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Image matting is of great importance in both computer vision and graphics applications. Most existing state-of-the-art techniques rely on large sparse matrices such as the matting Laplacian. However, solving these linear systems is often time-consuming, which is unfavored for the user interaction. In this paper, we propose a fast method for high quality matting. We first derive an efficient algorithm to solve a large kernel matting Laplacian. A large kernel propagates information more quickly and may improve the matte quality. To further reduce running time, we also use adaptive kernel sizes by a KD-tree trimap segmentation technique. A variety of experiments show that our algorithm provides high quality results and is 5 to 20 times faster than previous methods.