A Numerical Method for Shape-From-Shading From A Single Image

Unknown author (1979-01)

This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract N00014-75-C-0643. Thesis Supervisor: Berthold K. P. Horn Title: Associate Professor of Electrical Engineering and Computer Science

Working Paper

The shape of an object can be determined from the shading in a single image by solving a first-order, non-linear partial differential equation. The method of characteristics can be used to do this, but it suffers from a number of theoretical difficulties and implementation problems. This thesis presents an iterative relaxation algorithm for solving this equation on a grid of points. Here, repeated local computations eventually lead to a global solution. The algorithm solves for the surface orientation at each point by employing an iterative relaxation scheme. The constraint of surface smoothness is achieved while simultaneously satisfying the constraints imposed by the equation of image illumination. The algorithm has the distinct advantage of being capable of handling any reflectance function whether analytically or empirically specified. Included are brief overviews of some of the more important shape-from-shading algorithms in existence and a list of potential applications of this iterative approach to several image domains including scanning electron microscopy, remote sensing of topography and industrial inspection.