A Bottom up Algebraic Approach to Motion Segmentation

We present a bottom up algebraic approach for segmenting multiple 2D motion models directly from the partial derivatives of an image sequence. Our method fits a polynomial called the multibody brightness constancy constraint (MBCC) to a window around each pixel of the scene and obtains local motion models from the derivatives of the MBCC. These local models are then clustered to obtain the parameters of the motion models for the entire scene. Motion segmentation is obtained by assigning to each pixel the dominant motion model in a window around it. Our approach requires no initialization, can handle multiple motions in a window (thus dealing with the aperture problem) and automatically incorporates spatial regularization. Therefore, it naturally combines the advantages of both local and global approaches to motion segmentation. Experiments on real data compare our method with previous local and global approaches.