Visual interpretation of Lambertian surface deformation

The major topic of this thesis is the interpretation (as a three-dimensional velocity field) of the changing intensity pattern induced by a smoothly deform¬ ing Lambertian surface of uniform albedo illuminated by a distant point light source. A constraint is derived which shows how the changing intensity pattern induced by such a deforming surface is locally constrained by the three-dimen¬ sional motion of that surface. This constraint, the "Intensity Rate Constraint", a partial differential equation in the normal component of surface velocity, con¬ tains no terms relating to the tangential components of surface velocity, hence the problem of determining the three-dimensional motion is ill-posed. The ap¬ plication of an additional constraint on the motion, (implemented in the form of a stretch-based regulariser) is proposed. This enables certain psychologi¬ cally significant classes of three-dimensional velocity field over the surface to be estimated veridically from the image intensity rate, the velocity field along the boundary and static information. This technique is successfully tested on synthetic data in experiments requiring at least ten times greater accuracy in intensity measurement than is commonly available. The thesis concludes with a suggested technique for the interpretation of smoothly deforming space-curve motion