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Quick GIMP tutorial: how to detour a drawing on a solid background to make it transparent while keeping antialiasing pretty quickly

1. do a quick want selection of the background
2. invert the selection
3. shrink the selection to one pixel (or more if the borders are thicker, may be better to get good antialias)
4. invert the selection again
5. use the "color to alpha" option and select the background color

And voila!!