0221001  -0.0059687   1.0379300

Overall correlation between L*,a*,b* channels: cor_e =

   1.0000e+00    9.8428e-04   -1.7815e-02
   9.8428e-04    1.0000e+00   -5.5929e-03
  -1.7815e-02   -5.5929e-03    1.0000e+00


function lab = XYZ2Lab(xyz)

% XYZ2Lab(xyz)
%
% Converts colors in XYZ coordinates into CIEL*a*b* coordinates.
%
% xyz should be in the form [x-plane ; y-plane ; z-plane]
% whitepoint is a 3-vector of the xyz values of the white point.
%   If not given, use [95.05 100 108.88] as default (not recommended).
% exp is the exponent used in the formula. Default is the 
%   cube root used in standard CIELAB. If specified, use the number
%   as exponent.
%
% lab is returned as [L-plane ; a-plane ; b-plane].
%
% Formulae are taken from Wyszecki and Stiles, page 167.
%
% Created by Brian Wandell
% Last modified 4/15/96 by Xuemei Zhang
%
% modified by. G.F.
%

xyz = xyz';

exp = 1/3;
whitepoint = [96.42, 100, 82.49];

m = size(xyz);
xyz = reshape(xyz, prod(size(xyz))/3, 3);

Xn = whitepoint(1); 
Yn = whitepoint(2); 
Zn = whitepoint(3);

x = xyz(:,1)/Xn;
y = xyz(:,2)/Yn;
z = xyz(:,3)/Zn;

% Find out points < 0.008856
xx = find(x <= 0.008856);
yy = find(y <= 0.008856);
zz = find(z <= 0.008856);

% allocate space
lab = zeros(size(xyz));

% compute L* values
% fx, fy, fz represent cases <= 0.008856
fy = y(yy);
y = y.^exp;
lab(:,1) = 116*y-16;
lab(yy, 1) = 903.3 * fy;

% compute a* b* values
fx = 7.787 * x(xx) + 16/116;
fy = 7.787 * fy + 16/116;
fz = 7.787 * z(zz) + 16/116;
x = x.^exp;
z = z.^exp;
x(xx) = fx;
y(yy) = fy;
z(zz) = fz;

lab(:,2) = 500 * (x - y);
lab(:,3) = 200 * (y - z);

% return lab in the appropriate shape
lab = reshape(lab, m);

lab = lab';

