Numerical 3-D shape inference from shading with new type of constraint

In traditional three dimensional (3-D) shape inference from shading, surface normal distribution is estimated by using a traditional constraint imposed on the surface normal and image brightness. In this paper, we derive another new type of constraint imposed on the surface normal and gradient of image brightness, and propose a 3-D shape inference algorithm by using both the traditional constraint and the new type of constraint. We prove that incorporation of the new type of constraint in an algorithm for recovering surface normal distributions from image brightness speeds convergence as compared to a similar algorithm that does not employ this constraint. The usefulness of the new type of constraint is shown by numerical experiments.