Shape-from-shading (SFS) is the process of reconstructing a 3D surface from its luminance profile in an image. This problem is under-constrained, so one usually makes the simplifying assumptions that the surface reflectance is Lambertian and of constant albedo, and that the illumination comes from a unique (known) point light source. Then the image luminance arises from the 3D surface orientation in accordance with the image irradiance (IIR) equation. Even then, the surface recovery is ill-defined and needs regularization.

This paper follows the global approach to SFS pioneered by Horn and Brooks. The latter had proposed regularizing the surface reconstruction through a compromise between the two requirements of accuracy and smoothness. This was solved as a variational problem of minimizing an “energy” functional given as a weighted average of two global measures, one of the error with regard to the IIR, and one of the surface roughness. As explained by the authors, this method tends to oversmooth the recovered surface, at the expense of accuracy.

Thus, the authors propose making accuracy (with regard to the IIR equation) a hard constraint. Instead of using the best compromise between accuracy and smoothness, one will use the smoothest exact solution of the IIR equation. They also modify the initialization of the reconstruction algorithm, on the basis of a bias towards convex surfaces. They then investigate new ways of implementing the smoothness constraint, following three directions: surface smoothness; curvature consistency; and consistency with the image gradient field. They thus obtain nine variants of their algorithm, the first one corresponding to the original smoothness constraint of Horn and Brooks.

Experimental results on synthetic and natural images show a marked improvement in accuracy over the original approach of Horn and Brooks, as well as reduced noise, compared to the alternative methods of Bichsel and Pentland and of Tsai and Shah.