A Quaternion-Based Certifiably Optimal Solution to the Wahba Problem With Outliers
Name
1905.12536.pdf
Description
Accepted version
Size
3.92 MB
Format
Adobe PDF
Checksum (MD5)
93d76fc7e833c6f340450245c29e35c6
Author(s)
Yang, Heng
Carlone, Luca
Date Issued
October 2019
Journal
Proceedings of the IEEE International Conference on Computer Vision
Publisher
IEEE
Citation
Yang, Heng and Carlone, Luca. 2019. "A Quaternion-Based Certifiably Optimal Solution to the Wahba Problem With Outliers." Proceedings of the IEEE International Conference on Computer Vision, 2019-October.
Version
Author's final manuscript
Abstract
© 2019 IEEE. The Wahba problem, also known as rotation search, seeks to find the best rotation to align two sets of vector observations given putative correspondences, and is a fundamental routine in many computer vision and robotics applications. This work proposes the first polynomial-time certifiably optimal approach for solving the Wahba problem when a large number of vector observations are outliers. Our first contribution is to formulate the Wahba problem using a Truncated Least Squares (TLS) cost that is insensitive to a large fraction of spurious correspondences. The second contribution is to rewrite the problem using unit quaternions and show that the TLS cost can be framed as a Quadratically-Constrained Quadratic Program (QCQP). Since the resulting optimization is still highly non-convex and hard to solve globally, our third contribution is to develop a convex Semidefinite Programming (SDP) relaxation. We show that while a naive relaxation performs poorly in general, our relaxation is tight even in the presence of large noise and outliers. We validate the proposed algorithm, named QUASAR (QUAternion-based Semidefinite relAxation for Robust alignment), in both synthetic and real datasets showing that the algorithm outperforms RANSAC, robust local optimization techniques, global outlier-removal procedures, and Branch-and-Bound methods. QUASAR is able to compute certifiably optimal solutions (i.e. the relaxation is exact) even in the case when 95% of the correspondences are outliers.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
10.1109/iccv.2019.00175
