Inverse rendering in SUV space with a linear texture model

In this paper, we consider the problem of inverse rendering in the case where surface texture can be approximated by a linear basis. Assuming a dichromatic reflectance model, we show that spherical harmonic illumination coefficients and texture parameters can be estimated in a specular invariant colour subspace by solving a system of bilinear equations. We focus on the case of faces, where both shape and texture can be efficiently described by a linear statistical model. In this context, we are able to fit a 3D morphable model to a single colour image, accounting for both non-Lambertian specular reflectance and complex illumination of the same light source colour. We are able to recover statistical texture model parameters with an accuracy comparable to more computationally expensive analysis-by-synthesis approaches. Moreover, our approach requires only the solution of convex optimisation problems.