Usability of Digital Cameras for Verifying Physically Based ...

R G B
Min 0.81 (0.02%) 0.36 (0.009%) 0.15 (0.004%)
Max 193.93 (4.74%) 295.46 (7.22%) 167.69 (4.09%)
Median 57.44 (1.40%) 51.70 (1.26%) 46.30 (1.13%)
Mean 65.57 (1.60%) 63.98 (1.56%) 52.99 (1.29%)
Stdev 45.24 (1.10%) 51.31 (1.25%) 40.77 (1.00%)
Table 13: Minimum and maximum, median, mean values, and standard deviations
of the residuals of R, G, and B values with respect to the values of the RAW image.
The RGB values lie in the range of 0 to 4095. Relative errors are given in brackets.
the measured values for patch j, and n is the number of patches used in our tests.
We obtain the optimal coefficients for ri, gi and bi by minimizing ∆R, ∆G, and
∆B. We do this by using non-linear regression.
The spectra we use in this case are the spectra of the n = 140 patches of the
ColorChecker SG. Those were measured with a GretagMacbeth Spectrolino (see
section 6.3).
In order to avoid inaccuracies due to image enhancement we use the RAW
image for gaining the RGB values (see section 6.1.4). Again, we search for the
most representative RGB value in a subarea of each patch. As the Canon EOS
20D is a 12bit camera, the RGB values are in the range of 0 to 4095.
The results of the mapping cannot be compared to methods that are operat-
ing in L ∗ a ∗ b ∗ space. Our results are part of the camera’s RAW RGB space and
can therefore not easily be converted to XYZ and then L ∗ a ∗ b ∗ space. We would
have to find a mapping from camera’s RAW RGB to XYZ that again will intro-
duce some error. Therefore, we analyze the difference of calculated RGB values
to the ones that were actually produced by a camera. In order to test the quality
of our mapping, we use the 140 spectra (the same that were used to generate the
mapping) as input value and compare the result to the RGB values of the camera.
Absolute values for minimum, maximum, mean value, median, and standard de-
viation of this comparison can be found in table 13. The maximum error of 7.22%
occurs in the green channel. The mean value of 1.56% is much lower though
so we can assume that there are only a few outliers. The same tendency can be
observed for the other two channels. Moreover we can see that the blue channel
causes the least amount of error in general. The residuals for R, G, and B channels
for all 140 patches can be found in appendix E.5.
This method has two main advantages: We do not need any knowledge about
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