Extract the hard light from an image.

[coolperez8]

So, let's say I have 2 images, what I want to do is try to get the hard light from an image using an image with the effect applied and an image without the effect, so if I were to apply the effect itself to the image without the effect I'd get the image with the effect. Here's what I'm talking about:

Let's say I have these two images:
Image 1:

Image 2:


What command can I run using these two images to get Image 3, so if I were to run the following command I'd end up again with Image 2.
Command: Convert 5jJtxyI.png jTIWxXS.png -compose hard-light -composite Restore.png

Image 3:

[snibgo]

To rephrase the question:

If we have images dst.png and out.png, and we know that out.png came from

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convert dst.png src.png -compose HardLight -composite out.png

... we want to find src.png. Is that correct?

If you knew src.png and wanted to find dst.png, this would be quite simple. One of two formulae are used, depending on the value of src, and both the formulae are reversible.

The two formulae are:

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out = 2*src*dst
out = 1 - 2*(1-src)*(1-dst)

But you don't know src, so don't know for each pixel which formula is used.

I think you could assume one of the formulae, and try the reverse of that. This gves you a version of src.png. Use this with HardLight, and compare the result with your initial out.png. Some of the pixels will be wrong, so those had the wrong formula, so recalculate those pixels with the inverse of the other formula.

But there may be a simpler method.

[coolperez8]

Yes, that is correct, but I don't know the command the achieve the desired result.