Augmented Lagrangian-based Algorithm for Projective Reconstruction from Multiple Views with Minimization of 2D Reprojection Error

Abstract

In this paper, we propose a new factorization-based algorithm for projective reconstruction from multiple views by minimizing the 2D reprojection error in the images. In our algorithm, the projective reconstruction problem is formulated as a constrained minimization problem, which minimizes the 2D reprojection error in multiple images. To solve this constrained minimization problem, we use the augmented Lagrangian approach to generate a sequence of unconstrained minimization problems, which can be readily solved by standard least-squares technique. Thus we can estimate the projective depths, the projection matrices and the positions of 3D points simultaneously by iteratively solving a sequence of unconstrained minimization problems. The proposed algorithm does not require the projective depths as prior knowledge, unlike bundle adjustment techniques. It converges more robustly and rapidly than the penalty based method. Furthermore, it readily handles the case of partial occlusion, where some points cannot be observed in some images.