Recovering photometric properties of multiple strongly-reflective, partially-transparent surfaces from a single image

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 nonlinear 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