======= Color Correction Matrix =======
A.k.a. "CCM" or "CMX"

===== Purpose =====
Why do the color correction at all? A picture is worth a thousand words so here's a visual to demonstrate the original (left) and color-corrected (right) values. Click to enlarge:
{{ :isp:color_correction_sample.jpg?direct&200 |}}


===== CCM =====
Color Correction Matrix is often used as an "add-on" matrix during YUV->RGB conversion. In our case, since the de-bayering and RGB->YUV conversions happen literally on opposite sides of the imaging pipeline, we only use the portion of the corrections designed to compensate for the sensor's cross-talk, converting post-debayer values \(R_0, G_0, B_0\) into \(R, G, B\):

\[
 \begin{bmatrix} R & G & B\end{bmatrix}
 =
 \begin{bmatrix}
 CCM_{00} & CCM_{01} & CCM_{02} \\
 CCM_{10} & CCM_{11} & CCM_{12} \\
 CCM_{20} & CCM_{21} & CCM_{22} \\
 \end{bmatrix}
 \cdot
 \begin{bmatrix}
 R_0 \\
 G_0 \\
 B_0
 \end{bmatrix}
\]

Regular linear algebra rules apply, of course. The calculation itself (once expanded) looks like this:

\[
R = CCM_{00} * R_0 + CCM_{01} * G_0 + CCM_{02} * B_0 \\
G = CCM_{10} * R_0 + CCM_{11} * G_0 + CCM_{12} * B_0 \\
B = CCM_{20} * R_0 + CCM_{21} * G_0 + CCM_{22} * B_0
\]
===== 3x3 -> 4x4 =====
Industry papers on CCM use a \(3\times3\) matrix yet we tried to do a full \(4\times4\) so there was a need to find a way to convert from one to another (and also from an RGGB into BGGR ordering). Here's an [[https://math.stackexchange.com/questions/3957955/ccm-3x3-into-4x4-image-processing|article on Math StackExchange]] on that subject.

And if you'd like to play with the values in an Excel-like environment - here's a [[https://docs.google.com/spreadsheets/d/1X1n5hVDLHd-Z6ZLEcwPZijU2WQZ40QAtt9Z-ExZlRG0/edit?usp=sharing | link to Google Sheets]] for your enjoyment.

After some research and a bit of math crunching it turned out that such an approach is invalid. Primarily because it ignores a very important step - de-bayering, which affects the result in a critical manner.

Therefore we go with the "standard" approach of using a \(3\times3\) matrix in \(RGB\) space.