This paper introduces a method to recover photometric parameters of a set of 3D surfaces from a single image with significant global-illumination effects such as inter-reflections and transparencies. Since this problem is ambiguous for arbitrary unknown scenes, our formulation assumes that the scene consists of a small set of photometrically homogeneous surfaces with known 3D shapes, illuminated by known light sources.

We show that under these conditions, the system of non-linear equations that defines how the image is formed may be factorized into a vector composed only of products of some photometric parameters, and a matrix, whose elements depend non-linearly on both the known illumination, the known 3D shapes and the remaining photometric parameters. This factorization leads to an efficient optimization-based algorithm to compute all unknown photometric parameters from a single input image. Experiments with real data show that this algorithm is more stable and efficient than simpler alternatives.