Interpolation and regression of rotation matrices

Nicolas Boumal

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Scopus citations

Abstract

The problem of fitting smooth curves to data on the group of rotations is considered. This problem arises when resampling or denoising data points that consist in rotation matrices measured at different times. The rotation matrices typically correspond to the orientation of some physical object, such as a camera or a flying or submarine device. We propose to compute sequences of rotations (discretized curves) that strike a tunable balance between data fidelity and smoothness, where smoothness is assessed by means of a proposed notion of velocity and acceleration along discrete curves on the group of rotations. The best such curve is obtained via optimization on a manifold. Leveraging the simplicity of the cost, we present an efficient algorithm based on second-order Riemannian trust-region methods, implemented using the Manopt toolbox.

Original languageEnglish (US)
Title of host publicationGeometric Science of Information - First International Conference, GSI 2013, Proceedings
Pages345-352
Number of pages8
DOIs
StatePublished - Oct 8 2013
Externally publishedYes
Event1st International SEE Conference on Geometric Science of Information, GSI 2013 - Paris, France
Duration: Aug 28 2013Aug 30 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8085 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other1st International SEE Conference on Geometric Science of Information, GSI 2013
CountryFrance
CityParis
Period8/28/138/30/13

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Keywords

  • 3D motion planning
  • denoising of rotations
  • non-parametric regression
  • optimization on manifolds
  • video stabilization

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