Single Image Highlight Removal with a Sparse and Low-Rank Reflection Model

We propose a sparse and low-rank reflection model for specular highlight detection and removal using a single input image. This model is motivated by the observation that the specular highlight of a natural image usually has large intensity but is rather sparsely distributed while the remaining diffuse reflection can be well approximated by a linear combination of several distinct colors with a sparse and low-rank weighting matrix. We further impose the non-negativity constraint on the weighting matrix as well as the highlight component to ensure that the model is purely additive. With this reflection model, we reformulate the task of highlight removal as a constrained nuclear norm and $l_1$-norm minimization problem which can be solved effectively by the augmented Lagrange multiplier method. Experimental results show that our method performs well on both synthetic images and many real-world examples and is competitive with previous methods, especially in some challenging scenarios featuring natural illumination, hue-saturation ambiguity and strong noises.