Element-wise factorization for N-view projective reconstruction

Yuchao Dai*, Hongdong Li, Mingyi He

*Corresponding author for this work

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    16 Citations (Scopus)


    Sturm-Triggs iteration is a standard method for solving the projective factorization problem. Like other iterative algorithms, this method suffers from some common drawbacks such as requiring a good initialization, the iteration may not converge or only converge to a local minimum, etc. None of the published works can offer any sort of global optimality guarantee to the problem. In this paper, an optimal solution to projective factorization for structure and motion is presented, based on the same principle of low-rank factorization. Instead of formulating the problem as matrix factorization, we recast it as element-wise factorization, leading to a convenient and efficient semi-definite program formulation. Our method is thus global, where no initial point is needed, and a globally-optimal solution can be found (up to some relaxation gap). Unlike traditional projective factorization, our method can handle real-world difficult cases like missing data or outliers easily, and all in a unified manner. Extensive experiments on both synthetic and real image data show comparable or superior results compared with existing methods.

    Original languageEnglish
    Title of host publicationComputer Vision, ECCV 2010 - 11th European Conference on Computer Vision, Proceedings
    PublisherSpringer Verlag
    Number of pages14
    EditionPART 4
    ISBN (Print)364215560X, 9783642155604
    Publication statusPublished - 2010
    Event11th European Conference on Computer Vision, ECCV 2010 - Heraklion, Crete, Greece
    Duration: 10 Sept 201011 Sept 2010

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    NumberPART 4
    Volume6314 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349


    Conference11th European Conference on Computer Vision, ECCV 2010
    CityHeraklion, Crete


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