A graph spectral approach to shape-from-shading

This paper describes a graph-spectral method for shape-from-shading. The algorithm takes as its input a field of initial surface normal estimates computed using the Lambertian irradiance cone and the Canny edge gradient. We illustrate how to refine this field of surface normals using a graph-spectral method. From the initial field of surface normals we make curvature estimates. The curvature estimates are in turn used to compute a transition probability matrix. From the theory of random walks on graphs, the leading eigenvector of this matrix is a curvature minimising path through the field of surface normals. We impose curvature consistency on the initially noisy field of surface normals by rotating them about their irradiance cones so that they follow the path defined by the leading eigenvector. This method is applied to a variety of real-world images and is shown to lead to improved surface reconstruction.