Outlier-Robust Estimation: Hardness, Minimally Tuned Algorithms, and Applications
Nonlinear estimation in robotics and vision is typically plagued with outliers due to wrong data association or incorrect detections from signal processing and machine learning methods. This article introduces two unifying formulations for outlier-robust estimation, generalized maximum consensus (&l...
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| Veröffentlicht in: | IEEE transactions on robotics Jg. 38; H. 1; S. 281 - 301 |
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| Hauptverfasser: | , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
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IEEE
01.02.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1552-3098, 1941-0468 |
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| Abstract | Nonlinear estimation in robotics and vision is typically plagued with outliers due to wrong data association or incorrect detections from signal processing and machine learning methods. This article introduces two unifying formulations for outlier-robust estimation, generalized maximum consensus (<inline-formula><tex-math notation="LaTeX">\text{G}</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">\text{MC}</tex-math></inline-formula>) and generalized truncated least squares (<inline-formula><tex-math notation="LaTeX">\text{G-TLS}</tex-math></inline-formula>), and investigates fundamental limits, practical algorithms, and applications. Our first contribution is a proof that outlier-robust estimation is inapproximable: In the worst case, it is impossible to (even approximately) find the set of outliers, even with slower-than-polynomial-time algorithms (particularly, algorithms running in quasi-polynomial time). As a second contribution, we review and extend two general-purpose algorithms. The first, adaptive trimming (<inline-formula><tex-math notation="LaTeX">\text{ADAPT}</tex-math></inline-formula>), is combinatorial and is suitable for <inline-formula><tex-math notation="LaTeX">\text{G}</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">\text{MC}</tex-math></inline-formula>; the second, graduated nonconvexity (<inline-formula><tex-math notation="LaTeX">\text{GNC}</tex-math></inline-formula>), is based on homotopy methods and is suitable for <inline-formula><tex-math notation="LaTeX">\text{G-TLS}</tex-math></inline-formula>. We extend <inline-formula><tex-math notation="LaTeX">\text{ADAPT}</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">\text{GNC}</tex-math></inline-formula> to the case where the user does not have prior knowledge of the inlier-noise statistics (or the statistics may vary over time) and is unable to guess a reasonable threshold to separate inliers from outliers (as the one commonly used in RANdom SAmple Consensus <inline-formula><tex-math notation="LaTeX">(\text{RANSAC})</tex-math></inline-formula>. We propose the first minimally tuned algorithms for outlier rejection, which dynamically decide how to separate inliers from outliers. Our third contribution is an evaluation of the proposed algorithms on robot perception problems: mesh registration, image-based object detection ( shape alignment ), and pose graph optimization. <inline-formula><tex-math notation="LaTeX">\text{ADAPT}</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">\text{GNC}</tex-math></inline-formula> execute in real time, are deterministic, outperform <inline-formula><tex-math notation="LaTeX">\text{RANSAC}</tex-math></inline-formula>, and are robust up to 80-90% outliers. Their minimally tuned versions also compare favorably with the state of the art, even though they do not rely on a noise bound for the inliers. |
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| AbstractList | Nonlinear estimation in robotics and vision is typically plagued with outliers due to wrong data association or incorrect detections from signal processing and machine learning methods. This article introduces two unifying formulations for outlier-robust estimation, generalized maximum consensus ([Formula Omitted]-[Formula Omitted]) and generalized truncated least squares ([Formula Omitted]), and investigates fundamental limits, practical algorithms, and applications. Our first contribution is a proof that outlier-robust estimation is inapproximable: In the worst case, it is impossible to (even approximately) find the set of outliers, even with slower-than-polynomial-time algorithms (particularly, algorithms running in quasi-polynomial time). As a second contribution, we review and extend two general-purpose algorithms. The first, adaptive trimming ([Formula Omitted]), is combinatorial and is suitable for [Formula Omitted]-[Formula Omitted]; the second, graduated nonconvexity ([Formula Omitted]), is based on homotopy methods and is suitable for [Formula