We present a fast and robust system for estimating structure and motion using a stereo pair, with straight lines as features. Our first set of contributions are efficient algorithms to perform this estimation using a few (two or three) lines, which are well-suited for use in a hypothesize-and-test framework. Our second contribution is the design of an efficient structure from motion system that performs robustly in complex indoor environments. By using infinite lines rather than line segments, our approach avoids the issues arising due to uncertain determination of end-points. Our cost function stems from a rank condition on planes backprojected from corresponding image lines. We propose a framework that imposes orthonormality constraints on the rigid body motion and can perform estimation using only two or three lines, through efficient solution of an overdetermined system of polynomials. This is in contrast to simple approaches which first reconstruct 3D lines and then align them, but perform poorly in real-world scenes with narrow baseline stereo. Experiments using synthetic as well as real data illustrate the comparative advantage of our algorithms as well as demonstrate the speed, accuracy and reliability of our system.
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