A Polynomial-time Solution for Robust Registration with Extreme Outlier Rates
We propose a robust approach for the registration of two sets of 3D points in the presence of a large amount of outliers. Our first contribution is to reformulate the registration problem using a Truncated Least Squares (TLS) cost that makes the estimation insensitive to a large fraction of spuri...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Robotics: Science and Systems Foundation
2021
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| Online Access: | https://hdl.handle.net/1721.1/138101.2 |
| _version_ | 1811088788970012672 |
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| author | Yang, Heng Carlone, Luca |
| author2 | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems |
| author_facet | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Yang, Heng Carlone, Luca |
| author_sort | Yang, Heng |
| collection | MIT |
| description | We propose a robust approach for the registration of two sets of 3D points in
the presence of a large amount of outliers. Our first contribution is to
reformulate the registration problem using a Truncated Least Squares (TLS) cost
that makes the estimation insensitive to a large fraction of spurious
point-to-point correspondences. The second contribution is a general framework
to decouple rotation, translation, and scale estimation, which allows solving
in cascade for the three transformations. Since each subproblem (scale,
rotation, and translation estimation) is still non-convex and combinatorial in
nature, out third contribution is to show that (i) TLS scale and
(component-wise) translation estimation can be solved exactly and in polynomial
time via an adaptive voting scheme, (ii) TLS rotation estimation can be relaxed
to a semidefinite program and the relaxation is tight in practice, even in the
presence of an extreme amount of outliers. We validate the proposed algorithm,
named TEASER (Truncated least squares Estimation And SEmidefinite Relaxation),
in standard registration benchmarks showing that the algorithm outperforms
RANSAC and robust local optimization techniques, and favorably compares with
Branch-and-Bound methods, while being a polynomial-time algorithm. TEASER can
tolerate up to 99% outliers and returns highly-accurate solutions. |
| first_indexed | 2024-09-23T14:07:34Z |
| format | Article |
| id | mit-1721.1/138101.2 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:07:34Z |
| publishDate | 2021 |
| publisher | Robotics: Science and Systems Foundation |
| record_format | dspace |
| spelling | mit-1721.1/138101.22021-11-10T19:14:11Z A Polynomial-time Solution for Robust Registration with Extreme Outlier Rates Yang, Heng Carlone, Luca Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Massachusetts Institute of Technology. Department of Aeronautics and Astronautics We propose a robust approach for the registration of two sets of 3D points in the presence of a large amount of outliers. Our first contribution is to reformulate the registration problem using a Truncated Least Squares (TLS) cost that makes the estimation insensitive to a large fraction of spurious point-to-point correspondences. The second contribution is a general framework to decouple rotation, translation, and scale estimation, which allows solving in cascade for the three transformations. Since each subproblem (scale, rotation, and translation estimation) is still non-convex and combinatorial in nature, out third contribution is to show that (i) TLS scale and (component-wise) translation estimation can be solved exactly and in polynomial time via an adaptive voting scheme, (ii) TLS rotation estimation can be relaxed to a semidefinite program and the relaxation is tight in practice, even in the presence of an extreme amount of outliers. We validate the proposed algorithm, named TEASER (Truncated least squares Estimation And SEmidefinite Relaxation), in standard registration benchmarks showing that the algorithm outperforms RANSAC and robust local optimization techniques, and favorably compares with Branch-and-Bound methods, while being a polynomial-time algorithm. TEASER can tolerate up to 99% outliers and returns highly-accurate solutions. 2021-11-10T19:14:10Z 2021-11-10T13:22:47Z 2021-11-10T19:14:10Z 2019-06 2021-04-09T17:51:54Z Article http://purl.org/eprint/type/ConferencePaper https://hdl.handle.net/1721.1/138101.2 2019. "A Polynomial-time Solution for Robust Registration with Extreme Outlier Rates." Robotics: Science and Systems XV. en http://dx.doi.org/10.15607/RSS.2019.XV.003 Robotics: Science and Systems XV Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/octet-stream Robotics: Science and Systems Foundation arXiv |
| spellingShingle | Yang, Heng Carlone, Luca A Polynomial-time Solution for Robust Registration with Extreme Outlier Rates |
| title | A Polynomial-time Solution for Robust Registration with Extreme Outlier Rates |
| title_full | A Polynomial-time Solution for Robust Registration with Extreme Outlier Rates |
| title_fullStr | A Polynomial-time Solution for Robust Registration with Extreme Outlier Rates |
| title_full_unstemmed | A Polynomial-time Solution for Robust Registration with Extreme Outlier Rates |
| title_short | A Polynomial-time Solution for Robust Registration with Extreme Outlier Rates |
| title_sort | polynomial time solution for robust registration with extreme outlier rates |
| url | https://hdl.handle.net/1721.1/138101.2 |
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