Recovering shape from a single image of a mirrored surface from curvature constraints

This paper presents models and algorithms for estimating the shape of a mirrored surface from a single image of that surface, rendered under an unknown, natural illumination. While the unconstrained nature of this problem seems to make shape recovery impossible, the curvature of the surface cause characteristic image patterns to appear. These image patterns can be used to estimate how the surface curves in different directions. We show how these estimates can be used to produce constraints that can be used to estimate the shape of the surface. This approach is demonstrated on simple surfaces rendered under both natural and synthetic illuminations.