Tsai and Shah applied the discrete approximation of the gradientrst, then employed the linear approximation of the reflectance function in terms of the depth directly. Their algorithm recovered the depth at each point using a Jacobi iterative scheme. ( P. Tsai and M. Shah. Shape from shading using linear approximation. Image and Vision Computing, 12(8):487–498, 1994.)
Pentland used the linear approximation of the reflectance function in terms of the surface gradient, and applied a Fourier transform to the linear function to get a closed form solution for the depth at each point. (Pentland takes the Fourier transform of both sides of the equation). (Pentland, A., “Shape Information From Shading: A Theory About Human Perception,” Computer Vision., Second International Conference on , vol., no., pp.404-413, 5-8 Dec 1988.)
Classical “Shape from shading” theories assume that surfaces are perfectly
Lambertian (thus the radiance at the eye is perfectly proportional with irradiance) and
that each part of the surface is illuminated by the same source. Then the radiance received by the eye depends only upon the angle between the local surface normal and the net flux vector. Shape from shading is the problem of recovering the shape of a surface from this intensity variation is known as shape from shading. I prepared this presentation about “Shape from shading” and I decided to share it here as well 🙂 I love to learn new things and then teach (present) them to other people.