A fast algorithm for rigid structure from image sequences

The factorization method is a feature-based approach to recover 3D rigid structure from motion. In 1998, we extended their framework to recover a parametric description of the 3D shape. The 3D shape and 3D motion are computed by using an SVD to approximate a matrix that is rank 3 in a noiseless situation. In this paper, we develop a new algorithm that has two relevant advantages over the previous algorithms. First, instead of imposing a common origin for the parametric representation of the 3D surface patches, we allow the the specification of different origins for different patches. This improves the numerical stability of the image motion estimation algorithm and the accuracy of the 3D structure recovery algorithm. Second, we show how to compute the 3D shape and 3D motion by a simple factorization of a modified matrix that is rank 1 in a noiseless situation, instead of a rank 3 matrix. This allows the use of very fast algorithms even when using a large number of features (or regions) number of frames.