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We present a novel algorithm for optimally segmenting dynamic scenes containing multiple rigidly moving objects. We cast the motion segmentation problem as a constrained nonlinear least squares problem, which minimizes the reprojection error subject to all multibody epipolar constraints. By converting this constrained problem into an unconstrained one, we obtain an objective function that depends on the motion parameters only (fundamental matrices), but is independent on the segmentation of the image features. Therefore, our algorithm does not iterate between feature segmentation and single body motion estimation. Instead, it uses standard nonlinear optimization techniques to simultaneously recover all the fundamental matrices, without prior segmentation. We test our approach on a real sequence.