A matte is a grayscale image that is used to isolate part of an image for an effect. In general, full white is meant to indicate the parts of the image to use (usually the subject), full black is meant to indicate the parts of the image to ignore (usually the background), and grays are used to indicate some falloff between those extremes.
Mattes are usually derived from real footage. In your ink splatter example, you’re right in noting that it doesn’t take a lot of work to derive the matte from the footage. Not all mattes are this straightforward, though. Some require chromakeying (or other procedural effects), rotoscoping, or some combination of these techniques to generate. Once an object is separated from its background, though, you can export its alpha as a grayscale luma matte, which would be compatible with just about any compositor on the planet.
Mato has already described how to use a luma matte as a track matte in After Effects.
Walter Soyka
Principal & Designer at Keen Live
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