How to recolor grayscale image with fixed colors by ImageMagick using CLUT

[cagdabr]

I'm pretty new to image processing and ImageMagick, but I couldn't find a straightforward solution to my problem after some searching. I still don't have an understanding how the Color LookUp Table [CLUT] works in ImageMagick.

I have source image:


And I want it look like this:


The idea is that in source image I have gray values which should be converted to color values 1:1

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rgb(0, 0, 0)  -> transparent
rgb(1, 1, 1)  -> rgb(253,0,252)
rgb(2, 2, 2)  -> rgb(252,0,23)
rgb(3, 3, 3)  -> rgb(253,125,33)
rgb(4, 4, 4)  -> rgb(254,217,48)
rgb(5, 5, 5)  -> rgb(219, 255, 51)
rgb(6, 6, 6)  -> rgb(59, 255, 46)
rgb(7, 7, 7)  -> rgb(110, 165, 58)
rgb(8, 8, 8)  -> rgb(18, 139, 54)
rgb(9, 9, 9)  -> rgb(44, 255, 254)
rgb(10,10,10) -> rgb(18, 129, 252)
rgb(11,11,11) -> rgb(39, 19, 251)
rgb(12,12,12) -> rgb(115, 115, 115)
rgb(13,13,13) -> rgb(179,179,179)

But I don't know how to create CLUT image in order to make ImageMagick convert it as I want. I tried to create something like this:



... but when I do:

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$> convert region_128x128.png color_lookup_table.png -clut region_128x128_clut.png

I'm getting this:



So, the question is, Is it possible to create the CLUT for my problem? If so, could someone please explain it to me?

[snibgo]

This does the job. Windows BAT syntax.

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convert ^
  jLHjz.png ^
  -auto-level ^
  ( -size 1x1 ^
    xc:rgb(253,0,252) ^
    xc:rgb(252,0,23) ^
    xc:rgb(253,125,33) ^
    xc:rgb(254,217,48) ^
    xc:rgb(219,255,46) ^
    +append ^
  ) ^
  -clut ^
  out.png

Your input has only 5 shades of gray, from 1 to 5 out of 255, so I auto-levelled to widen the range to 0 to 100%, then supplied a clut with 5 values.

Instead, I could have omitted the auto-level, and supplied a clut with 256 values.

[cagdabr]

...
Your input has only 5 shades of gray, from 1 to 5 out of 255, so I auto-levelled to widen the range to 0 to 100%, then supplied a clut with 5 values.

Instead, I could have omitted the auto-level, and supplied a clut with 256 values.

Thank you for your reply @snibgo. This particular source image may not have all gray values but clut should be able to handle the rest of them in case if they will be in the image.