Fast Bilinear SfM with Side Information

We study the beneficial effect of side information on the Structure from Motion (SfM) estimation problem. The side information that we consider is measurement of a 'reference vector' and distance from fixed plane perpendicular to that reference vector. Firstly, we show that in the presence of this information, the SfM equations can be rewritten similar to a bilinear form in its unknowns. Secondly, we describe a fast iterative estimation procedure to recover the structure of both stationary scenes and moving objects that capitalizes on this information. We also provide a refinement procedure in order to tackle incomplete or noisy side information. We characterize the algorithm with respect to its reconstruction accuracy, memory requirements and stability. Finally, we describe two classes of commonly occurring real-world scenarios in which this algorithm will be effective: (a) presence of a dominant ground plane in the scene and (b) presence of an inertial measurement unit on board. Experiments using both real data and rigorous simulations show the efficacy of the algorithm.