We study the problem of estimating the illuminant?s direction from images of textured surfaces. Given an isotropic, Gaussian random surface with constant albedo, Koenderink and Pont [JOSA 03] developed a theory for recovering the illuminant?s azimuthal angle from a single image of the texture formed under a Lambertian model. In this paper, we extend the theory to deal with cases of spatially varying albedo.

First, we generalise the theory to explain why their method should work even for certain types of spatially varying albedo. Our generalisation also predicts that the coherence of the structure tensor should lie below 0.8 in such non-constant albedo cases and accurately predicts the "deviation" from the true value observed by Koenderink and Pont on the Columbia-Utrecht (CUReT) texture database. Next, we extend the theory to account for arbitrarily varying albedo. We also investigate local, rather than global, estimates of the direction, and demonstrate our theory on the CUReT and the Heriot-Watt TextureLab databases where estimated directions are compared to ground truth.