Error characterization of the factorization method

This paper studies error characterization of the factorization method for 3 -D shape and motion recovery from image sequences using matrix perturbation theory and covariance propagation for linear models. Given the 2-D project ions of a set of feature points across multiple image frames and small pert urbations/covariances of the feature point coordinates, first-order perturb ation and covariance matrices of 3-D shape and motion are derived and valid ated with the ground truth. This work provides quantitative analysis of err or sensitivity of 3-D shape and motion estimation subject to small feature correspondence errors. It can be used to pinpoint system performance, such as which point/frame/coordinate has relatively higher uncertainty, and gain insight for further improvement. We show the 3-D shape uncertainty as elli psoids on top of the 3-D reconstruction as an enhanced visualization, leadi ng to better use of the factorization method in engineering applications. E xperimental results are demonstrated to support the analysis and to show ho w the error analysis and error measures can be used. (C) 2001 Academic Pres s.