Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
A Factorization Based Algorithm for Multi-Image Projective Structure and Motion
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume II - Volume II
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
Structure from Many Perspective Images with Occlusions
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Factorization Methods for Projective Structure and Motion
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
3D Reconstruction by Fitting Low-Rank Matrices with Missing Data
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Damped Newton Algorithms for Matrix Factorization with Missing Data
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Iterative Extensions of the Sturm/Triggs Algorithm: Convergence and Nonconvergence
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Convex Approach to Low Rank Matrix Approximation with Missing Data
SCIA '09 Proceedings of the 16th Scandinavian Conference on Image Analysis
A subspace method for projective reconstruction from multiple images with missing data
Image and Vision Computing
Fixed point and Bregman iterative methods for matrix rank minimization
Mathematical Programming: Series A and B
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part IV
A Simple Prior-Free Method for Non-rigid Structure-from-Motion Factorization
International Journal of Computer Vision
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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.