The browser you are using is not supported by this website. All versions of Internet Explorer are no longer supported, either by us or Microsoft (read more here: https://www.microsoft.com/en-us/microsoft-365/windows/end-of-ie-support).

Please use a modern browser to fully experience our website, such as the newest versions of Edge, Chrome, Firefox or Safari etc.

On the Minimal Problems of Low-Rank Matrix Factorization

På svenska

Author

Editor

  • Kristen Grauman
  • Erik Learned-Miller
  • Antonio Torralba
  • Andrew Zisserman

Summary, in English

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.

Publishing year

2015

Language

English

Pages

2549-2557

Publication/Series

Computer Vision and Pattern Recognition (CVPR), 2015 IEEE Conference on

Document type

Conference paper

Publisher

IEEE - Institute of Electrical and Electronics Engineers Inc.

Topic

  • Mathematics

Keywords

  • Computer vision
  • low rank matrix factorization
  • minimal problems
  • robust methods

Conference name

IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015

Conference date

2015-06-07 - 2015-06-12

Conference place

Boston, United States

Status

Published

Research group

  • Mathematical Imaging Group

ISBN/ISSN/Other

  • ISBN: 978-1-4673-6963-3