On the Minimal Problems of Low-Rank Matrix Factorization
(2015) IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015 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:
https://lup.lub.lu.se/record/8052439
- author
- Jiang, Fangyuan LU ; Oskarsson, Magnus LU and Åström, Karl LU
- organization
- publishing date
- 2015
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Computer vision, low rank matrix factorization, minimal problems, robust methods
- host publication
- 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
- conference location
- Boston, United States
- conference dates
- 2015-06-07 - 2015-06-12
- 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
- 2016-04-04 10:49:47
- date last changed
- 2022-05-01 20:34:03
@inproceedings{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}}, booktitle = {{Computer Vision and Pattern Recognition (CVPR), 2015 IEEE Conference on}}, editor = {{Grauman, Kristen and Learned-Miller, Erik and Torralba, Antonio and Zisserman, Andrew}}, isbn = {{978-1-4673-6963-3}}, keywords = {{Computer vision; low rank matrix factorization; minimal problems; robust methods}}, language = {{eng}}, pages = {{2549--2557}}, publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}}, title = {{On the Minimal Problems of Low-Rank Matrix Factorization}}, url = {{http://dx.doi.org/10.1109/CVPR.2015.7298870}}, doi = {{10.1109/CVPR.2015.7298870}}, year = {{2015}}, }