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A Simple Method for Subspace Estimation with Corrupted Columns

Larsson, Viktor LU ; Olsson, Carl LU and Kahl, Fredrik LU (2016) 15th IEEE International Conference on Computer Vision Workshops, ICCVW 2015 In Proceedings - 2015 IEEE International Conference on Computer Vision Workshops, ICCVW 2015 2016-February. p.841-849
Abstract

This paper presents a simple and effective way of solving the robust subspace estimation problem where the corruptions are column-wise. The method we present can handle a large class of robust loss functions and is simple to implement. It is based on Iteratively Reweighted Least Squares (IRLS) and works in an iterative manner by solving a weighted least-squares rank-constrained problem in every iteration. By considering the special case of column-wise loss functions, we show that each such surrogate problem admits a closed form solution. Unlike many other approaches to subspace estimation, we make no relaxation of the low-rank constraint and our method is guaranteed to produce a subspace estimate with the correct dimension. Subspace... (More)

This paper presents a simple and effective way of solving the robust subspace estimation problem where the corruptions are column-wise. The method we present can handle a large class of robust loss functions and is simple to implement. It is based on Iteratively Reweighted Least Squares (IRLS) and works in an iterative manner by solving a weighted least-squares rank-constrained problem in every iteration. By considering the special case of column-wise loss functions, we show that each such surrogate problem admits a closed form solution. Unlike many other approaches to subspace estimation, we make no relaxation of the low-rank constraint and our method is guaranteed to produce a subspace estimate with the correct dimension. Subspace estimation is a core problem for several applications in computer vision. We empirically demonstrate the performance of our method and compare it to several other techniques for subspace estimation. Experimental results are given for both synthetic and real image data including the following applications: linear shape basis estimation, plane fitting and non-rigid structure from motion.

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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Closed-form solutions, Computer vision, Convergence, Estimation, Optimization, Robustness, Shape
in
Proceedings - 2015 IEEE International Conference on Computer Vision Workshops, ICCVW 2015
volume
2016-February
pages
9 pages
publisher
Institute of Electrical and Electronics Engineers Inc.
conference name
15th IEEE International Conference on Computer Vision Workshops, ICCVW 2015
external identifiers
  • Scopus:84962024830
DOI
10.1109/ICCVW.2015.113
language
English
LU publication?
yes
id
01276c1c-638f-47a7-b1ed-1026924bcb9f
date added to LUP
2016-09-20 07:55:03
date last changed
2017-02-02 10:25:55
@inproceedings{01276c1c-638f-47a7-b1ed-1026924bcb9f,
  abstract     = {<p>This paper presents a simple and effective way of solving the robust subspace estimation problem where the corruptions are column-wise. The method we present can handle a large class of robust loss functions and is simple to implement. It is based on Iteratively Reweighted Least Squares (IRLS) and works in an iterative manner by solving a weighted least-squares rank-constrained problem in every iteration. By considering the special case of column-wise loss functions, we show that each such surrogate problem admits a closed form solution. Unlike many other approaches to subspace estimation, we make no relaxation of the low-rank constraint and our method is guaranteed to produce a subspace estimate with the correct dimension. Subspace estimation is a core problem for several applications in computer vision. We empirically demonstrate the performance of our method and compare it to several other techniques for subspace estimation. Experimental results are given for both synthetic and real image data including the following applications: linear shape basis estimation, plane fitting and non-rigid structure from motion.</p>},
  author       = {Larsson, Viktor and Olsson, Carl and Kahl, Fredrik},
  booktitle    = {Proceedings - 2015 IEEE International Conference on Computer Vision Workshops, ICCVW 2015},
  keyword      = {Closed-form solutions,Computer vision,Convergence,Estimation,Optimization,Robustness,Shape},
  language     = {eng},
  month        = {02},
  pages        = {841--849},
  publisher    = {Institute of Electrical and Electronics Engineers Inc.},
  title        = {A Simple Method for Subspace Estimation with Corrupted Columns},
  url          = {http://dx.doi.org/10.1109/ICCVW.2015.113},
  volume       = {2016-February},
  year         = {2016},
}