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We present an analytic solution to the problem of estimating multiple - D and 3 - D motion models from two - view correspondences or optical flow The key to our approach is to view the estimation of multiple motion models as the estimation of a single  multibody motion model This is possible thanks to two im - portant algebraic facts First, we show that all the image measurements, regardless of their associated motion model, can be  fit  with a real or complex  polynomial Second, we show that the parameters of the motion model associated with an im - age measurement can be obtained from the  derivatives  of the polynomial at the measurement This leads to a novel motion segmentation algorithm that applies to most of the two - view motion models adopted in computer vision Our experi - ments show that the proposed algorithm outperforms existing algebraic methods in terms of efficiency and robustness, and provides a good initialization for itera - tive techniques, such as EM, which is strongly dependent on correct initialization

A Unified Algebraic Approach to 2-D and 3-D Motion Segmentation