Fast and accurate algorithms for projective multi-image structure from motion

We describe algorithms for computing projective structure and motion from a multi-image sequence of tracked points. The algorithms are essentially linear, work for any motion of moderate size, and give accuracies similar to those of a maximum-likelihood estimate. They give better results than the factorization approach of Sturm and Triggs (1996) and are equally fast and they are much faster than bundle adjustment. Our experiments show that the (iterated) Sturm-Triggs approach often fails for linear camera motions. In addition, we study experimentally the common situation where the calibration is fixed and approximately known, comparing the projective versions of our algorithms to mixed projective/Euclidean strategies. We clarify the nature of dominant-plane compensation, showing that it can be considered a small-translation approximation rather than an approximation that the scene is planar. We show that projective algorithms accurately recover the (projected) inverse depths and homographies despite the possibility of transforming the structure and motion by a projective transformation.