Accurate Optimization of Weighted Nuclear Norm for Non-Rigid Structure from Motion

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding


Fitting a matrix of a given rank to data in a least squares sense can be done very effectively using 2nd order methods such as Levenberg-Marquardt by explicitly optimizing over a bilinear parameterization of the matrix. In contrast, when applying more general singular value penalties, such as weighted nuclear norm priors, direct optimization over the elements of the matrix is typically used. Due to non-differentiability of the resulting objective function, first order sub-gradient or splitting methods are predominantly used. While these offer rapid iterations it is well known that they become inefficient near the minimum due to zig-zagging and in practice one is therefore often forced to settle for an approximate solution. In this paper we show that more accurate results can in many cases be achieved with 2nd order methods. Our main result shows how to construct bilinear formulations, for a general class of regularizers including weighted nuclear norm penalties, that are provably equivalent to the original problems. With these formulations the regularizing function becomes twice differentiable and 2nd order methods can be applied. We show experimentally, on a number of structure from motion problems, that our approach outperforms state-of-the-art methods.


External organisations
  • Chalmers University of Technology
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Computer Vision and Robotics (Autonomous Systems)
  • Computational Mathematics
Original languageEnglish
Title of host publicationComputer Vision – ECCV 2020 - 16th European Conference, 2020, Proceedings
EditorsAndrea Vedaldi, Horst Bischof, Thomas Brox, Jan-Michael Frahm
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages17
ISBN (Print)9783030585822
Publication statusPublished - 2020
Publication categoryResearch
Event16th European Conference on Computer Vision, ECCV 2020 - Glasgow, United Kingdom
Duration: 2020 Aug 232020 Aug 28

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12372 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference16th European Conference on Computer Vision, ECCV 2020
CountryUnited Kingdom