Recovering three-dimensional shape from a single image of curved objects

An algorithm to recover three-dimensional shape, i.e., surface orientation and relative depth from a single segmented image is presented. It is assumed that the scene is composed of opaque regular solid objects bounded by piecewise smooth surfaces with no markings or textures. It is also assumed that the reflectance map R(n) is known. For the canonical case of Lambertian surfaces illuminated by a point light source, this implies knowing the light-source direction. A variational formulation of line drawing and shading constraints in a common framework is developed. The global constraints are partitioned into constraint sets corresponding to the faces, edges and vertices in the scene. For a face, the constraints are given by Horn's image irradiance equation. A variational formulation of the constraints at an edge both from the known direction of the image curve corresponding to the edge and shading is developed. At a vertex, the constraints are modeled by a system of nonlinear equations. An algorithm is presented to solve this system of constraints.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>