Usability of Digital Cameras for Verifying Physically Based ...

Using an ICC profile obviously improves the quality of camera characteriz-
ation compared to relying on the camera’s color space only. Although the mean
∆E∗ ab
10∆E∗ ab .
value is only slightly lower, the maximum value could be reduced by around
7.3 Implementing an Adapted Mapping
In order to be able to convert the RGB values of a photograph to XYZ space one
has to find a transformation that provides a best agreement between these RGB
values and the measured XYZ values. ICC profiles internally use either look-up-
tables or matrices to implement this transformation. We implemented a mapping
by ourselves for two reasons: first, this mapping possibly yields better results be-
cause we can better address particular properties of our data and secondly, because
we also wanted to provide an approach that does not rely on expensive profiling
software, but gives more accurate results than using the camera’s color space.
Izadan and Nobbs [Iza06] did a comparison between iteration and regression
methods using either XYZ or L ∗ a ∗ b ∗ color space. Basically, all methods yield
comparable results. They conclude that regression method with L ∗ a ∗ b ∗ approach
will lead to the best results.
We based our calculations on polynomial regression with least squares fitting
described by Hong et al. [HLR00], who have shown that a higher order polynomial
is able to produce satisfactory characterization accuracy.
Let R ∈ R n×m denote a matrix of RGB vectors and L ∈ R n×3 the correspond-
ing matrix of L ∗ a ∗ b ∗ vectors, the mapping from RGB to L ∗ a ∗ b ∗ can be represented
by
L = RM, (1)
where the matrix M ∈ R m×3 is derived by the following equation:
M = (R T R) −1 R T L. (2)
Here, n is the number of samples and m is the number of terms of the polyno-
mials. The number and the grade of these terms define the type of the mapping.
As our image is gamma corrected and therefore not linear, a higher order polyno-
mial will most probably give better results than a linear polynomial. On the other
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