Editing Color balance (section)

===Scaling monitor R, G, and B===
In principle, one wants to scale all relative luminances in an image so that objects which are believed to be [[grey|neutral]] appear so. If, say, a surface with <math>R=240</math> was believed to be a white object, and if 255 is the count which corresponds to white, one could multiply all [[red]] values by 255/240. Doing analogously for [[green]] and [[blue]] would result, at least in theory, in a color balanced image. In this type of transformation the 3x3 matrix is a [[diagonal matrix]].

: <math>\left[\begin{array}{c} R \\ G \\ B \end{array}\right]=\left[\begin{array}{ccc}255/R'_w & 0 & 0 \\ 0 & 255/G'_w & 0 \\ 0 & 0 & 255/B'_w\end{array}\right]\left[\begin{array}{c}R' \\ G' \\ B' \end{array}\right]</math>

where <math>R</math>, <math>G</math>, and <math>B</math> are the color balanced red, green, and blue components of a [[pixel]] in the image; <math>R'</math>, <math>G'</math>, and <math>B'</math> are the red, green, and blue components of the image before color balancing, and <math>R'_w</math>, <math>G'_w</math>, and <math>B'_w</math> are the red, green, and blue components of a pixel which is believed to be a white surface in the image before color balancing. This is a simple scaling of the red, green, and blue channels, and is why color balance tools in [[Photoshop]] have a white eyedropper tool.  It has been demonstrated that performing the white balancing in the phosphor set assumed by [[sRGB]] tends to produce large errors in chromatic colors, even though it can render the neutral surfaces perfectly neutral.<ref name="Viggiano2004">{{cite book|doi=10.1117/12.524922|chapter=Comparison of the accuracy of different white-balancing options as quantified by their color constancy|title=Sensors and Camera Systems for Scientific, Industrial, and Digital Photography Applications V|volume=5301|pages=323–333|year=2004|last1=Viggiano|first1=J A Stephen|s2cid=8971750|editor3-first=Ricardo J|editor3-last=Motta|editor2-first=Nitin|editor2-last=Sampat|editor1-first=Morley M|editor1-last=Blouke}}</ref>