A quadratic optimisation approach for shading and specularity recovery from a single image

In this paper we present a method to recover the shading and specularities in the scene from a single image. The method presented here is based on the dichromatic model and enforces a local smoothness assumption over the object surfaces in the scene. This naturally leads to a setting where the estimate of the shading at a particular pixel can be expressed in terms of its neighbours up to a pair of Gaussian kernels accounting for the irradiance similarity between pixels and their spatial proximity on the image plane. This yields a quadratic cost function for both, the specular coefficient and the shading factor of the dicromatic model which can be solved using gradient descent. We show results for both, specular highlight recovery and shading estimation and compare them against a number of alternatives.