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On the Minimal Problems of Low-Rank Matrix Factorization

Jiang, Fangyuan LU ; Oskarsson, Magnus LU and Åström, Karl LU (2015) IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015 In Computer Vision and Pattern Recognition (CVPR), 2015 IEEE Conference on p.2549-2557
Abstract
Low-rank matrix factorization is an essential problem in many areas including computer vision, with applications in e.g. affine structure-from-motion, photometric stereo, and non-rigid structure from motion. However, very little attention has been drawn to minimal cases for this problem or to using the minimal configuration of observations to find the solution. Minimal problems are useful when either outliers are present or the observation matrix is sparse. In this paper, we first give some theoretical insights on how to generate all the minimal problems of a given size using Laman graph theory. We then propose a new parametrization and a building-block scheme to solve these minimal problems by extending the solution from a small sized... (More)
Low-rank matrix factorization is an essential problem in many areas including computer vision, with applications in e.g. affine structure-from-motion, photometric stereo, and non-rigid structure from motion. However, very little attention has been drawn to minimal cases for this problem or to using the minimal configuration of observations to find the solution. Minimal problems are useful when either outliers are present or the observation matrix is sparse. In this paper, we first give some theoretical insights on how to generate all the minimal problems of a given size using Laman graph theory. We then propose a new parametrization and a building-block scheme to solve these minimal problems by extending the solution from a small sized minimal problem. We test our solvers on synthetic data as well as real data with outliers or a large portion of missing data and show that our method can handle the cases when other iterative methods, based on convex relaxation, fail. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Computer vision, low rank matrix factorization, minimal problems, robust methods
in
Computer Vision and Pattern Recognition (CVPR), 2015 IEEE Conference on
editor
Grauman, Kristen; Learned-Miller, Erik; Torralba, Antonio and Zisserman, Andrew
pages
9 pages
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
conference name
IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015
external identifiers
  • Scopus:84959226982
ISBN
978-1-4673-6963-3
DOI
10.1109/CVPR.2015.7298870
language
English
LU publication?
yes
id
a190a386-ae3d-4078-be7b-86c26f57472e (old id 8052439)
alternative location
http://www.cv-foundation.org/openaccess/content_cvpr_2015/html/Jiang_On_the_Minimal_2015_CVPR_paper.html
date added to LUP
2016-01-15 20:07:46
date last changed
2016-10-13 04:42:19
@misc{a190a386-ae3d-4078-be7b-86c26f57472e,
  abstract     = {Low-rank matrix factorization is an essential problem in many areas including computer vision, with applications in e.g. affine structure-from-motion, photometric stereo, and non-rigid structure from motion. However, very little attention has been drawn to minimal cases for this problem or to using the minimal configuration of observations to find the solution. Minimal problems are useful when either outliers are present or the observation matrix is sparse. In this paper, we first give some theoretical insights on how to generate all the minimal problems of a given size using Laman graph theory. We then propose a new parametrization and a building-block scheme to solve these minimal problems by extending the solution from a small sized minimal problem. We test our solvers on synthetic data as well as real data with outliers or a large portion of missing data and show that our method can handle the cases when other iterative methods, based on convex relaxation, fail.},
  author       = {Jiang, Fangyuan and Oskarsson, Magnus and Åström, Karl},
  editor       = {Grauman, Kristen and Learned-Miller, Erik and Torralba, Antonio and Zisserman, Andrew},
  isbn         = {978-1-4673-6963-3},
  keyword      = {Computer vision,low rank matrix factorization,minimal problems,robust methods},
  language     = {eng},
  pages        = {2549--2557},
  publisher    = {ARRAY(0x92fb938)},
  series       = {Computer Vision and Pattern Recognition (CVPR), 2015 IEEE Conference on},
  title        = {On the Minimal Problems of Low-Rank Matrix Factorization},
  url          = {http://dx.doi.org/10.1109/CVPR.2015.7298870},
  year         = {2015},
}