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.


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    Titel :

    Globally optimal estimates for geometric reconstruction problems


    Beteiligte:
    Kahl, F. (Autor:in) / Henrion, D. (Autor:in)


    Erscheinungsdatum :

    01.01.2005


    Format / Umfang :

    486501 byte





    Medientyp :

    Aufsatz (Konferenz)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch



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