PNG image

PNG image

PNG image

PNG image

% ID  C M Y K  X Y Z

data = [
1 53.187 75.464 50.422 51.963 7.6500 6.9400 5.9500 
2 88.140 99.838 82.291 67.042 4.3600 4.3600 3.1800 
3 27.176 100.00 100.00 69.637 5.9100 5.6300 3.5500 
4 99.002 25.611 87.238 74.781 4.5300 5.4100 4.1700 
5 73.356 24.877 6.8796 88.879 3.4400 3.5600 3.4400 
6 79.865 20.970 81.973 24.537 11.080 15.160 7.3900 
7 23.643 28.781 0.50102 88.485 4.6100 4.6700 4.3400 
8 98.245 99.684 33.578 17.226 5.8700 5.2500 8.1100 
9 23.886 100.00 30.996 11.603 19.690 11.670 8.8200 
10 24.977 24.522 15.144 11.890 37.320 36.950 32.180 
11 23.966 16.377 81.476 19.763 33.300 36.210 10.200 
12 66.182 100.00 3.1914 81.972 4.6700 4.5300 3.9400 
13 77.959 21.067 13.197 20.914 15.910 19.020 27.080 
14 24.706 78.409 78.636 4.2468 30.190 23.060 8.5400 
15 0.35211 22.326 84.834 71.516 10.010 10.150 3.9200 
16 15.118 82.983 0.0000 68.043 6.5600 5.0900 4.9100 
17 74.165 81.653 81.258 12.733 9.6800 9.1500 5.8500 
18 47.564 0.0000 40.236 67.572 9.5600 11.090 8.6700 
19 100.00 69.344 37.872 89.861 4.4100 4.5200 3.9700 
20 19.187 49.324 64.328 0.95179 40.470 36.500 13.260 
21 52.092 0.60643 57.099 0.0000 33.090 42.680 20.180 
22 25.259 5.7217 49.493 25.617 26.740 30.550 14.090 
23 73.865 70.343 0.13377 0.22552 16.850 14.390 28.370 
24 58.070 0.0000 99.558 48.678 8.0200 10.680 4.2300 
25 70.037 70.108 83.373 83.939 4.6800 5.0000 3.7900 
26 99.326 68.285 9.1737 44.309 5.3600 5.5300 9.2400 
27 39.660 100.00 45.130 100.00 4.2900 4.3200 3.2300 
28 7.3604 100.00 59.952 36.892 12.870 8.4000 4.7700 
29 68.153 69.534 4.1435 89.463 3.7000 3.6200 3.4500 
30 0.0000 66.349 83.328 23.421 26.630 20.930 5.3000 
31 84.625 13.014 47.290 29.546 9.9000 13.580 12.010 
32 49.789 100.00 17.901 46.190 6.7500 5.2500 5.8300 
33 74.546 30.943 99.773 0.0000 16.760 22.460 6.1800 
34 50.371 100.00 99.335 37.715 8.2600 7.0100 3.7900 
35 50.529 0.29566 8.6259 38.056 17.600 20.420 23.520 
36 16.655 66.455 36.812 100.00 3.5500 3.6500 2.8600 
37 76.145 100.00 41.174 69.922 5.0500 4.8800 4.2100 
38 98.334 52.193 56.142 0.0000 8.8900 12.080 14.850 
39 66.084 71.203 40.852 5.6471 17.990 16.060 16.820 
40 0.12100 25.886 7.6635 48.915 19.040 17.530 14.530 
41 90.327 53.274 76.288 40.690 6.0400 7.1800 5.7700 
42 0.0000 100.00 48.408 100.00 4.6900 4.7100 3.5900 
43 44.124 12.193 83.742 81.622 4.3000 4.9400 3.2100 
44 51.048 51.311 31.308 47.840 11.260 11.180 10.760 
45 9.8653 67.199 47.066 47.104 13.900 11.440 6.7100 
46 45.512 40.909 82.291 35.927 14.810 15.390 6.3200 
47 48.805 44.541 61.687 90.504 4.3600 4.6400 3.6300 
48 90.381 26.233 21.682 52.831 6.9900 8.5500 12.070 
49 22.766 75.350 11.042 16.669 25.960 18.940 19.270 
50 29.580 21.170 47.221 1.7911 45.310 47.750 28.290 
51 22.676 70.441 87.009 85.874 5.3800 5.2200 3.5600 
52 86.278 15.338 52.237 91.967 3.9100 4.3800 3.5700 
53 10.563 20.916 41.225 82.015 5.4800 5.5400 3.7300 
54 53.187 75.464 50.422 51.963 7.9200 7.2200 6.1700 
55 88.140 99.838 82.291 67.042 4.4400 4.5800 3.3600 
56 27.176 100.00 100.00 69.637 6.7000 6.0200 3.7000 
57 99.002 25.611 87.238 74.781 3.9100 4.6400 3.4200 
58 73.356 24.877 6.8796 88.879 4.1300 4.3400 4.3900 
59 79.865 20.970 81.973 24.537 9.7700 13.680 6.9700 
60 23.643 28.781 0.50102 88.485 4.5700 4.5800 4.4100 
61 98.245 99.684 33.578 17.226 5.7300 5.1300 8.9700 
62 23.886 100.00 30.996 11.603 20.660 12.080 9.0200 
63 24.977 24.522 15.144 11.890 37.980 37.410 33.190 
64 23.966 16.377 81.476 19.763 29.000 32.040 8.4500 
65 66.182 100.00 3.1914 81.972 4.4300 4.2500 3.8500 
66 77.959 21.067 13.197 20.914 14.990 18.050 26.230 
67 24.706 78.409 78.636 4.2468 29.920 22.770 7.9000 
68 0.35211 22.326 84.834 71.516 9.6100 9.6500 3.4200 
69 15.118 82.983 0.0000 68.043 8.4700 6.6500 6.4900 
70 74.165 81.653 81.258 12.733 10.860 9.9900 6.7800 
71 47.564 0.0000 40.236 67.572 8.4600 9.8900 7.4800 
72 100.00 69.344 37.872 89.861 4.3300 4.4300 3.7000 
73 19.187 49.324 64.328 0.95179 39.900 35.330 12.690 
74 52.092 0.60643 57.099 0.0000 33.710 43.700 20.850 
75 25.259 5.7217 49.493 25.617 30.980 34.660 17.490 
76 73.865 70.343 0.13377 0.22552 18.010 15.610 29.670 
77 58.070 0.0000 99.558 48.678 7.6800 10.110 3.8900 
78 70.037 70.108 83.373 83.939 4.1700 4.4200 3.3500 
