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

Abstract

We present an analytic solution to the problem of estimating multiple 2-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 important 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 image 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 experiments show that the proposed algorithm outperforms existing algebraic methods in terms of efficiency and robustness, and provides a good initialization for iterative techniques, such as EM, which is strongly dependent on correct initialization.