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This paper proposes a new Bayesian framework for solving the matting problem, i.e. extracting a foreground element from a background image by estimating an opacity for each pixel of the foreground element. Our approach models both the foreground and background color distributions with spatially-varying sets of Gaussians, and assumes a fractional blending of the foreground and background colors to produce the final output. It then uses a maximum-likelihood criterion to estimate the optimal opacity, foreground and background simultaneously. In addition to providing a principled approach to the matting problem, our algorithm effectively handles objects with intricate boundaries, such as hair strands and fur, and provides an improvement over existing techniques for these difficult cases.