On the Minimal Problems of Low-Rank Matrix Factorization

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingpeer-review


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.
Original languageEnglish
Title of host publicationComputer Vision and Pattern Recognition (CVPR), 2015 IEEE Conference on
EditorsKristen Grauman, Erik Learned-Miller, Antonio Torralba, Andrew Zisserman
PublisherIEEE - Institute of Electrical and Electronics Engineers Inc.
Number of pages9
ISBN (Print)978-1-4673-6963-3
Publication statusPublished - 2015
EventIEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015 - Boston, United States
Duration: 2015 Jun 72015 Jun 12


ConferenceIEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015
Country/TerritoryUnited States

Subject classification (UKÄ)

  • Mathematics

Free keywords

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


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