Quasi-perspective projection with applications to 3D factorization from uncalibrated image sequences

The paper addresses the problem of factorization-based 3D reconstruction from uncalibrated image sequences. We propose a quasi-perspective projection model and apply the model to structure and motion recovery of rigid and nonrigid objects based on factorization of tracking matrix. The novelty and contribution of the paper lies in three aspects. First, under the assumption that the camera is far away from the object with small rotations, we propose and prove that the imaging process can be modeled by quasi-perspective projection. The model is more accurate than affine since the projective depths are implicitly embedded. Second, we apply the model to the factorization algorithm and establish the framework of rigid and nonrigid factorization under quasi-perspective assumption. Third, we propose a new and robust method to recover the transformation matrix that upgrades the factorization to the Euclidean space. The proposed method is validated and evaluated on synthetic and real image sequences and good improvements over existing solutions are observed.