We apply a new algebraic multigrid method for solving computer vision problems with constraints, in particular "shape from photometric stereo". A variational formulation is applied to the problem of shape reconstruction from three or more images of an object with the same viewing direction and different lighting conditions, supplemented by some pointwise height constraints. In order to obtain a smooth reconstruction, we choose a weight-function that is singular at the constrained points, resulting in an elliptic equation with constraints and singular coefficients, which is solved efficiently by our algebraic multigrid algorithm.