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Convex relaxations of SE(2) and SE(3) for visual pose estimation

Horowitz, Matanya B. and Matni, Nikolai and Burdick, Joel W. (2014) Convex relaxations of SE(2) and SE(3) for visual pose estimation. In: 2014 IEEE International Conference on Robotics and Automation (ICRA). IEEE , Piscataway, NJ, pp. 1148-1154. ISBN 978-1-4799-3685-4 . https://resolver.caltech.edu/CaltechAUTHORS:20170124-162242370

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Abstract

This paper proposes a new method for rigid body pose estimation based on spectrahedral representations of the tautological orbitopes of SE(2) and SE(3). The approach can use dense point cloud data from stereo vision or an RGB-D sensor (such as the Microsoft Kinect), as well as visual appearance data as input. The method is a convex relaxation of the classical pose estimation problem, and is based on explicit linear matrix inequality (LMI) representations for the convex hulls of SE(2) and SE(3). Given these representations, the relaxed pose estimation problem can be framed as a robust least squares problem with the optimization variable constrained to these convex sets. Although this formulation is a relaxation of the original problem, numerical experiments indicates that it is indeed exact - i.e. its solution is a member of SE(2) or SE(3) - in many interesting settings. We additionally show that this method is guaranteed to be exact for a large class of pose estimation problems.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ICRA.2014.6906998DOIArticle
http://ieeexplore.ieee.org/document/6906998/PublisherArticle
https://arxiv.org/abs/1401.3700arXivDiscussion Paper
ORCID:
AuthorORCID
Matni, Nikolai0000-0003-4936-3921
Additional Information:© 2014 IEEE. The authors would like to thank Venkat Chandresakaran for discussion on the topics present in this paper. The first author is grateful for the support of a National Science Foundation graduate fellowship. This work was partially supported by DARPA under the ARM-S and DRC programs.
Funders:
Funding AgencyGrant Number
NSF Graduate Research FellowshipUNSPECIFIED
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Record Number:CaltechAUTHORS:20170124-162242370
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170124-162242370
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73682
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:26 Jan 2017 00:30
Last Modified:03 Oct 2019 16:30

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