Abstract: The recently proposed matting Laplacian (Levin et al., IEEE Trans. Pattern Anal. Mach. Intell. 30(2):228-242, 2008) has been proven to be a state-of-the-art method for solving the image matting problem. Using this method, matting is formulated as solving a high-order linear system which is hard-constrained by the input trimap. The main drawback of this method, however, is the high computational cost. As the size of the input image increases, the matting Laplacian becomes expensive to solve in terms of both memory and computational time. In this paper we propose a GPU-based matting Laplacian solution which is dramatically faster than a conventional CPU solution, and at the same time largely reduces the memory consumption, making this method practical for the first time for high resolution image matting. To achieve this end, we employ a novel hierarchical windowing scheme to approximate the global optimal solution by solving a serial of local regions at multiple scales. We further employ a GPU-based local solver which can efficiently evaluate local solutions under various boundary conditions. Experimental results show that our system in general is more than two orders of magnitude faster than traditional CPU-based solvers, with about 80% less memory footprint.