Element-Wise Factorization for N-View Projective Reconstruction

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.