79 99.326 68.285 9.1737 44.309 4.6500 4.8600 8.6000 
80 39.660 100.00 45.130 100.00 4.7100 4.7900 3.6400 
81 7.3604 100.00 59.952 36.892 12.960 8.3700 4.3400 
82 68.153 69.534 4.1435 89.463 4.1400 4.1400 3.6700 
83 0.0000 66.349 83.328 23.421 25.780 20.320 5.2400 
84 84.625 13.014 47.290 29.546 10.170 13.900 12.590 
85 49.789 100.00 17.901 46.190 6.5300 5.1000 5.4700 
86 74.546 30.943 99.773 0.0000 18.080 23.290 6.3700 
87 50.371 100.00 99.335 37.715 7.9800 6.7500 3.7000 
88 50.529 0.29566 8.6259 38.056 17.420 20.480 23.220 
89 16.655 66.455 36.812 100.00 4.1000 4.2700 3.3700 
90 76.145 100.00 41.174 69.922 4.4300 4.0700 3.6200 
91 98.334 52.193 56.142 0.0000 9.0600 12.150 15.990 
92 66.084 71.203 40.852 5.6471 15.140 13.940 15.090 
93 0.12100 25.886 7.6635 48.915 19.760 18.100 15.110 
94 90.327 53.274 76.288 40.690 5.5500 6.6300 5.1600 
95 0.0000 100.00 48.408 100.00 4.2200 4.4000 3.1400 
96 44.124 12.193 83.742 81.622 4.6600 5.2800 3.7000 
97 51.048 51.311 31.308 47.840 11.170 10.500 9.8500 
98 9.8653 67.199 47.066 47.104 12.450 10.170 6.1700 
99 45.512 40.909 82.291 35.927 14.200 15.350 6.9500 
100 48.805 44.541 61.687 90.504 3.7000 3.9100 3.0400 
101 90.381 26.233 21.682 52.831 6.4400 7.8300 10.880 
102 22.766 75.350 11.042 16.669 24.060 17.670 18.260 
103 29.580 21.170 47.221 1.7911 42.990 46.090 23.190 
104 22.676 70.441 87.009 85.874 4.2400 4.4500 2.9900 
105 86.278 15.338 52.237 91.967 3.3400 3.6300 3.0100 
106 10.563 20.916 41.225 82.015 7.5700 7.5800 4.8600 
107 53.187 75.464 50.422 51.963 6.7300 6.1600 5.2500 
108 88.140 99.838 82.291 67.042 4.7100 4.6900 3.4600 
109 27.176 100.00 100.00 69.637 6.2800 6.0000 3.7700 
110 99.002 25.611 87.238 74.781 3.7600 4.5400 3.3900 
111 73.356 24.877 6.8796 88.879 4.0300 4.2800 4.5400 
112 79.865 20.970 81.973 24.537 10.070 14.040 7.6800 
113 23.643 28.781 0.50102 88.485 4.7200 4.6700 4.4100 
114 98.245 99.684 33.578 17.226 5.6800 4.9800 8.9900 
115 23.886 100.00 30.996 11.603 20.020 11.870 9.1100 
116 24.977 24.522 15.144 11.890 40.470 40.750 35.370 
117 23.966 16.377 81.476 19.763 29.840 32.710 8.2700 
118 66.182 100.00 3.1914 81.972 4.7400 4.5400 4.0500 
119 77.959 21.067 13.197 20.914 15.670 18.920 27.000 
120 24.706 78.409 78.636 4.2468 27.180 20.400 7.1700 
121 0.35211 22.326 84.834 71.516 8.4400 8.7200 3.4200 
122 15.118 82.983 0.0000 68.043 6.5700 5.2800 4.9100 
123 74.165 81.653 81.258 12.733 10.050 9.2700 5.9200 
124 47.564 0.0000 40.236 67.572 8.2300 9.5600 7.0200 
125 100.00 69.344 37.872 89.861 4.2300 4.4000 3.6400 
126 19.187 49.324 64.328 0.95179 39.020 34.520 11.760 
127 52.092 0.60643 57.099 0.0000 33.320 43.060 20.630 
128 25.259 5.7217 49.493 25.617 31.010 34.950 17.180 
129 73.865 70.343 0.13377 0.22552 16.430 14.190 28.610 
130 58.070 0.0000 99.558 48.678 7.6500 10.170 4.1100 
131 70.037 70.108 83.373 83.939 4.3600 4.6400 3.4600 
132 99.326 68.285 9.1737 44.309 5.0000 5.1100 8.6100 
133 39.660 100.00 45.130 100.00 4.6900 4.6800 3.5400 
134 7.3604 100.00 59.952 36.892 14.510 9.3800 5.1500 
135 68.153 69.534 4.1435 89.463 3.2500 3.2500 2.9500 
136 0.0000 66.349 83.328 23.421 26.600 20.970 5.8600 
137 84.625 13.014 47.290 29.546 10.290 14.280 12.620 
138 49.789 100.00 17.901 46.190 6.8700 5.4400 5.9400 
139 74.546 30.943 99.773 0.0000 17.800 23.470 6.0900 
140 50.371 100.00 99.335 37.715 8.3400 6.4700 3.3200 
141 50.529 0.29566 8.6259 38.056 17.220 20.300 23.270 
142 16.655 66.455 36.812 100.00 3.8500 3.9600 3.1300 
143 76.145 100.00 41.174 69.922 4.8000 4.6900 3.9700 
144 98.334 52.193 56.142 0.0000 8.1300 11.290 14.240 
145 66.084 71.203 40.852 5.6471 15.000 13.560 13.710 
146 0.12100 25.886 7.6635 48.915 25.430 24.040 20.510 
147 90.327 53.274 76.288 40.690 5.3800 6.7200 5.3000 
148 0.0000 100.00 48.408 100.00 4.6300 4.7200 3.5300 
149 44.124 12.193 83.742 81.622 5.1700 5.7800 3.5900 
150 51.048 51.311 31.308 47.840 10.110 9.5800 9.1600 
151 9.8653 67.199 47.066 47.104 13.050 10.540 5.8800 
152 45.512 40.909 82.291 35.927 13.590 14.600 6.1000 
153 48.805 44.541 61.687 90.504 4.3500 4.5700 3.5900 
154 90.381 26.233 21.682 52.831 5.6900 6.7300 8.8600 
155 22.766 75.350 11.042 16.669 26.560 19.540 19.460 
156 29.580 21.170 47.221 1.7911 40.920 43.170 20.680 
157 22.676 70.441 87.009 85.874 4.3300 4.4600 3.2100 
