Numerical shape-from-shading revisited

This paper revisits the numerical shape-from-shading method proposed in early 1980s. The original problem is non-convex due to the unit norm constraint for surface normal, and the existing approaches including the original Ikeuchi and Horn’s work uses approximate solution strategies for the original problem. This paper instead studies relaxation strategies for the original non-convex constraint and describes corresponding solution techniques that are built upon advanced convex optimization. We analyze the effect of the relaxations in terms of resulting accuracy and computational complexity.