Perspective photometric stereo with shadows

High resolution reconstruction of 3D surfaces from images remains an active area of research since most of the methods in use are based on practical assumptions that limit their applicability. Furthermore, an additional complication in all active illumination 3D reconstruction methods is the presence of shadows, whose presence cause loss of information in the image data. We present an approach for the reconstruction of surfaces via Photometric Stereo, based on the perspective formulation of the Shape from Shading problem, solved via partial differential equations. Unlike many photometric stereo solvers that use computationally costly variational methods or a two-step approach, we use a novel, well-posed, differential formulation of the problem that enables us to solve a first order partial differential equation directly via an alternating directions raster scanning scheme. The resulting formulation enables surface computation for very large images and allows reconstruction in the presence of shadows.