Fast and Precise Weak-Perspective Factorization

We address the problem of moving object reconstruction. Several methods have been published in the past 20 years including stereo reconstruction as well as multi-view factorization methods. In general, reconstruction algorithms estimate the 3D structure of the object and the camera parameters in a non-optimal way and then a nonlinear optimization method refines the estimated camera parameters and 3D object coordinates. In this paper, an adjustment method is proposed which is the fast version of the well-known down-hill alternation method. The novelty which yields the high speed of the algorithm is that the steps of the alternation give optimal solution to the subproblems by closed-form formulas. The proposed algorithm is discussed here and it is compared to the widely used bundle adjustment method.