The multilayer feedforward network has been usually used for learning
a nonlinear mapping based on a set of examples of the input-output dat
a, In this paper, we present a novel use of the network, in which the
example data are not explicitly given, We consider the problem of shap
e from shading in computer vision, where the input (image coordinates)
and the output (surface depth) satisfy only a known differential equa
tion, We use the feedforward network as a parametric representation of
the object surface and reformulate the shape from shading problem as
the minimization of an error function over the network weights, The st
ochastic gradient and conjugate gradient methods are used for the mini
mization, Boundary conditions for either surface depth or surface norm
als (or both) can be imposed by adjusting the same network at differen
t levels, It is further shown that the light source direction can be e
stimated, based on an initial guess, by integrating the source estimat
ion with the surface estimation, Extensions of the method to a wider c
lass of problems are discussed, The efficiency of the method is verifi
ed by examples of both synthetic and real images.