Where and why local shading analysis works

An apparent contradiction in the shape-from-shading literature is examined. Although practical experience suggests that shape can be inferred from the local analysis of shading, mathematical analyses support the opposite. A criterion for exact surface recovery is derived, and it is shown that, as a result of surface geometry, elliptic, hyperbolic, and doubly curved surfaces could be recovered to reasonable accuracy provided that surface curvature and/or foreshortening were limited. In other words, by relaxing the requirement that surfaces be recovered exactly, it is found that local analysis of shading can provide useful descriptions of shape as evidenced by the results presented