Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Principal Component Analysis with Missing Data and Its Application to Polyhedral Object Modeling
IEEE Transactions on Pattern Analysis and Machine Intelligence
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
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
Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
SIAM Journal on Computing
On the Wiberg Algorithm for Matrix Factorization in the Presence of Missing Components
International Journal of Computer Vision
Non-rigid structure from motion using ranklet-based tracking and non-linear optimization
Image and Vision Computing
Multiple Camera Calibration Using Robust Perspective Factorization
3DPVT '06 Proceedings of the Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06)
Multiframe Motion Segmentation with Missing Data Using PowerFactorization and GPCA
International Journal of Computer Vision
Optimization Algorithms on Subspaces: Revisiting Missing Data Problem in Low-Rank Matrix
International Journal of Computer Vision
Estimating 3D shape from degenerate sequences with missing data
Computer Vision and Image Understanding
An Iterative Multiresolution Scheme for SFM with Missing Data
Journal of Mathematical Imaging and Vision
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The problem of low-rank matrix factorization with missing data has attracted many significant attention in the fields related to computer vision. The previous model mainly minimizes the total errors of the recovered low-rank matrix on observed entries. It may produce an optimal solution with less physical meaning. This paper gives a theoretical analysis of the sensitivities of the original model and proposes a modified constrained model and iterative methods for solving the constrained problem. We show that solutions of original model can be arbitrarily far from each others. Two kinds of sufficient conditions of this catastrophic phenomenon are given. In general case, we also give a low bound of error between an @e-optimal solution that is practically obtained in computation and a theoretically optimal solution. A constrained model on missing entries is considered for this missing data problem. We propose a two-step projection method for solving the constrained problem. We also modify the method by a successive alternate technique. The proposed algorithm, named as SALS, is easy to implement, as well as converges very fast even for a large matrix. Numerical experiments on simulation data and real examples are given to illuminate the algorithm behaviors of SALS.