Abstract
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 projective to Euclidean structure by computing the projective distortion matrix in a way that is analogous to estimating the absolute quadric. Using the Singular Value Decomposition (SVD) as a main tool, and from the 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.