Improving the numerical stability of structure from motion by algebraic elimination

Structure from motion (SFM) is the problem of reconstructing the geometry of a scene from a stream of images on which features have been tracked. In this paper, we consider a projective camera model and assume that the internal parameters of the camera are known. Our goal is to reconstruct the geometry of the scene up to a rigid motion (i.e. Euclidean reconstruction.) It has been shown that estimating the pose of the camera from the images is an ill-conditioned problem, as variations in the camera orientation and camera position cannot be distinguished. Unfortunately, the camera pose parameters are an intrinsic part of current formulations of SFM. This leads to numerical instability in the reconstruction of the scene. Using algebraic methods, we obtain a basis for a new formulation of SFM which does not involve pose estimation and thus eliminates this cause of instability.