Element-Wise Factorization for N-View Projective Reconstruction

  • Yuchao Dai
  • Hongdong Li
  • Mingyi He
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6314)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yuchao Dai
    • 1
    • 2
  • Hongdong Li
    • 2
    • 3
  • Mingyi He
    • 1
  1. 1.School of Electronics and InformationNorthwestern Polytechnical University, Shaanxi Key Laboratory of Information Acquisition and ProcessingXi’anChina
  2. 2.Australian National UniversityAustralia
  3. 3.Canberra Research LabNICTAAustralia

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