Abstract: This article addresses the problem of natural shadow matting, the removal or extraction of natural shadows from a single image. Because textures are maintained in the shadowless image after the extraction process, our approach produces some of the best results to date among shadow removal techniques. Using the image formation equation typical of computer vision, we advocate a new model for shadow formation where shadow effect is understood as light attenuation instead of a mixture of two colors governed by the conventional matting equation. This leads to a new shadow equation with fewer unknowns to solve, where a three-channel shadow matte and a shadowless image are considered in our optimization. Our problem is formulated as one of energy minimization guided by user-supplied hints in the form of a quadmap which can be specified easily by the user. This formulation allows for robust shadow matte extraction while maintaining texture in the shadowed region by considering color transfer, texture gradient, and shadow smoothness. We demonstrate the usefulness of our approach in shadow removal, image matting, and compositing.