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This paper presents a new framework for solving geometric structure and motion problems based on {$L_\infty$}-norm. Instead of using the common sum-of-squares cost-function, that is, the {$L_\two$}-norm, the model-fitting errors are measured using the {$L_\infty$}-norm. Unlike traditional methods based on {$L_\two$}, our framework allows for efficient computation of global estimates. We show that a variety of structure and motion problems, for example, triangulation, camera resectioning and homography estimation can be recast as quasi-convex optimization problems within this framework. These problems can be efficiently solved using Second-Order Cone Programming (SOCP) which is a standard technique in convex optimization. The methods have been implemented in Matlab and the resulting toolbox has been made publicly available. The algorithms have been validated on real data in different settings on problems with small and large dimensions and with excellent performance.
Image Processing and Computer Vision, Convex programming, Constrained optimization, Global optimization
Fredrik Kahl, Richard Hartley, "Multiple-View Geometry Under the {$L_\infty$}-Norm", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 30, no. , pp. 1603-1617, September 2008, doi:10.1109/TPAMI.2007.70824
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