Shape-from-shading under complex natural illumination

We present a shape-from-shading algorithm for Lambertian surfaces of uniform but unknown albedo, illuminated by unknown, arbitrarily complex environment lighting. Our approach is based on a first order spherical harmonic approximation to the reflectance map. This is estimated from the image using surface normals interpolated from boundary points. The shape-from-shading step minimises local brightness error and an edge sensitive smoothness constraint. This involves the solution of a linear least squares problem with a quadratic equality constraint, the global optimum of which can be found using the method of Lagrange multipliers. We demonstrate the performance of the algorithm on complex objects rendered under realworld illumination.