Shape from shading using discrete polynomials

Given a monocular image, we propose a new method for extracting the shape of objects from the pixel intensities. The problem of solving the partial differential equation corresponding to the reflectance map is reduced to that of solving a finite set of nonlinear algebraic equations. The method involves patchwise approximation of the surfaces in the scene by discrete polynomials. Distinctive features of the method are as follows: a) Shape extraction without initial depth information of any form, (b) Handling of discontinuity (obtained by a zero-crossing operator) by splitting the region into multiple patches around the discontinuities contour and fitting the depth polynomial separately in each patch, (c) Algebraic evaluation of the quadratic polynomial coefficients in the case of identical source and viewer direction, and (d) Facility to integrate stereo information.