Robust Factorization

Factorization algorithms for recovering structure and motion from an image stream have many advantages, but they usually require a set of well tracked features. Such a set is in general not available in practical applications. There is thus a need for making factorization algorithms deal effectively with errors in the tracked features. We propose a new and computationally efficient algorithm for applying an arbitrary error function in the factorization scheme. This algorithm enables the use of robust statistical techniques and arbitrary noise models for the individual features. These techniques and models enable the factorization scheme to deal effectively with mismatched features, missing features and noise on the individual features. The proposed approach further includes a new method for Euclidean reconstruction that significantly improves convergence of the factorization algorithms. The proposed algorithm has been implemented as a modification of the Christy–Horaud factorization scheme, which yields a perspective reconstruction. Based on this implementation a considerable increase in error tolerance is demonstrated on real and synthetic data. The proposed scheme can however be applied to most other factorization algorithms. keywords: Robust statistics, feature tracking, perspective reconstruction, Euclidean reconstruction, structure from motion. 1