Invert the Transparency in an Image with Gimp

You can easily invert the transparent parts of an image with Gimp. Gimp is an open source Photoshop alternative.

Follow these steps:
  1. Choose Colors -> Components -> Decompose from the menu and set Color model to RGBA.
  2. A new image is opened with all color channels (including alpha channel) decomposed as single layers.
  3. Select the layer alpha and choose Colors -> Invert from the menu.
  4. Choose Colors -> Components -> Compose from the menu, set Color model to RGBA and make sure the layers are correctly mapped to the channels (should default correctly if you did not reorder the layers)

It will open a few new Gimp tabs but it will, indeed, invert the transparent areas of the image. This worked well for me on an image of a single color with transparency.