Convex relaxations of SE(2) and SE(3) for visual pose estimation
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.
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.Attached Files
Submitted - 1401.3700.pdf
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Additional details
- Eprint ID
- 73682
- Resolver ID
- CaltechAUTHORS:20170124-162242370
- NSF Graduate Research Fellowship
- Defense Advanced Research Projects Agency (DARPA)
- Created
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2017-01-26Created from EPrint's datestamp field
- Updated
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2021-11-11Created from EPrint's last_modified field