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Projective Multiview Structure and Motion from Element-Wise Factorization
Sept. 2013 (vol. 35 no. 9)
pp. 2238-2251
Yuchao Dai, Sch. of Electron. & Inf., Northwestern Polytech. Univ., Xi'an, China
Hongdong Li, NICTA, ANU, Canberra, ACT, Australia
Mingyi He, ShaanXi Key Lab. of Inf. Acquisition & Process., Northwestern Polytech. Univ., Xi'an, China
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.
Index Terms:
iterative methods,convex programming,image motion analysis,continuation-based algorithm,projective multiview structure,Sturm-Triggs type iteration,projective structure-from-motion factorization problem,element-wise factorization,projective depths,scene structure,camera motions,projective SfM problem,convex optimization,Cameras,Minimization,Iterative methods,Matrix decomposition,Educational institutions,Indexes,Image reconstruction,outlier,Element-wise factorization,projective structure and motion,semidefinite programming,missing data
Citation:
Yuchao Dai, Hongdong Li, Mingyi He, "Projective Multiview Structure and Motion from Element-Wise Factorization," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 35, no. 9, pp. 2238-2251, Sept. 2013, doi:10.1109/TPAMI.2013.20
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