Omitted]. We extend [Formula Omitted] and [Formula Omitted] to the case where the user does not have prior knowledge of the inlier-noise statistics (or the statistics may vary over time) and is unable to guess a reasonable threshold to separate inliers from outliers (as the one commonly used in RANdom SAmple Consensus [Formula Omitted]. We propose the first minimally tuned algorithms for outlier rejection, which dynamically decide how to separate inliers from outliers. Our third contribution is an evaluation of the proposed algorithms on robot perception problems: mesh registration, image-based object detection ( shape alignment ), and pose graph optimization. [Formula Omitted] and [Formula Omitted] execute in real time, are deterministic, outperform [Formula Omitted], and are robust up to 80–90% outliers. Their minimally tuned versions also compare favorably with the state of the art, even though they do not rely on a noise bound for the inliers. Nonlinear estimation in robotics and vision is typically plagued with outliers due to wrong data association or incorrect detections from signal processing and machine learning methods. This article introduces two unifying formulations for outlier-robust estimation, generalized maximum consensus (<inline-formula><tex-math notation="LaTeX">\text{G}</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">\text{MC}</tex-math></inline-formula>) and generalized truncated least squares (<inline-formula><tex-math notation="LaTeX">\text{G-TLS}</tex-math></inline-formula>), and investigates fundamental limits, practical algorithms, and applications. Our first contribution is a proof that outlier-robust estimation is inapproximable: In the worst case, it is impossible to (even approximately) find the set of outliers, even with slower-than-polynomial-time algorithms (particularly, algorithms running in quasi-polynomial time). As a second contribution, we review and extend two general-purpose algorithms. The first, adaptive trimming (<inline-formula><tex-math notation="LaTeX">\text{ADAPT}</tex-math></inline-formula>), is combinatorial and is suitable for <inline-formula><tex-math notation="LaTeX">\text{G}</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">\text{MC}</tex-math></inline-formula>; the second, graduated nonconvexity (<inline-formula><tex-math notation="LaTeX">\text{GNC}</tex-math></inline-formula>), is based on homotopy methods and is suitable for <inline-formula><tex-math notation="LaTeX">\text{G-TLS}</tex-math></inline-formula>. We extend <inline-formula><tex-math notation="LaTeX">\text{ADAPT}</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">\text{GNC}</tex-math></inline-formula> to the case where the user does not have prior knowledge of the inlier-noise statistics (or the statistics may vary over time) and is unable to guess a reasonable threshold to separate inliers from outliers (as the one commonly used in RANdom SAmple Consensus <inline-formula><tex-math notation="LaTeX">(\text{RANSAC})</tex-math></inline-formula>. We propose the first minimally tuned algorithms for outlier rejection, which dynamically decide how to separate inliers from outliers. Our third contribution is an evaluation of the proposed algorithms on robot perception problems: mesh registration, image-based object detection ( shape alignment ), and pose graph optimization. <inline-formula><tex-math notation="LaTeX">\text{ADAPT}</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">\text{GNC}</tex-math></inline-formula> execute in real time, are deterministic, outperform <inline-formula><tex-math notation="LaTeX">\text{RANSAC}</tex-math></inline-formula>, and are robust up to 80-90% outliers. Their minimally tuned versions also compare favorably with the state of the art, even though they do not rely on a noise bound for the inliers. |
| Author | Yang, Heng Antonante, Pasquale Carlone, Luca Tzoumas, Vasileios |
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| Snippet | Nonlinear estimation in robotics and vision is typically plagued with outliers due to wrong data association or incorrect detections from signal processing and... |
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| SubjectTerms | Adaptive algorithms Algorithms Approximation algorithms autonomous systems Combinatorial analysis computational complexity computer vision Estimation Formulations Inliers (landforms) Machine learning maximum likelihood estimation Measurement uncertainty Object recognition Optimization Outliers (statistics) Particle measurements Polynomials Probabilistic logic resilient perception Robotics robust estimation Robustness Signal processing Signal processing algorithms Simultaneous localization and mapping |
| Title | Outlier-Robust Estimation: Hardness, Minimally Tuned Algorithms, and Applications |
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