Projective multiview structure and motion from element-wise factorization

The Sturm-Triggs type iteration is a classic approach for solving the projective structure-from-motion (SfM) factorization problem, which iteratively solves the projective depths, scene structure, and camera motions in an alternated fashion. Like many other iterative algorithms, the Sturm-Triggs iteration suffers from common drawbacks, such as requiring a good initialization, the iteration may not converge or may only converge to a local minimum, and so on. In this paper, we formulate the projective SfM problem as a novel and original element-wise factorization (i.e., Hadamard factorization) problem, as opposed to the conventional matrix factorization. Thanks to this formulation, we are able to solve the projective depths, structure, and camera motions simultaneously by convex optimization. To address the scalability issue, we adopt a continuation-based algorithm. Our method is a global method, in the sense that it is guaranteed to obtain a globally optimal solution up to relaxation gap. Another advantage is that our method can handle challenging real-world situations such as missing data and outliers quite easily, and all in a natural and unified manner. Extensive experiments on both synthetic and real images show comparable results compared with the state-of-the-art methods.