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Title: Multiple View Geometry Under the L-infinity Norm
Authors: Kahl, Fredrik and Hartley, Richard
Year: 2008
Publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume: 30
Issue: 9
Pages: 1603--1617
Document Type:Journal Paper
Status: Published
Refereed: Yes
Keywords: geometry
BibTeX item:BibTeX
Extra: L-infinity Toolbox for Matlab
Abstract: 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 L2-norm, the model-fitting errors are measured using the $L_{infty}$-norm. Unlike traditional methods based on L2, 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.




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