The Optical Flow of Planar Surfaces

Abstract

The human visual system can recover the 3D shape of moving objects on the basis of motion information alone. Computational studies of this capacity have considered primarily non-planar rigid objects. With respect to moving planar surfaces, previous studies by Hay (1966), Tsai and Huang (1981), Longuet-Higgins (1984), have shown that the planar velocity field has in general a two-fold ambiguity: there are two different planes engaged in different motions that can induce the same velocity field. The current analysis extends the analysis of the planar velocity field in four directions: (1) the use of flow parameters of the type suggested by Koenderink and van Doorn (1975), (2) the exclusion of confusable non-planar solutions, (3) a new proof and a new method for computing the 3D motion and surface orientation, and (4) a comparison with the information available in orthographic velocity fields, which is important for determining the stability of the 3D recovery process.