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<p><b>Abstract</b>—The paper describes the <it>rank 1 weighted factorization</it> solution to the <it>structure from motion</it> problem. This method recovers the 3D structure from the factorization of a data matrix that is rank 1 rather than rank 3. This matrix collects the estimates of the 2D motions of a set of feature points of the rigid object. These estimates are weighted by the inverse of the estimates error standard deviation so that the 2D motion estimates for "sharper" features, which are usually well-estimated, are given more weight, while the noisier motion estimates for "smoother" features are weighted less. We analyze the performance of the <it>rank 1 weighted factorization</it> algorithm to determine what are the most suitable 3D shapes or the best 3D motions to recover the 3D structure of a rigid object from the 2D motions of the features. Our approach is developed for the orthographic camera model. It avoids expensive singular value decompositions by using the power method and is suitable to handle dense sets of feature points and long video sequences. Experimental studies with synthetic and real data illustrate the good performance of our approach.</p>
Factorization methods, structure from motion, image sequence analysis, rigid body motion, uncertainty in motion analysis, power method, weighted factorization.

J. M. Moura and P. M. Aguiar, "Rank 1 Weighted Factorization for 3D Structure Recovery: Algorithms and Performance Analysis," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 25, no. , pp. 1134-1049, 2003.
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