Most of the classic black-and-white movies have been "colorized," mainly so that they can be shown on television in color. It turns out that the process used to add the color is extremely tedious -- someone has to work on the movie frame by frame, adding the colors one at a time to each part of the individual frame.
To speed up the process, the coloring is done on a computer using a digital version of the film. The film is scanned into the computer and the coloring artist can view the movie one frame at a time on the computer's screen. The artist draws the outline for each color area, and the computer fills it in. The original black-and-white film holds all of the brightness information, so the artist can paint large areas with a single color and let the original film handle the brightness gradients. This means that the artist might only have to add 10 or so actual colors to a scene.
To speed up the process even more, interpolation is common. From frame to frame, there is normally very little variation in the position of objects and actors. (See, for example, the frame-by-frame demonstration on this page of How Television Works.) Therefore, the artist might manually color every tenth frame and let the computer fill in the frames in between.
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