158 86.278 15.338 52.237 91.967 4.0200 4.4000 3.7800 
159 10.563 20.916 41.225 82.015 4.2000 4.3400 2.9700 
160 53.187 75.464 50.422 51.963 7.3200 6.7300 5.7000 
161 88.140 99.838 82.291 67.042 4.3600 4.3900 3.2400 
162 27.176 100.00 100.00 69.637 6.2100 5.9300 3.7500 
163 99.002 25.611 87.238 74.781 4.6700 5.4700 4.0700 
164 73.356 24.877 6.8796 88.879 3.7000 3.8700 3.6800 
165 79.865 20.970 81.973 24.537 10.830 14.960 7.4900 
166 23.643 28.781 0.50102 88.485 4.1400 4.0800 3.8300 
167 98.245 99.684 33.578 17.226 6.0600 5.3100 7.9500 
168 23.886 100.00 30.996 11.603 21.020 12.200 8.7800 
169 24.977 24.522 15.144 11.890 39.110 38.900 34.820 
170 23.966 16.377 81.476 19.763 30.630 33.980 8.7100 
171 66.182 100.00 3.1914 81.972 4.4200 4.3400 3.7900 
172 77.959 21.067 13.197 20.914 14.540 17.610 25.610 
173 24.706 78.409 78.636 4.2468 28.480 21.490 7.7200 
174 0.35211 22.326 84.834 71.516 8.1600 8.2000 3.4400 
175 15.118 82.983 0.0000 68.043 7.8300 6.0800 5.9500 
176 74.165 81.653 81.258 12.733 10.860 9.9000 6.6200 
177 47.564 0.0000 40.236 67.572 7.4000 8.8000 6.3400 
178 100.00 69.344 37.872 89.861 3.6900 3.7800 3.4100 
179 19.187 49.324 64.328 0.95179 40.130 35.980 12.320 
180 52.092 0.60643 57.099 0.0000 33.670 43.320 20.510 
181 25.259 5.7217 49.493 25.617 29.070 32.940 14.860 
182 73.865 70.343 0.13377 0.22552 18.030 15.740 30.100 
183 58.070 0.0000 99.558 48.678 8.8400 11.860 4.5100 
184 70.037 70.108 83.373 83.939 4.5200 4.7700 3.6300 
185 99.326 68.285 9.1737 44.309 5.2300 5.4500 9.4900 
186 39.660 100.00 45.130 100.00 4.2700 4.2200 3.2000 
187 7.3604 100.00 59.952 36.892 12.970 8.4800 4.5300 
188 68.153 69.534 4.1435 89.463 4.1700 4.1900 3.7500 
189 0.0000 66.349 83.328 23.421 25.770 20.340 5.4900 
190 84.625 13.014 47.290 29.546 9.9200 13.580 12.970 
191 49.789 100.00 17.901 46.190 8.4700 6.3700 7.1700 
192 74.546 30.943 99.773 0.0000 16.150 21.400 5.4600 
193 50.371 100.00 99.335 37.715 8.0000 6.6900 3.7900 
194 50.529 0.29566 8.6259 38.056 18.170 21.310 24.350 
195 16.655 66.455 36.812 100.00 3.7300 3.7000 2.9400 
196 76.145 100.00 41.174 69.922 4.9600 4.6700 4.1100 
197 98.334 52.193 56.142 0.0000 8.5100 11.820 14.790 
198 66.084 71.203 40.852 5.6471 16.580 15.040 15.210 
199 0.12100 25.886 7.6635 48.915 20.330 18.520 15.370 
200 90.327 53.274 76.288 40.690 4.9100 5.9600 4.8600 
201 0.0000 100.00 48.408 100.00 4.4700 4.4300 3.3300 
202 44.124 12.193 83.742 81.622 4.7400 5.3200 3.4100 
203 51.048 51.311 31.308 47.840 9.9000 9.5500 9.1400 
204 9.8653 67.199 47.066 47.104 12.260 9.9000 5.5400 
205 45.512 40.909 82.291 35.927 12.650 13.350 5.3700 
206 48.805 44.541 61.687 90.504 4.0600 4.3000 3.3200 
207 90.381 26.233 21.682 52.831 7.5800 9.3200 12.960 
208 22.766 75.350 11.042 16.669 24.100 17.380 17.720 
209 29.580 21.170 47.221 1.7911 41.790 44.650 22.320 
210 22.676 70.441 87.009 85.874 4.2800 4.3400 3.1300 
211 86.278 15.338 52.237 91.967 3.2600 3.4800 2.9300 
212 10.563 20.916 41.225 82.015 6.2400 6.4600 4.0700 
213 53.187 75.464 50.422 51.963 6.3100 5.7400 4.7400 
214 88.140 99.838 82.291 67.042 4.4600 4.4700 3.2900 
215 27.176 100.00 100.00 69.637 5.7000 5.3500 3.1900 
216 99.002 25.611 87.238 74.781 4.0500 4.7900 3.5800 
217 73.356 24.877 6.8796 88.879 3.5800 3.8100 4.0700 
218 79.865 20.970 81.973 24.537 10.390 14.440 7.5600 
219 23.643 28.781 0.50102 88.485 4.2700 4.2500 3.8700 
220 98.245 99.684 33.578 17.226 5.3900 4.8900 7.7500 
221 23.886 100.00 30.996 11.603 19.750 11.440 8.5800 
222 24.977 24.522 15.144 11.890 39.330 39.630 34.590 
223 23.966 16.377 81.476 19.763 29.240 32.170 8.7300 
224 66.182 100.00 3.1914 81.972 4.2000 3.9800 3.7400 
225 77.959 21.067 13.197 20.914 16.710 20.020 28.290 
226 24.706 78.409 78.636 4.2468 27.360 20.570 7.5100 
227 0.35211 22.326 84.834 71.516 6.8800 7.0000 3.1100 
228 15.118 82.983 0.0000 68.043 6.3300 4.8900 4.8200 
229 74.165 81.653 81.258 12.733 11.650 10.500 6.7000 
230 47.564 0.0000 40.236 67.572 7.1200 8.4000 6.1600 
231 100.00 69.344 37.872 89.861 4.5100 4.5800 3.8800 
232 19.187 49.324 64.328 0.95179 41.170 37.040 14.250 
233 52.092 0.60643 57.099 0.0000 34.790 44.130 22.230 
234 25.259 5.7217 49.493 25.617 29.340 33.130 15.120 
235 73.865 70.343 0.13377 0.22552 16.060 13.760 28.180 
