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.)
The pixel subtraction operator takes two images as input and produces as output a third image whose pixel values are simply those of the first image minus the corresponding pixel values from the second image. It is also often possible to just use a single image as input and subtract a constant value from all the pixels. Some versions of the operator will just output the absolute difference between pixel values, rather than the straightforward signed output.
I will use absolute difference of two images in the background subtraction in the next post 🙂