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I am having a little bit of a mathematical approach here... I suppose that all the transformation we can make to an image which operate on one pixel per time (for example levels, saturation, color balance) can just be done with curves.

Is there a way to take the orginal image, the transformed one and find out what curve adjustment can give the same result?

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You say:

I suppose that all the transformation we can make to an image which operate on one pixel per time (for example levels, saturation, color balance) can just be done with curves.

This is not correct. Some examples include converting to monochrome, making the image sepia toned, or even your example of changing the saturation. Increasing the saturation involves moving the maximum of the red, green, and blue channels away from the other 2 channels. (Or if there are 2 maxima, moving them both away from the third channel.) Since curves applies a separate curve to each channel (or the same curve to all channels), there's no way to achieve that sort of effect for all pixels with just an application of curves.

There is, however, a tool that is able to capture all of these things, and that's a look-up table (aka LUT). A 3D LUT has a red axis, a green axis, and a blue axis. Any triple in the input image can be used to look up a new triple in the LUT. You can apply the same LUT to different images to give them a similar look.

You can figure out the LUT if you have a before and after picture. (Or at least you can figure out a good portion of it, if not the whole thing.) You simply take each pixel in the original image, find its coordinates in the LUT and set it to whatever the corresponding pixel in the output is. If your input image covers most of the range from dark to light in most of the colors, you should get back a LUT that performs the same function.

There are a variety of algorithms for automating the copying of styles from one image to another one. They often do more than just color transfers. Here are a few:

  • Your entire first paragraph is wrong. True monochrome and true sepia tone (two tone print as opposed to just visually) are not pixel level transformations so irrelevant to the original question. Saturation (or visually making something sepia tone or even monochrome) however can all be done with curves. – RyanFromGDSE Apr 7 '17 at 14:48
  • @RyanFromGDSE Really? Do you have a reference I could read about it? I'm having a hard time understanding how for monochrome you could multiply all the channels by different constants, add those values together, and distribute the result to all 3 channels. But it sounds intriguing! I'd love to learn more. – user1118321 Apr 7 '17 at 15:38
  • Please post a new question. Include two images - an original and one monochrome using your current "multiply, add, distribute" methodology but ask how you could do the same thing with curves. I'll do my best to answer it for you. It may be a better fit for graphicdeesign.stackexchange.com but I don't think its off-topic here either. – RyanFromGDSE Apr 7 '17 at 15:57
  • @RyanFromGDSE OK, I've posted it here. Thanks for your time! – user1118321 Apr 8 '17 at 3:28
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    Curves is a 3d LUT – joojaa Apr 17 '17 at 14:18
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At best you can only makes guesses because you'll have no way to know if it was only one curve applied to the entire image.

For example when I'm working on nearly any photo I almost always have a folder structure that includes:

  • Local Adjustments
  • Global Adjustments

Anything that I intend to have on the entire image I put in my global adjustments group. Anything that contains a mask I put in local adjustments.

So if you only have a flattened jpg. You could approximate it by analyzing the images brightest point and darkest point and setting them as white and black. But that in no way guarantees an accurate result. Its at best an approximation because if the person say also did a basic "ND Gradient Layer Mask" [a black to white gradient as a layer mask] and applied a Curve to that you wouldn't know it, or be accounting for it in your attempt to reverse engineer the original.

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