Shape from shading: Analysis by synthesis of implicit and general surfaces

Abstract

The shape from shading (SfS) problem in computer vision requires complete knowledge of the image conditions under which an image is created to produce surface descriptions. Almost all the methods rely on modeling the image formation process view and invert it mathematically which in turn places constraints on imaging conditions. These methods make constraining assumptions on camera model (orthographic projections), light source (singlepoint source at infinity) and reflectance model (Lambertian). In this paper, we present a general framework for solving the SfS problem under general imaging conditions by using powerful image synthesis techniques from computer graphics and thus moving the complexity of producing surface descriptions from analysis to the synthesis side. The technique relies on iterative synthesis of images from object descriptions in order to minimize an error function. The technique is illustrated in detail for quadric surfaces, with the ellipsoid as the specific example. To extend the method to general surfaces, the surfaces are modeled under the Bezier framework. The proposed framework is found to be very general with the capability to accommodate widely varying reflectance models and light source types.