On the Minimal Problems of Low-Rank Matrix Factorization

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.

• Författare: Fangyuan Jiang; Magnus Oskarsson; Karl Åström
• Redaktör: Kristen Grauman; Erik Learned-Miller; Antonio Torralba; Andrew Zisserman
• Avdelning/ar: Matematik LTH; Mathematical Imaging Group; ELLIIT: the Linköping-Lund initiative on IT and mobile communication; eSSENCE: The e-Science Collaboration
• Publiceringsår: 2015
• Språk: Engelska
• Sidor: 2549-2557
• Publikation/Tidskrift/Serie: Computer Vision and Pattern Recognition (CVPR), 2015 IEEE Conference on
• Länkar: http://www.cv-foundation.org/openaccess/content_cvpr_2015/html/Jiang_On_the_Minimal_2015_CVPR_paper.html; http://dx.doi.org/10.1109/CVPR.2015.7298870
• Dokumenttyp: Konferensbidrag
• Förlag: IEEE - Institute of Electrical and Electronics Engineers Inc.
• Ämne: Mathematics
• Nyckelord: 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
• Forskningsgrupp: Mathematical Imaging Group
• ISBN/ISSN/Övrigt: ISBN: 978-1-4673-6963-3