The direct computation of height from shading

A method for recovering shape from shading that solves directly for the surface height is presented. By using a discrete formulation of the problem, it is possible to achieve good convergence behavior by employing numerical solution techniques more powerful than gradient descent methods derived from variational calculus. Because this method solves directly for height, it avoids the problem of finding an integrable surface maximally consistent with surface orientation. Furthermore, since additional constraints are not needed to make the problem well posed, a smoothness constraint is used only to drive the system towards a good solution; the weight of the smoothness term is eventually reduced to near zero. By solving directly for height, stereo processing may be used to provide initial and boundary conditions. The shape from shading technique, as well as its relation to stereo, is demonstrated on both synthetic and real imagery.