236 58.070 0.0000 99.558 48.678 10.400 13.510 4.9500 
237 70.037 70.108 83.373 83.939 4.0300 4.3400 3.2500 
238 99.326 68.285 9.1737 44.309 4.8800 5.0400 8.5600 
239 39.660 100.00 45.130 100.00 4.8400 4.8000 3.6400 
240 7.3604 100.00 59.952 36.892 11.610 7.7300 4.2100 
241 68.153 69.534 4.1435 89.463 3.6900 3.6600 3.4100 
242 0.0000 66.349 83.328 23.421 27.870 22.050 5.7700 
243 84.625 13.014 47.290 29.546 9.7300 13.570 12.380 
244 49.789 100.00 17.901 46.190 6.9400 5.3500 5.8400 
245 74.546 30.943 99.773 0.0000 15.970 20.720 5.5800 
246 50.371 100.00 99.335 37.715 8.5800 6.8700 3.7000 
247 50.529 0.29566 8.6259 38.056 17.680 20.790 23.820 
248 16.655 66.455 36.812 100.00 4.1300 4.2700 3.3700 
249 76.145 100.00 41.174 69.922 4.6200 4.4400 3.8700 
250 98.334 52.193 56.142 0.0000 8.3300 11.490 15.220 
251 66.084 71.203 40.852 5.6471 16.320 15.040 16.110 
252 0.12100 25.886 7.6635 48.915 24.110 22.840 19.340 
253 90.327 53.274 76.288 40.690 5.7700 6.7500 5.3900 
254 0.0000 100.00 48.408 100.00 4.1400 4.2100 3.1000 
255 44.124 12.193 83.742 81.622 4.2100 4.8400 3.3300 
256 51.048 51.311 31.308 47.840 10.420 10.160 9.6600 
257 9.8653 67.199 47.066 47.104 12.840 10.280 6.0600 
258 45.512 40.909 82.291 35.927 12.460 13.170 5.5700 
259 48.805 44.541 61.687 90.504 4.3100 4.4700 3.5500 
260 90.381 26.233 21.682 52.831 5.7800 6.9600 8.9800 
261 22.766 75.350 11.042 16.669 22.800 16.500 16.730 
262 29.580 21.170 47.221 1.7911 41.960 44.640 21.760 
263 22.676 70.441 87.009 85.874 4.4700 4.3000 2.7800 
264 86.278 15.338 52.237 91.967 3.4800 3.7600 3.1400 
265 10.563 20.916 41.225 82.015 5.6100 5.7700 3.7300 
266 53.187 75.464 50.422 51.963 7.3800 6.7200 5.9400 
267 88.140 99.838 82.291 67.042 5.0600 5.1900 3.9700 
268 27.176 100.00 100.00 69.637 6.4300 5.6400 3.4200 
269 99.002 25.611 87.238 74.781 4.6600 5.4300 4.0900 
270 73.356 24.877 6.8796 88.879 3.8500 4.0000 3.7400 
271 79.865 20.970 81.973 24.537 10.510 14.390 6.7800 
272 23.643 28.781 0.50102 88.485 4.3000 4.2700 3.9200 
273 98.245 99.684 33.578 17.226 5.8100 5.2600 8.0600 
274 23.886 100.00 30.996 11.603 20.090 11.810 9.2200 
275 24.977 24.522 15.144 11.890 40.320 40.140 35.090 
276 23.966 16.377 81.476 19.763 28.810 31.470 7.8800 
277 66.182 100.00 3.1914 81.972 4.5100 4.3600 3.8900 
278 77.959 21.067 13.197 20.914 14.480 17.500 25.170 
279 24.706 78.409 78.636 4.2468 27.990 20.930 7.2600 
280 0.35211 22.326 84.834 71.516 8.7300 9.0500 3.6400 
281 15.118 82.983 0.0000 68.043 8.6600 6.6800 6.4700 
282 74.165 81.653 81.258 12.733 10.540 9.7400 6.7200 
283 47.564 0.0000 40.236 67.572 9.0100 10.370 7.7100 
284 100.00 69.344 37.872 89.861 3.9500 4.1300 3.4700 
285 19.187 49.324 64.328 0.95179 39.730 35.270 12.370 
286 52.092 0.60643 57.099 0.0000 33.840 43.410 20.760 
287 25.259 5.7217 49.493 25.617 30.950 34.980 17.600 
288 73.865 70.343 0.13377 0.22552 16.780 14.680 28.870 
289 58.070 0.0000 99.558 48.678 8.3300 10.870 4.2200 
290 70.037 70.108 83.373 83.939 4.5300 4.7800 3.6500 
291 99.326 68.285 9.1737 44.309 5.1600 5.1100 8.2700 
292 39.660 100.00 45.130 100.00 4.8200 4.8500 3.6500 
293 7.3604 100.00 59.952 36.892 11.880 7.8900 4.0100 
294 68.153 69.534 4.1435 89.463 3.4500 3.4100 3.0400 
295 0.0000 66.349 83.328 23.421 27.640 22.000 5.9900 
296 84.625 13.014 47.290 29.546 10.750 14.520 12.910 
297 49.789 100.00 17.901 46.190 6.9700 5.4900 5.9900 
298 74.546 30.943 99.773 0.0000 17.360 22.840 6.1200 
299 50.371 100.00 99.335 37.715 9.0400 7.3200 3.8600 
300 50.529 0.29566 8.6259 38.056 19.510 22.660 25.780 
301 16.655 66.455 36.812 100.00 3.9500 4.0200 3.1900 
302 76.145 100.00 41.174 69.922 4.6900 4.5700 3.9200 
303 98.334 52.193 56.142 0.0000 8.6600 11.880 15.240 
304 66.084 71.203 40.852 5.6471 16.020 14.860 14.420 
305 0.12100 25.886 7.6635 48.915 18.660 17.030 14.040 
306 90.327 53.274 76.288 40.690 6.1700 7.3400 6.1600 
307 0.0000 100.00 48.408 100.00 4.7500 4.8000 3.6100 
308 44.124 12.193 83.742 81.622 5.6400 6.3500 3.9100 
309 51.048 51.311 31.308 47.840 9.1900 8.8800 8.4400 
310 9.8653 67.199 47.066 47.104 12.650 10.160 5.6200 
311 45.512 40.909 82.291 35.927 15.300 16.240 6.7500 
312 48.805 44.541 61.687 90.504 4.2500 4.4700 3.5200 
313 90.381 26.233 21.682 52.831 6.7100 7.9000 10.600 
