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Issue No.08 - August (2004 vol.26)
pp: 1051-1063
ABSTRACT
<p><b>Abstract</b>—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 <it>reliable</it> 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.</p>
INDEX TERMS
Imputation, missing-data problem, rank constraint, singular value decomposition, denoising capacity, structure from motion, affine SFM, linear subspace.
CITATION
Pei Chen, David Suter, "Recovering the Missing Components in a Large Noisy Low-Rank Matrix: Application to SFM", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.26, no. 8, pp. 1051-1063, August 2004, doi:10.1109/TPAMI.2004.52
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