Abstract

We study the multi-frame structure from motion problem when the camera translates on a plane with small baselines and arbitrary rotations. This case shows up in many practical applications, for exam- ple, in ground robot navigation. We consider the framework for small baselines presented in [8], in which a factorization method is used to compute the structure and motion parameters accurately, efficiently and with guaranteed convergence. When the camera translates on a plane, the algorithm in [8] cannot be applied because the estimation matrix drops rank, causing the equations to be no longer linear. In this paper, we show how to linearly solve those equations, while preserving the accu- racy, speed and convergence properties of the non-planar algorithm. We evaluate the proposed algorithms on synthetic and real image sequences, and compare our results with those of the optimal algorithm. The pro- posed algorithms are very fast and accurate, have less than 0.3% outliers and work well for small–to–medium baselines and non-planar as well as planar motions.