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Globally optimal estimates for geometric reconstruction problems

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2 Author(s)
F. Kahl ; Comput. Sci. & Eng., California Univ., San Diego, CA, USA ; D. Henrion

We introduce a framework for computing statistically optimal estimates of geometric reconstruction problems. While traditional algorithms often suffer from either local minima or nonoptimality - or a combination of both - we pursue the goal of achieving global solutions of the statistically optimal cost-function. Our approach is based on a hierarchy of convex relaxations to solve nonconvex optimization problems with polynomials. These convex relaxations generate a monotone sequence of lower bounds and we show how one can detect whether the global optimum is attained at a given relaxation. The technique is applied to a number of classical vision problems: triangulation, camera pose, homography estimation and last, but not least, epipolar geometry estimation. Experimental validation on both synthetic and real data is provided. In practice, only a few relaxations are needed for attaining the global optimum

Published in:

Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1  (Volume:2 )

Date of Conference:

17-21 Oct. 2005