Recovering 3D metric structure and motion from multiple uncalibrated cameras

An optimized linear factorization method for recovering both the 3D geometry of a scene and the camera parameters from multiple uncalibrated images is presented. In a first step, we recover a projective approximation using a well-known iterative approach. Then we are able to upgrade from a projective to a Euclidean structure by computing the projective distortion matrix in a way that is analogous to estimating the absolute quadric. Using singular value decomposition (SVD) as the main tool, and from a study of the ranks of the matrices involved in the process, we are able to enforce an accurate Euclidean reconstruction. Moreover, in contrast to other approaches, our process is essentially a linear one and does not require an initial estimation of the solution. Examples of synthetic and real data reconstructions are presented.