Structure from Motion by Fast Alternation1)

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.