Multiple View Geometry and the L_"-norm

  • Authors:

  • Fredrik Kahl

  • Affiliations:

  • University of California at San Diego and Lund University

  • Venue:
  • ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
  • Year:
  • 2005

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Abstract

This paper presents a new framework for solving geometric structure and motion problems based on L_驴 -norm. Instead of using the common sum-of-squares cost-function, that is, theL_驴 -norm, the model-fitting errors are measured using the L_驴 -norm. Unlike traditional methods based on L_驴, 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 a quasi-convex optimization problem within this framework. These problems can be efficiently solved using Second Order Cone Programming (SOCP) which is a standard technique in convex optimization. The proposed solutions have been validated on real data in different settings with small and large dimensions and with excellent performance.