Photometric Invariants Related to Solid Shape

Abstract

An attempt is made to identify the structural invariants of the field of isophotes on lambertian surfaces of arbitrary shape under arbitrary illumination. It is a priori clear that such invariants play an important part in the perception of solid shape by means of chiaroscuro. We have found several such invariants. The topological structure of the field of isophotes is determined by the collection of nested, closed parabolic curves on the surface. An important class of stationary points of the field clings to these parabolic lines. The isophotes cut the parabolic lines at a constant angle, irrespective of the location of the light sources. For certain canonical surface undulations the field of isophotes is explicitly given.