Hi all.
I would like to ask you to help me.
I'm trying to to understand with the work of MixerYCbCr in G'MIC-plug-in.
I want to understand the algorithm of this effect.
But I do not understand how it works.
I'm not sure about my knowledge of the work of this effect. But I read how it should work in other programs.
-----------------------------------------
For example in Edius (videoeditor for windows):
U and V are similar but you control the balance between two primaries and their complementary color. U and V have same abscissa value range on the X axis while they differ for the Y axis:

With U (Cb), the higher value you are, the more you're on the blue primary color. If you go to the low values then you're on blue complementary color, i.e. yellow.

With V (Cr), this is the same principle but with Red and Cyan.
If you push U full blue and V full red, you get magenta. If you push U full yellow and V full Cyan then you get green
------------------------------

In practice, I move the sliders Blue chroma gain and Red chroma gain and this mixer gives me a completely different color than I expected.
For example I move the slider Blue chroma gain to the in the leftmost position and look forward to gain yellows,
but blue sky turns green and yellow colors - purple ..
I move B chroma gain and R chroma gain to the in the leftmost position, but I get black-white image..
I do not understand why ..

Explain, please.

In newer versions these are labeled:
<color_name> chroma contrast,
<color_name> chroma brightness,
<color_name> chroma smoothness.

Does that help? But I dont understand any of this...

No.
I want to understand on what principle there is a change in color.
Are you acquainted with the system YUV ?

Basically, the control 'contrast' multiplies the value (in Y, Cb or Cr) and the control 'brightness' add an offset to the value.
So if you add 'brightness' to the Cb component, your image looks more blue.
If you remove brightness to the Cb component, your image looks more yellow (the complement color to the blue).

user_gimp: No I am not, but if I recall correctly I read somewhere in these forums that Ronounours is directly affiliated with G'MIC somehow, so I would accept his word as gospel (if I recall correctly that is...)

Ronounours is the creator of the G'MIC plug-in for GIMP. Thank you David.

Unfortunately I did not get an answer to my question.

using Brightness instead of Contrast, as understood from David

What is function of option smoothness ?
Explain please.

Smoothness applies a blur in the specified channel (Y,Cb or Cr) of the image.
Each pixel diffuses its value to its neighborhood, creating so a kind of 'halo' effect.

Thanks, Ronounours.
Luminance contrast (gain) and Luminance brightness (offset).
What is the difference ? If I'm not mistaken: the higher the Luminance brightness value, the brighter the colors. And vice versa.
But Luminance contrast ?
Explain please.

I've already explained it: the 'contrast' parameter is a multiplying factor you apply on your channel values (Y,Cb or Cr), while the 'brightness' parameter is a number you add to your channel values.

So if you add 'brightness' to the Cb component, your image looks more blue.
If you remove brightness to the Cb component, your image looks more yellow (the complement color to the blue).
:-) Good. I understand the math.
If I increase "contrast" to the Cb component, image looks also more blue. So ?
If I reduce "contrast (gain)" to the Cb component, blue-yellow color is removed from the image.
In the picture remain the red-green color.
But I do not understand how this principles is reflected in practice with Y.
If we make the offset value Y increases or decreases. If we do the multiplication, the value also increases or decreases.
So what's the difference?

The difference is only that in a case you do a multiplication to increase/decrease the values, while in the other case you do an addition.
It has a difference on the final histogram. Making an addition just shifts the histogram to the right (positive addition) or to the left (negative addition -> subtraction).
The multiplication scales the entire histogram (so pixel with initial values 0 stay with value 0). The multiplication changes the difference between the max and min of your image
(so it increases/decreases contrast), while the addition preserves the min-max difference (it only acts on the global brightness).

I load a picture in blue - absolutely pure blue 0, 0, 255.
I move the sliders Blue chroma contrast or Blue chroma brightness and
get a green color.
But why green color ? From absolutely pure blue .. ?
The same situation with absolutely pure red

Explain, please.

My answer to myself - Just look attentively at picture
https://en.wikipedia.org/wiki/File:YUV_UV_plane.svg
-----------------------

But I have a other question.
In YCbCr color space Y range - from 16 to 235 for 8-bit. Cr and Cb ranges - from 16 to 240

But in MixerYCbCr Luminance brightness and Blue/Red chroma brightness have ranges from 0 to 255
Please explain this "contradiction". What am I misunderstand?

Here's a quote from the book 'Video Demystified' by Keith Jack.