Height and gradient from shading

摘要

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.