Quadratic Penalty Methods for Shape from Shading.

Shape from shading" (SFS) denotes the problem of reconstructing a 3D surface, starting from only one image showing a shaded representation of the surface itself. Minimization techniques are commonly used for solving the SFS problem, where the functional that must be optimized is a weighted combination of the brightness functional plus one or more regularization terms. A critical role in this context is played by the weights used in the functional, which markedly affect the possibility of obtaining a good reconstruction. However the choice of these weights in not trivial. We present a quadratic penalty method where the SFS problem is first formulated as a constrained minimization problem, so that an a-priori choice of the smoothing weight is not needed. Then the SFS constrained problem is replaced by a sequence of unconstrained subproblems, which are efficiently solved by a Barzilei-Borwein method.