Recovering the missing components in a large noisy low-rank matrix: application to SFM
- 21 June 2004
- journal article
- research article
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 26 (8) , 1051-1063
- https://doi.org/10.1109/tpami.2004.52
Abstract
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.Keywords
This publication has 20 references indexed in Scilit:
- Rank 1 weighted factorization for 3D structure recovery: Algorithms and performance analysisPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2003
- Fast online SVD revisions for lightweight recommender systemsPublished by Society for Industrial & Applied Mathematics (SIAM) ,2003
- A Framework for Robust Subspace LearningInternational Journal of Computer Vision, 2003
- Estimation of Rank Deficient Matrices from Partial Observations: Two-Step Iterative AlgorithmsPublished by Springer Nature ,2003
- Missing value estimation methods for DNA microarraysBioinformatics, 2001
- Dealing with Noise in Multiframe Structure from MotionComputer Vision and Image Understanding, 1999
- Automatic 3D Model Construction for Turn-Table SequencesPublished by Springer Nature ,1998
- A paraperspective factorization method for shape and motion recoveryPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1997
- Principal component analysis with missing data and its application to polyhedral object modelingPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1995
- Shape and motion from image streams under orthography: a factorization methodInternational Journal of Computer Vision, 1992