L₁ matting

Natural image matting continues to play a large role in a wide variety of applications. As an ill-posed problem, matting is a very difficult to solve due to its underconstrained nature. Current approaches can require a lot of user input, restrict themselves to a sparse subset of the image, and often make assumptions that are unlikely to hold. In this paper, we pose a way to better satisfy smoothness assumptions of some of these methods utilizing the nonlinear median filter which arises naturally from the L₁ norm. The median has the property that it tends to smooth the foreground and background of the image while leaving any edges relatively unaltered. We then show that such an image is often more suitable as input than the original image, even when user interaction is minimal, suggesting that our method is more amenable to automatic matting.