A two-frame theory of motion, lighting and shape

This paper explores how shape, motion, and lighting interact in the case of a two-frame motion sequence. We consider a rigid object with Lambertian reflectance properties undergoing small motion with respect to both a camera and a stationary point light source. Assuming orthographic projection, we derive a single, first order quasilinear partial differential equation that relates shape, motion, and lighting, while eliminating out the albedo. We show how this equation can be solved, when the motion and lighting parameters are known, to produce a 3D reconstruction of the object. A solution is obtained using the method of characteristics and can be refined by adding regularization. We further show that both smooth bounding contours as well as surface markings can be used to derive Dirichlet boundary conditions. Experimental results demonstrate the quality of this reconstruction.