Factorization-based structure-and-motion computation for generalized camera model

Generalized camera model (GCM) has been introduced recently to unify the analysis and description of a variety of non-conventional camera designs (e.g. catadioptric and omnidirectional), as well as multi-camera systems. In this paper, we extend the well-known and powerful Tomasi-Kanade type factorization framework to generalized cameras. We first prove that even for such seemingly more complicated generalized cameras there is also a rank-4 constraint, similar to the case of using a single pinhole projective camera. This result is much simpler and more compact than a recent work suggesting a rank-13 tensor factorization. Secondly, we propose two GCM factorization algorithms to recover the structure and motion. We also provide theoretic convergence analysis for the algorithms. Experiments on synthetic data validate the theory and the proposed algorithms.