LEARNING SHAPE FROM SHADING BY A MULTILAYER NETWORK

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.