Direct method for reconstructing shape from shading

An approach to shape-from-shading that is based on a connection with a calculus of variations/optimal control problem is proposed. An explicit representation corresponding to a shaded image is given for the surface; uniqueness of the surface (under suitable conditions) is an immediate consequence. The approach leads naturally to an algorithm for shape reconstruction that is simple, fast, provably convergent (in many cases, provably convergent to the correct solution), and does not require regularization. Given a continuous image, the algorithm can be proved to converge to the continuous surface solution as the image sampling frequency is taken to infinity. Experimental results are presented for synthetic and real images