An optimal time algorithm for shape from shading

An optimal numerical algorithm for the reconstruction of a surface from its shading image is presented. The algorithm solves the 3D reconstruction from a single shading image problem. The shading image is treated as a penalty function and the hight of the reconstructed surface is a weighted distance. A first order numerical scheme based on Sethian's Fast Marching Method [19, 18] is used to compute the reconstructed surface. The surface is a viscosity solution to an Eikonal equation for the vertical light source case. For the oblique light source case, the surface is the viscosity solution to a different partial differential equation. A small modification of the Fast Marching Method yields a numerically consistent fast algorithm for the general shape from shading problem.

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