314 22.766 75.350 11.042 16.669 26.900 19.550 19.450 
315 29.580 21.170 47.221 1.7911 43.950 46.020 26.560 
316 22.676 70.441 87.009 85.874 4.0300 4.0200 2.9100 
317 86.278 15.338 52.237 91.967 4.0300 4.3100 3.6200 
318 10.563 20.916 41.225 82.015 5.4700 5.6400 3.7300 
319 53.187 75.464 50.422 51.963 7.0700 6.5700 5.6100 
320 88.140 99.838 82.291 67.042 4.8700 4.7900 3.5900 
321 27.176 100.00 100.00 69.637 6.5500 6.1600 3.7200 
322 99.002 25.611 87.238 74.781 3.7000 4.4600 3.2800 
323 73.356 24.877 6.8796 88.879 3.7900 3.8100 3.7300 
324 79.865 20.970 81.973 24.537 13.410 18.060 9.2400 
325 23.643 28.781 0.50102 88.485 5.4600 5.4300 5.1500 
326 98.245 99.684 33.578 17.226 6.3400 5.6300 9.7600 
327 23.886 100.00 30.996 11.603 19.740 11.750 9.4200 
328 24.977 24.522 15.144 11.890 38.070 37.930 33.790 
329 23.966 16.377 81.476 19.763 28.780 31.420 7.9000 
330 66.182 100.00 3.1914 81.972 4.5800 4.3200 3.9800 
331 77.959 21.067 13.197 20.914 17.320 20.510 28.380 
332 24.706 78.409 78.636 4.2468 27.810 20.690 6.8600 
333 0.35211 22.326 84.834 71.516 7.5000 7.6200 3.2200 
334 15.118 82.983 0.0000 68.043 6.9200 5.4100 5.1600 
335 74.165 81.653 81.258 12.733 9.8300 8.8500 5.6100 
336 47.564 0.0000 40.236 67.572 7.3400 8.5500 6.2900 
337 100.00 69.344 37.872 89.861 4.4400 4.5300 3.8300 
338 19.187 49.324 64.328 0.95179 41.880 38.520 14.590 
339 52.092 0.60643 57.099 0.0000 33.220 42.990 20.510 
340 25.259 5.7217 49.493 25.617 30.190 33.590 17.110 
341 73.865 70.343 0.13377 0.22552 16.660 14.290 28.390 
342 58.070 0.0000 99.558 48.678 9.3800 12.420 4.5000 
343 70.037 70.108 83.373 83.939 4.6900 4.9500 3.7600 
344 99.326 68.285 9.1737 44.309 5.6300 5.9400 9.7900 
345 39.660 100.00 45.130 100.00 4.7700 4.7800 3.6300 
346 7.3604 100.00 59.952 36.892 14.060 8.9900 4.9400 
347 68.153 69.534 4.1435 89.463 3.7900 3.7000 3.3900 
348 0.0000 66.349 83.328 23.421 26.130 20.330 5.2400 
349 84.625 13.014 47.290 29.546 11.530 15.300 15.430 
350 49.789 100.00 17.901 46.190 7.0500 5.2900 5.7500 
351 74.546 30.943 99.773 0.0000 18.170 23.390 6.6600 
352 50.371 100.00 99.335 37.715 8.2000 6.9200 3.9000 
353 50.529 0.29566 8.6259 38.056 21.020 24.300 27.730 
354 16.655 66.455 36.812 100.00 4.0100 4.1800 3.2900 
355 76.145 100.00 41.174 69.922 4.7800 4.5800 4.0500 
356 98.334 52.193 56.142 0.0000 7.9600 11.120 13.940 
357 66.084 71.203 40.852 5.6471 15.230 13.720 14.060 
358 0.12100 25.886 7.6635 48.915 20.490 18.980 15.700 
359 90.327 53.274 76.288 40.690 5.3600 6.3000 5.1000 
360 0.0000 100.00 48.408 100.00 4.3000 4.3400 3.2600 
361 44.124 12.193 83.742 81.622 4.1400 4.7200 3.1000 
362 51.048 51.311 31.308 47.840 8.7700 8.5300 7.9000 
363 9.8653 67.199 47.066 47.104 13.800 11.070 6.5000 
364 45.512 40.909 82.291 35.927 14.730 15.560 6.5100 
365 48.805 44.541 61.687 90.504 4.2000 4.3800 3.5000 
366 90.381 26.233 21.682 52.831 6.0600 7.3200 9.9200 
367 22.766 75.350 11.042 16.669 24.130 17.200 17.380 
368 29.580 21.170 47.221 1.7911 46.020 49.140 27.070 
369 22.676 70.441 87.009 85.874 4.2100 4.2700 2.9200 
370 86.278 15.338 52.237 91.967 3.4700 3.7600 3.1800 
371 10.563 20.916 41.225 82.015 4.8500 5.0200 3.3500 
372 53.187 75.464 50.422 51.963 6.8100 6.2100 5.2200 
373 88.140 99.838 82.291 67.042 4.9600 5.0700 3.7000 
374 27.176 100.00 100.00 69.637 6.4400 5.7900 3.4100 
375 99.002 25.611 87.238 74.781 4.2700 4.8800 3.6800 
376 73.356 24.877 6.8796 88.879 3.6200 3.7800 3.7800 
377 79.865 20.970 81.973 24.537 9.9300 13.750 6.5800 
378 23.643 28.781 0.50102 88.485 3.7500 3.6600 3.3300 
379 98.245 99.684 33.578 17.226 5.9900 5.3700 8.2400 
380 23.886 100.00 30.996 11.603 22.140 12.980 10.000 
381 24.977 24.522 15.144 11.890 39.960 40.220 34.880 
382 23.966 16.377 81.476 19.763 30.920 34.070 8.3100 
383 66.182 100.00 3.1914 81.972 4.5700 4.3600 4.1100 
384 77.959 21.067 13.197 20.914 15.030 17.980 25.520 
385 24.706 78.409 78.636 4.2468 27.870 20.950 6.9700 
386 0.35211 22.326 84.834 71.516 9.0500 9.2700 3.6800 
387 15.118 82.983 0.0000 68.043 9.3400 7.1800 7.2100 
388 74.165 81.653 81.258 12.733 10.610 10.050 6.7500 
389 47.564 0.0000 40.236 67.572 7.4000 8.4700 6.5300 
390 100.00 69.344 37.872 89.861 4.1300 4.2200 3.5100 
391 19.187 49.324 64.328 0.95179 39.960 35.760 12.080 
392 52.092 0.60643 57.099 0.0000 34.430 43.680 21.260 
