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for days I cannot find the answer on that question.
Thing is simple: when I increase contrast (both with contrast slider, or with S-curve) in Lightroom/Photoshop, a saturation of the color is also increases on the photo. And vice versa: when I decrease contrast, saturation also visually goes down.
Why that is happened? Is there any explanation? Thank you.
Saturation is roughly the difference between max(r,g,b) and min(r,g,b). I.e. in a rgb color space 0-1.0, a saturated blue is b=.9, r=g=0.1. A pale blue has b=0.9 r=g=0.7.
If you enhance contrast in the r,g,b space the saturation will be affected. This is the fastest way to compute contrast change. Increasing contrast is to move (either by s curve or contrast slider) values below 0.5 further down, and values above 0.5 further up, and vice versa for lower contrast. This is done to each color channel independently. So the b 0.9 becomes 1.0 and r=g=0.0, now a difference of 1.0 versus 0.8 before. The difference between max and min is thus higher. The pale blue has both the max and min color channel value go up to maybe clipping at b=1.0 and r=g=0.95 , a difference of 0.05 versus 0.2 before.
Also gamma changes the relationship between the channels, so it will affect the saturation. Now, instead of applying contrast change to RGB values, we can convert the color space to YUV, LAB, or HSV/HSI where we separate the brightness from the color. Then we can change gamma and contrast without changing color. Complexities arise with human perception that the perception of colors and saturation changes with brightness, and the monitors and prints also undergo transfer functions that affect these things. So the formulas are not perfect. the XYZ->LAB tried to take this into account, but it takes a lot of processing to convert one way and then back again to display the result.
Contrast in photography is a subjective judgment as to what is “normal” vs. abnormal with regards to tonal range. A full scale image has both black and white tones that key off the scale of the image. A “normal” contrast image depicts gradual changes in tones from black to white. In terms of range, “average” constitutes a range of about 256:1 on a computer screen. That’s about 8 f-stops. Since each f-stop is a 2x change, then 2x2x2x2x2x2x2x2 = 256 (2^8) written 256:1). Such an image, when plotted has an “average slope” angle. Should we up the contrast, we drop off some of the intermediate tones. Now a high contrast image likely contracts that range to 6 f-stops = 64:1 or 5 f-stops = 32:1.
Now colors are perceived in varying proportions of saturation ranging from bright to dark. Light color combinations are towards the white whereas as dark colors blend towards black. As you up the contrast you are compressing the range hues occupy. When a hues range is squeezed it tends to slide towards black thus its appearance becomes harsher.
