Vector field smoothing via heat flow

We develop a new method for recovering and smoothing fields of surface normals in shape-from shading. We show how to transform the problem of recovering surface normals that satisfy Lambert's law into that of solving the steady state heat equation for a scalar potential. According to this picture, the smoothed field of surface normals is found by taking the gradient of the scalar field. The heat equation for the scalar field can be solved using simple finite difference methods, and leads to an iterative procedure for vector estimation. We illustrate the utility of the new method on real world imagery and compare our results with those delivered by an alternative.