393 25.259 5.7217 49.493 25.617 28.420 32.040 14.740 
394 73.865 70.343 0.13377 0.22552 16.870 14.380 29.070 
395 58.070 0.0000 99.558 48.678 8.9900 11.690 4.4500 
396 70.037 70.108 83.373 83.939 4.7100 4.8400 3.8100 
397 99.326 68.285 9.1737 44.309 5.5700 5.8200 9.7300 
398 39.660 100.00 45.130 100.00 4.6100 4.6600 3.5500 
399 7.3604 100.00 59.952 36.892 12.360 8.4500 4.7400 
400 68.153 69.534 4.1435 89.463 4.2400 4.0700 4.0300 
401 0.0000 66.349 83.328 23.421 27.980 22.250 6.3200 
402 84.625 13.014 47.290 29.546 9.3700 12.880 12.020 
403 49.789 100.00 17.901 46.190 6.5200 4.9800 5.3800 
404 74.546 30.943 99.773 0.0000 16.940 22.250 5.9400 
405 50.371 100.00 99.335 37.715 8.2000 6.9600 3.8500 
406 50.529 0.29566 8.6259 38.056 17.400 20.460 23.540 
407 16.655 66.455 36.812 100.00 3.9200 4.0300 3.2000 
408 76.145 100.00 41.174 69.922 4.6200 4.4900 3.8100 
409 98.334 52.193 56.142 0.0000 8.1300 11.310 13.680 
410 66.084 71.203 40.852 5.6471 15.110 13.860 14.020 
411 0.12100 25.886 7.6635 48.915 21.110 19.660 16.400 
412 90.327 53.274 76.288 40.690 5.7600 6.9100 5.7200 
413 0.0000 100.00 48.408 100.00 4.4600 4.6000 3.4200 
414 44.124 12.193 83.742 81.622 5.2800 6.0300 3.7400 
415 51.048 51.311 31.308 47.840 9.7400 9.3800 8.6300 
416 9.8653 67.199 47.066 47.104 12.080 9.7100 5.6300 
417 45.512 40.909 82.291 35.927 12.880 13.790 5.6700 
418 48.805 44.541 61.687 90.504 4.3400 4.5800 3.5900 
419 90.381 26.233 21.682 52.831 6.5500 8.1700 11.420 
420 22.766 75.350 11.042 16.669 25.420 18.340 18.370 
421 29.580 21.170 47.221 1.7911 40.280 42.800 22.030 
422 22.676 70.441 87.009 85.874 3.7400 3.9100 2.8500 
423 86.278 15.338 52.237 91.967 3.3700 3.6800 3.1000 
424 10.563 20.916 41.225 82.015 6.6600 6.8800 4.4900 
425 53.187 75.464 50.422 51.963 7.0100 6.5800 5.5600 
426 88.140 99.838 82.291 67.042 5.1200 5.1700 3.8400 
427 27.176 100.00 100.00 69.637 6.7500 6.2300 3.8300 
428 99.002 25.611 87.238 74.781 4.5100 5.2100 3.9200 
429 73.356 24.877 6.8796 88.879 3.3400 3.4300 3.2400 
430 79.865 20.970 81.973 24.537 11.150 15.550 7.5400 
431 23.643 28.781 0.50102 88.485 5.4200 5.1900 4.9400 
432 98.245 99.684 33.578 17.226 6.1800 5.5800 9.0700 
433 23.886 100.00 30.996 11.603 19.740 11.570 9.0100 
434 24.977 24.522 15.144 11.890 39.780 39.870 34.090 
435 23.966 16.377 81.476 19.763 31.050 34.020 8.7100 
436 66.182 100.00 3.1914 81.972 4.6900 4.4400 4.0100 
437 77.959 21.067 13.197 20.914 15.420 18.640 26.990 
438 24.706 78.409 78.636 4.2468 28.940 21.660 8.0500 
439 0.35211 22.326 84.834 71.516 8.9300 9.0800 3.6300 
440 15.118 82.983 0.0000 68.043 7.4900 5.8600 5.5800 
441 74.165 81.653 81.258 12.733 10.500 9.7800 6.6100 
442 47.564 0.0000 40.236 67.572 7.7800 9.1400 6.5900 
443 100.00 69.344 37.872 89.861 4.4200 4.4700 3.9800 
444 19.187 49.324 64.328 0.95179 40.180 36.530 12.470 
445 52.092 0.60643 57.099 0.0000 33.880 43.580 22.530 
446 25.259 5.7217 49.493 25.617 29.840 33.890 15.910 
447 73.865 70.343 0.13377 0.22552 17.360 14.930 28.880 
448 58.070 0.0000 99.558 48.678 8.5100 11.430 4.4400 
449 70.037 70.108 83.373 83.939 4.9100 5.1500 3.9100 
450 99.326 68.285 9.1737 44.309 5.6000 5.8400 10.100 
451 39.660 100.00 45.130 100.00 4.7600 4.8300 3.6600 
452 7.3604 100.00 59.952 36.892 14.620 9.4500 5.2100 
453 68.153 69.534 4.1435 89.463 4.1200 4.0000 3.6400 
454 0.0000 66.349 83.328 23.421 24.750 19.440 5.2400 
455 84.625 13.014 47.290 29.546 11.280 15.460 15.240 
456 49.789 100.00 17.901 46.190 6.6800 5.3500 5.9300 
457 74.546 30.943 99.773 0.0000 15.780 21.080 5.5900 
458 50.371 100.00 99.335 37.715 8.3700 7.1400 3.8800 
459 50.529 0.29566 8.6259 38.056 18.280 21.540 24.960 
460 16.655 66.455 36.812 100.00 3.6200 3.7000 2.8800 
461 76.145 100.00 41.174 69.922 3.9200 3.7400 3.2600 
462 98.334 52.193 56.142 0.0000 7.6100 10.770 12.720 
463 66.084 71.203 40.852 5.6471 15.230 14.030 13.970 
464 0.12100 25.886 7.6635 48.915 19.930 18.460 15.420 
465 90.327 53.274 76.288 40.690 6.1500 7.4100 5.5900 
466 0.0000 100.00 48.408 100.00 4.7900 4.8000 3.6200 
467 44.124 12.193 83.742 81.622 4.5300 5.0700 3.5000 
468 51.048 51.311 31.308 47.840 8.8500 8.3800 7.9800 
469 9.8653 67.199 47.066 47.104 14.900 12.180 7.1300 
470 45.512 40.909 82.291 35.927 12.140 12.860 5.2100 
