An Analysis of Linear Subspace Approaches for Computer Vision and Pattern Recognition
International Journal of Computer Vision
On the Wiberg Algorithm for Matrix Factorization in the Presence of Missing Components
International Journal of Computer Vision
Journal of Mathematical Imaging and Vision
Optimization Algorithms on Subspaces: Revisiting Missing Data Problem in Low-Rank Matrix
International Journal of Computer Vision
Motion Segmentation from Feature Trajectories with Missing Data
IbPRIA '07 Proceedings of the 3rd Iberian conference on Pattern Recognition and Image Analysis, Part I
An Iterative Multiresolution Scheme for SFM with Missing Data
Journal of Mathematical Imaging and Vision
An iterative multiresolution scheme for SFM with missing data: Single and multiple object scenes
Image and Vision Computing
Rigid Structure from Motion from a Blind Source Separation Perspective
International Journal of Computer Vision
Low-rank matrix completion with noisy observations: a quantitative comparison
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
The power of convex relaxation: near-optimal matrix completion
IEEE Transactions on Information Theory
Matrix completion from a few entries
IEEE Transactions on Information Theory
A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
Rank Estimation in Missing Data Matrix Problems
Journal of Mathematical Imaging and Vision
A linear solution to 1-dimensional subspace fitting under incomplete data
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part II
Hessian Matrix vs. Gauss-Newton Hessian Matrix
SIAM Journal on Numerical Analysis
An iterative multiresolution scheme for SFM
ICIAR'06 Proceedings of the Third international conference on Image Analysis and Recognition - Volume Part I
Factorization with missing and noisy data
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
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In computer vision, it is common to require operations on matrices with "missing data," for example, because of occlusion or tracking failures in the Structure from Motion (SFM) problem. Such a problem can be tackled, allowing the recovery of the missing values, if the matrix should be of low rank (when noise free). The filling in of missing values is known as imputation. Imputation can also be applied in the various subspace techniques for face and shape classification, online "recommender" systems, and a wide variety of other applications. However, iterative imputation can lead to the "recovery" of data that is seriously in error. In this paper, we provide a method to recover the most reliable imputation, in terms of deciding when the inclusion of extra rows or columns, containing significant numbers of missing entries, is likely to lead to poor recovery of the missing parts. Although the proposed approach can be equally applied to a wide range of imputation methods, this paper addresses only the SFM problem. The performance of the proposed method is compared with Jacobs' and Shum's methods for SFM.