Height and gradient from shading

Abstract

The method described here for recovering the shape of a surface from a shaded image can deal with complex, wrinkled surfaces. Integrability can be enforced easily because both surface height and gradient are represented. (A gradient field is integrable if it is the gradient of some surface height function.) The robustness of the method stems in part from linearization of the reflectance map about the current estimate of the surface orientation at each picture cell. (The reflectance map gives the dependence of scene radiance on surface orientation.) The new scheme can find an exact solution of a given shape-from-shading problem even though a regularizing term is included. The reason is that the penalty term is needed only to stabilize the iterative scheme when it is far from the correct solution; it can be turned off as the solution is approached. This is a reflection of the fact that shape-from-shading problems are not ill posed when boundary conditions are available, or when the image contains singular points. This article includes a review of previous work on shape from shading and photoclinometry. Novel features of the new scheme are introduced one at a time to make it easier to see what each contributes. Included is a discussion of implementation details that are important if exact algebraic solutions of synthetic shape-from-shading problems are to be obtained. The hope is that better performance on synthetic data will lead to better performance on real data.