Surface height recovery using heat flow and manifold embedding

We make two contributions to the problem of shape-from-shading. First, we develop a new method for surface normal recovery. We pose the problem as that of solving the steady state heat equation subject to the hard constraint that Lambert's law is satisfied. According to this picture, the surface normals are found by taking the gradient of a scalar field. The heat equation for the scalar field can be solved using simple finite difference methods and leads to an iterative procedure for surface normal estimation. The second contribution is to show how surface height recovery from the field of surface normals can be posed as one of low dimensional embedding. We experiment with the resulting method on a variety of real-world image data, where it produces qualitatively good reconstructed surfaces.