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Probably most lines represent edges and "rims": the places where the line
grazes the boundary of an object:
We get a wealth of information about the 3-D geometry from these lines and the relation between them. This is very well understood: see Visual Intelligence: How We Create What We See by Donald D. Hoffman, from which the image comes. There is a summary in "Donald Hoffman's Rules of Visual Intelligence". A more recent explanation, concerned mainly with line drawings rather than images in general, is Part III of Doug DeCarlo's "Line Drawings and Perception" SIGGRAPH 2005 Course Notes.