Projective Reconstruction from Incomplete Trajectories by Global and Local Constraints

The paper deals with projective shape and motion reconstruction by subspace iterations. A prerequisite of factorization-style algorithms is that all feature points need be observed in all images, a condition which is hardly realistic in real videos. We therefore address the problem of estimating structure and motion considering missing features. The proposed algorithm does not require initialization and uniformly handles all available data. The computed solution is global in the sense that it does not merge partial solutions incrementally or hierarchically. The global cost due to the factorization is further amended by local constraints to regularize and stabilize the estimations. It is shown how both costs can be jointly minimized in the presence of unobserved points. By synthetic and real image sequences with up to $60\%$ missing data we demonstrate that our algorithm is accurate and reliable.