Trajectory reconstruction for affine structure-from-motion by global and local constraints

The problem of reconstructing a 3D scene from a moving camera can be solved by means of the so-called Factorization method. It directly computes a global solution without the need to merge several partial reconstructions. However, if the trajectories are not complete, i.e. not every feature point could be observed in all the images, this method cannot be used. We use a Factorization-style algorithm for recovering the unobserved feature positions in a non-incremental way. This method uniformly utilizes all data and finds a global solution without any need of sequential or hierarchical merging. Two contributions are made in this work: Firstly, partially known trajectories are completed by minimizing the distance between the subspace and the trajectory within an affine subspace associated with the trajectory. This amounts to imposing a global constraint on the data. Secondly, we propose to further include local constraints derived from epipolar geometry into the estimation. It is shown how to simultaneously optimize both constraints. By using simulated and real image sequences we show the improvements achieved with our algorithm.