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A class of inferences is described which allows the recovery of three-dimensional structures from the two-dimensional curves in an image. Unlike most previous methods, these inferences do not require restrictive assumptions or prior knowledge regarding the scene. They are based on the assumption that the camera viewpoint and the positions of the illumination sources are independent of the objects in the scene. From these independence assumptions, it can be shown that many potential interpretations of image curves are highly improbable. By eliminating these improbable interpretations it is possible to segment the image into sets of related image features and derive many three-space relations.