Double and Triple Ambiguities in the Interpretation of Two Views of a Scene

It is known (Longuet-Higgins 1984) that if two spherical images of a visually textured surface, from f in i te ly separated viewpoints, allow more than one 3D interpretation, then the surface must be part of a quadric passing through the two viewpoints. It is here shown that this quadric is either a plane or a ruled surface of a type f i r s t considered by Maybank (1985) in a study of ambiguous optic f low f ields; and that three is the maximum number of interpretations that the two images can sustain. An explanation is offered for the fact that two images of just 5 points general ly permi t two d i s t i nc t 3D interpretations,