How to make similar pixels transparent while accounting transparency

[scarf005]

ImageMagick version

6.9.11

Operating system, version and so on

ubuntu 23.04

Description

a	b	expected

i want to remove background (a) from an image (b). the backgrounds are identical. in other words, a + expected = b. now from a.png and b.png, i want to subtract a.png from b.png to get expected (with transparency), however changemask command

composite a.png b.png -compose ChangeMask  res.png

gives me this instead because the red spray has transparency:

would there be any way to achieve this?

[snibgo]

I name your images transA.png, transB.png and transExp.png.

transA.png has no ICC colour profile, but the other two do have a profile. Why is that?

transExp.png is entirely red, with varying transparency.

in other words, a + expected = b. now from a.png and b.png, i want to subtract a.png from b.png to get expected (with transparency), ...

Some experimentation shows that you are wrong. Adding transA.png and transExp.png does not give transB.png.

magick transA.png transExp.png -compose Plus -composite x.png

x.png is not the same as `transB.png. Therefore subtracting transA from transB will not give the expected result.

However, using over does work:

magick transA.png transExp.png -compose Over -composite +depth x.png

x.png is virtually the same as transB.png. (If we use depth 8, it is exactly the same.)

So we need the inverse of "-compose Over -composite". For that, see Inverse composites and Watermarks.

Window syntax:

magick ^
  -define compose:clamp=off ^
  ( transA.png transB.png ^
    -strip -colorspace sRGB ^
    -compose MinusDst -composite ^
  ) ^
  ( transA.png ^
    -strip -colorspace sRGB ^
    ( +clone -fill Red -colorize 100 +write mpr:RED ) ^
    -compose MinusDst -composite ^
  ) ^
  -compose DivideSrc -composite ^
  +depth ^
  +write a.png ^
  -grayscale Average ^
  mpr:RED ^
  +swap ^
  -alpha off -compose CopyOpacity -composite ^
  a2.png

a.png has three channels, the calculated alpha for the R, G and B channels. They are slightly different because the input images are only 8 bits per channel. We use the average for the required single alpha value.

We use that alpha with red pixels for a2.png, the calculated "expected" image. How close is it to transExp.png?

magick compare -metric RMSE a2.png transExp.png NULL:

8.03125 (0.000122549)

This is very close.

[scarf005]

thank you for the detailed explanation! however, i should have stated it more clearly, that this was a simplified question, and that the actual image in question is not necessarily red. would the solution work for other type of overlayed images that are mixed in color (i.e transparent house)?

about ICC profile, it's because i used the first image as-is but edited on graphic tool for other images.

[snibgo]

... the actual image in question is not necessarily red.

See the pages I linked to. For each pixel, if we know the colour then we can calculate the opacity. Or, if we know the opacity, we can calculate the colour. If we know neither the colour nor the opacity, an almost infinite number of solutions are possible.