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This work addresses the problems of (i) self-calibration of a moving camera observing a 3D scene composed by planar structures and (ii) scene segmentation and reconstruction. Although there exist some works intending to deal with these problems, most of them are based on the estimation of the epipolar geometry, non-linear optimization, or linear systems that do not incorporate geometrical consistency and may produce undesirable side-effects. In this paper, we propose a novel iterative linear algorithm that exploits the geometrical and algebraic constraints induced by rigidity and planarity in the scene. Instead of solving a complex multi-linear problem, we solve iteratively several linear problems: coplanar features segmentation, planar projective transferring, epipole computation, and all the plane intersections. Linear methods allow our approach to be suitable for real-time localization and 3D reconstruction, e.g. for autonomous mobile robots applications. Furthermore, we avoid the explicit epipolar geometry computation and all the stability problems commonly associated with it.