Shape from shading using probability functions and belief propagation

Shape-from-shading (SFS) aims to reconstruct the three-dimensional shape of an object from a single shaded image. This article proposes an improved framework based on belief propagation for computing SFS. The implementation of the well-known brightness, integrability and smoothness constraints inside this framework is shown. We implement the constraints as probability density functions. For example, the brightness constraint is a two-dimensional probability density function that relates all possible surface gradients at a pixel to their probability given the pixel intensity. A straightforward extension of the framework to photometric stereo is presented, where multiple images of the same scene taken under different lighting conditions are available. The results are promising, especially since the solution is obtained by iteratively applying simple operations on a regular grid of points. The presented framework therefore can be implemented in parallel and is a reasonably likely biological scheme.