A Survey on Natural Image Matting With Closed-Form Solutions

Natural image matting refers to the interactive process of estimating the foreground opacity (alpha matte) of an input image and extracting the foreground layer. Various approaches have been proposed utilizing affinity-based strategy, sampling-based strategy or hybrid of both. Affinity-based approaches and hybrid approaches generally derive a quadratic cost function concerning alpha matte smoothness as well as user input and estimate the alpha matte through solving a sparse linear system of equations. These approaches, which have closed-form solutions, are called closed-form matting approaches. This paper provides an extensive overview on the closed-form matting theory. A hierarchical matting model is presented, classifying affinity-based approaches into three categories. The basis of each model and the relationships between them are analyzed. Using manifold learning theory, we unify the closed-form matting approaches into one framework and provide explanations of: 1) how various affinity-based strategies generate the alpha matte; 2) why sampling-based strategies help improve the precision of alpha matte. Evaluation of the representative algorithms on an image matting dataset and a video matting dataset demonstrates the strength and weakness of each matting model. Not only summary of the traditional matting methods is provided but also several suggestions on future directions for matting research are proposed.