The “shading twist,” a dynamical shape cue

When a light source moves, the isophotes of the illuminance field (observed as “shading” in the case of Lambertian surfaces) move over the surfaces of illuminated objects. The sense of rotation of the isophotes relative to the sense of rotation of the “surface illuminance flow,” that is the tangential component of the illumination direction over the surface, depends on the Gaussian curvature of the surface. The temporal change of orientation, the “shading twist,” reveals this purely surface related quality. Since the shading twist depends only on the local curvature of the surface it doesn’t matter at all how the light source moves or where the light sources are, the “shading twist” is a pure surface property, that is to say, it behaves as being painted upon the surface. The formal relations pertaining to the shading twist are analyzed and a numerical simulation is presented that fully corroborates the conclusions from the formal study. The algorithm is also tested on a real scene.