Interpreting trihedral vertices by using assumptions about the angles between the edges

This paper considers the geometry of mapping a trihedral vertex onto lines in an image. Where previous analyses of the issue have concentrated on the problem of fitting fully specified models, ours is motivated by considering the assumptions that human vision uses to interpret images of corners, particularly assumptions about the angles between edges. We describe evidence that assumptions of that kind are used in human vision. We then develop an analysis which makes explicit the relationship between projected angles and known or assumed angles at the vertex. This can be used directly to arrive at interpretations. It also allows us to identify limiting cases which show how a projection can be used to constrain possible hypotheses about the angles at vertices.