A Simple Method for Subspace Estimation with Corrupted Columns
(2016) 15th 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.
(Less)
- author
- Larsson, Viktor LU ; Olsson, Carl LU and Kahl, Fredrik LU
- organization
- publishing date
- 2016-02-11
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Closed-form solutions, Computer vision, Convergence, Estimation, Optimization, Robustness, Shape
- host publication
- Proceedings - 2015 IEEE International Conference on Computer Vision Workshops, ICCVW 2015
- volume
- 2016-February
- article number
- 7406462
- pages
- 9 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- conference name
- 15th IEEE International Conference on Computer Vision Workshops, ICCVW 2015
- conference location
- Santiago, Chile
- conference dates
- 2015-12-11 - 2015-12-18
- external identifiers
-
- wos:000380434700103
- scopus:84962024830
- ISBN
- 9781467383905
- 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
- 2024-07-12 16:22:47
@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}}, isbn = {{9781467383905}}, keywords = {{Closed-form solutions; Computer vision; Convergence; Estimation; Optimization; Robustness; Shape}}, language = {{eng}}, month = {{02}}, pages = {{841--849}}, publisher = {{IEEE - 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}}, doi = {{10.1109/ICCVW.2015.113}}, volume = {{2016-February}}, year = {{2016}}, }