471 48.805 44.541 61.687 90.504 4.3000 4.6000 3.5800 
472 90.381 26.233 21.682 52.831 6.3400 7.6300 10.700 
473 22.766 75.350 11.042 16.669 24.310 17.330 17.450 
474 29.580 21.170 47.221 1.7911 43.640 46.740 23.300 
475 22.676 70.441 87.009 85.874 4.5600 4.6500 3.2200 
476 86.278 15.338 52.237 91.967 3.5900 3.8700 3.3200 
477 10.563 20.916 41.225 82.015 6.7700 6.9900 4.3800 
478 53.187 75.464 50.422 51.963 7.3600 6.7500 6.1500 
479 88.140 99.838 82.291 67.042 5.1700 5.1800 4.0300 
480 27.176 100.00 100.00 69.637 5.7500 5.4400 3.3000 
481 99.002 25.611 87.238 74.781 4.3600 4.9600 3.7400 
482 73.356 24.877 6.8796 88.879 3.9900 4.2100 4.3200 
483 79.865 20.970 81.973 24.537 10.160 14.140 7.2900 
484 23.643 28.781 0.50102 88.485 4.5300 4.5300 4.2700 
485 98.245 99.684 33.578 17.226 5.6200 4.9800 7.6000 
486 23.886 100.00 30.996 11.603 20.510 12.220 9.3000 
487 24.977 24.522 15.144 11.890 37.300 37.290 32.800 
488 23.966 16.377 81.476 19.763 27.720 30.240 7.3500 
489 66.182 100.00 3.1914 81.972 3.9000 3.6500 3.1600 
490 77.959 21.067 13.197 20.914 14.720 17.410 25.280 
491 24.706 78.409 78.636 4.2468 27.090 20.370 7.2900 
492 0.35211 22.326 84.834 71.516 6.9700 7.0900 2.9100 
493 15.118 82.983 0.0000 68.043 7.0500 5.4000 5.0100 
494 74.165 81.653 81.258 12.733 10.000 9.3800 6.4400 
495 47.564 0.0000 40.236 67.572 7.0800 8.2000 6.0400 
496 100.00 69.344 37.872 89.861 4.3800 4.4400 3.7200 
497 19.187 49.324 64.328 0.95179 41.080 37.230 13.590 
498 52.092 0.60643 57.099 0.0000 34.650 44.150 21.640 
499 25.259 5.7217 49.493 25.617 28.720 32.220 14.350 
500 73.865 70.343 0.13377 0.22552 18.630 16.430 29.920 
501 58.070 0.0000 99.558 48.678 8.2200 10.970 4.3500 
502 70.037 70.108 83.373 83.939 4.6900 4.9800 3.7900 
503 99.326 68.285 9.1737 44.309 5.3800 5.6500 9.6100 
504 39.660 100.00 45.130 100.00 4.7400 4.7600 3.5900 
505 7.3604 100.00 59.952 36.892 13.040 8.6400 4.8000 
506 68.153 69.534 4.1435 89.463 3.7600 3.7000 3.3700 
507 0.0000 66.349 83.328 23.421 26.460 20.540 5.4800 
508 84.625 13.014 47.290 29.546 9.2200 12.500 11.700 
509 49.789 100.00 17.901 46.190 6.5200 5.0600 5.8300 
510 74.546 30.943 99.773 0.0000 15.810 21.000 5.7700 
511 50.371 100.00 99.335 37.715 8.1700 6.8500 3.9000 
512 50.529 0.29566 8.6259 38.056 20.330 23.190 26.150 
513 16.655 66.455 36.812 100.00 3.5900 3.6300 2.8900 
514 76.145 100.00 41.174 69.922 4.6600 4.4500 3.8500 
515 98.334 52.193 56.142 0.0000 8.1800 11.350 14.230 
516 66.084 71.203 40.852 5.6471 17.120 15.510 16.210 
517 0.12100 25.886 7.6635 48.915 20.450 18.840 15.830 
518 90.327 53.274 76.288 40.690 5.8300 7.0000 5.8500 
519 0.0000 100.00 48.408 100.00 4.1000 4.1700 2.9900 
520 44.124 12.193 83.742 81.622 4.7400 5.2600 3.5900 
521 51.048 51.311 31.308 47.840 11.350 10.680 10.240 
522 9.8653 67.199 47.066 47.104 13.320 10.690 6.0600 
523 45.512 40.909 82.291 35.927 13.070 13.740 5.5300 
524 48.805 44.541 61.687 90.504 3.5400 3.7300 2.9100 
525 90.381 26.233 21.682 52.831 5.1900 6.3500 8.7200 
526 22.766 75.350 11.042 16.669 25.720 18.560 18.470 
527 29.580 21.170 47.221 1.7911 41.380 44.050 22.760 
528 22.676 70.441 87.009 85.874 4.7600 4.8000 3.3700 
529 86.278 15.338 52.237 91.967 3.7300 3.9100 3.3000 
530 10.563 20.916 41.225 82.015 6.0000 6.1700 4.0300 
];

XYZ = data(:,6:8)';
Lab = XYZ2Lab(XYZ);

LabN = reshape(Lab,3,53,"");
mn = mean(LabN,3);
st = std(LabN,1,3);

e = LabN;
for i = 1:10
    e(:,:,i) -= mn;
    cov(e(:,:,i)');
endfor

e_all = reshape(e,3,"")';

printf("Overall variance [L*,a*,b*]: ");
var_all = var(e_all)
printf("Overall standard deviation [L*,a*,b*]: ");
std_all = std(e_all)

printf("Overall average MSE: ")
mse_all = sum(var_all)
printf("Overall average RMSE (RMS dE): ")
rmse_all = sqrt(mse_all)
printf("\n");

printf("Overall covariance between L*,a*,b* channels: ");
cov_e = cov(e_all)
printf("Overall correlation between L*,a*,b* channels: ");
cor_e = cor(e_all)

grid on
title("Overall L* error PDF");
hist(e_all(:,1),30);
input(">");

title("Overall a* error PDF");
hist(e_all(:,2),30);
input(">");

title("Overall b* error PDF");
hist(e_all(:,3),30);
input(">");

dE = sqrt(sum(e_all.*e_all,2));

title("Overall dE PDF");
hist(dE,30);
input(">");

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