Intrinsic Image Decomposition Using a Sparse Representation of Reflectance

Intrinsic image decomposition is an important problem that targets the recovery of shading and reflectance components from a single image. While this is an ill-posed problem on its own, we propose a novel approach for intrinsic image decomposition using reflectance sparsity priors that we have developed. Our sparse representation of reflectance is based on a simple observation: Neighboring pixels with similar chromaticities usually have the same reflectance. We formalize and apply this sparsity constraint on local reflectance to construct a data-driven second-generation wavelet representation. We show that the reflectance component of natural images is sparse in this representation. We further propose and formulate a global sparse constraint on reflectance colors using the assumption that each natural image uses a small set of material colors. Using this sparse reflectance representation and the global constraint on a sparse set of reflectance colors, we formulate a constrained $(l_1)$-norm minimization problem for intrinsic image decomposition that can be solved efficiently. Our algorithm can successfully extract intrinsic images from a single image without using color models or any user interaction. Experimental results on a variety of images demonstrate the effectiveness of the proposed technique.