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I am very confused with the following situation, let's say we have an image with two colors: (RGB 0,60,60) and (RGB 255,0,0).

(RGB 0,60,60) and (RGB 255,0,0)

I have noticed that the tone curve in Adobe Lightroom works differently than Photoshop. What i have understanded is that photoshop's RGB curve remapps the tone values of each color channel to the new determined by the curve. For instance if we make the following change to the curve:

Curve change in Photoshop

The left color which was (RGB 0,60,60) now is (RGB 0,0,0) because the value 60 in both green and blue channel has remapped now to 0. The right color (pure red, (RGB 255,0,0)) hasn't change at all, because we have not moved the point of the curve which corresponds to 255.

What makes me confused is that in lightroom when doing the same change in the tone curve, something different happens.

Straight curve in Lightroom Curve change in Lightroom

Now the red color(RGB 255,0,0) has turned to black (0,0,0) but i haven't moved the point which corresponds to 255. I also know that Lightroom uses the ProPhotoRGB color space and not sRGB. But in general i don't understand exactly what happens when i change the curves and also why photoshop and Lightroom make different changes. I have find some other similar questions in Photo.Stackexchange but they didn't helped me. Can someone please explain me what happens exactly in depth?

Thanks in advance.

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LR uses ProPhoto with a gamma of 1 for calculations, but it uses a gamma of 2.2 for the interface (histogram, tone curve). Photoshop uses whatever gamma is correct for the chosen color space (2.2 sRGB, 1.8 ProPhoto)... but none of that really matters and it's not what is causing your issue.

Your issue is that the RGB numbers mean different things in different color spaces. I.e. when describing a larger color space (ProPhoto) with the same 8bit integers (0-255) 255-0-0 is a different color than it is in a smaller color space. Here's an example for a green color (I already had these from a lesson I made; note that the positions are only representative).

enter image description here enter image description here

If you look at the curves histograms you will see that the red color exists at the right edge in Photoshop (sRGB) and it exists left of the right edge in LR (ProPhoto); just as the 255 value dropped to 237 in my green example. Also note that the LR histogram has additional RGB levels displayed; just as the red value changed from 0 to 138 in my green example. But it is still the same color... the only difference is where it is w/in the overall color space gamut.

Also note that LR is working in 16bit color (except for HDR) and PS is using whatever you tell it to (8bit default).

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