Recovering the missing components in a large noisy low-rank matrix: Application to SFM
Recovering the missing components in a large noisy low-rank matrix: Application to SFM
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DOI：
10.1109/tpami.2004.52
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发表时间：
2004-08-01
影响因子：
23.6
通讯作者：
Suter, D
中科院分区：
文献类型：
--
作者：
Chen, P;Suter, D
在计算机视觉中，通常需要对具有“丢失数据”的矩阵进行操作，例如，由于运动结构（SFM）问题中的遮挡或跟踪失败。这样的问题是可以解决的，允许恢复缺失的值，如果矩阵应该是低秩的（当无噪声时）。对缺失值的填充称为补全。插补也可以应用于人脸和形状分类的各种子空间技术，在线“推荐”系统，以及各种各样的其他应用。然而，迭代归算可能导致严重错误数据的“恢复”。在本文中，我们提供了一种方法来恢复最可靠的输入，在确定何时包含额外的行或列，包含大量的缺失条目，可能导致缺失部分的恢复不佳。虽然所提出的方法可以同样适用于广泛的归算方法，但本文只讨论了SFM问题。将该方法的性能与Jacobs和Shum的SFM方法进行了比较。
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.