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This paper studies the problem of multibody motion segmentation, which is an important, but challenging problem due to its well-known chicken-and-egg-type recursive character. We propose a new mixture-of-fundamental-matrices model to describe the multibody motions from two views. Based on the maximum likelihood estimation, in conjunction with a random sampling scheme, we show that the problem can be naturally formulated as a linear programming (LP) problem. Consequently, the motion segmentation problem can be solved efficiently by linear program relaxation. Experiments demonstrate that: without assuming the actual number of motions our method produces accurate segmentation result. This LP formulation has also other advantages, such as easy to handle outliers and easy to enforce prior knowledge etc.