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

Abstract

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.