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 projections of a set of feature points across multiple image frames and small perturbations/covariances of the feature point coordinates, first-order perturbation and covariance matrices of 3-D shape and motion are derived and validated with the ground truth. This work provides quantitative analysis of error 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 ellipsoids on top of the 3-D reconstruction as an enhanced visualization, leading to better use of the factorization method in engineering applications. Experimental results are demonstrated to support the analysis and to show how the error analysis and error measures can be used.