A Polynomial-time Solution for Robust Registration with Extreme Outlier Rates

Yang, Heng; Carlone, Luca

doi:10.15607/rss.2019.xv.003

Cited by 106 publications

(94 citation statements)

References 56 publications

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“…Robust estimation is a crucial tool for robotics and computer vision, being concerned with the estimation of unknown quantities (e.g., the state of a robot, or of variables describing the external world) from noisy and potentially corrupted measurements. Corrupted measurements (i.e., outliers) can be caused by sensor malfunction, but are more commonly associated with incorrect data association and model misspecification [1], [2].…”

Section: Introductionmentioning

confidence: 99%

Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection

Yang

Antonante

Tzoumas

et al. 2020

IEEE Robot. Autom. Lett.

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222

175

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Semidefinite Programming (SDP) and Sums-of-Squares (SOS) relaxations have led to certifiably optimal non-minimal solvers for several robotics and computer vision problems. However, most non-minimal solvers rely on least squares formulations, and, as a result, are brittle against outliers. While a standard approach to regain robustness against outliers is to use robust cost functions, the latter typically introduce other non-convexities, preventing the use of existing non-minimal solvers. In this paper, we enable the simultaneous use of non-minimal solvers and robust estimation by providing a general-purpose approach for robust global estimation, which can be applied to any problem where a non-minimal solver is available for the outlier-free case. To this end, we leverage the Black-Rangarajan duality between robust estimation and outlier processes (which has been traditionally applied to early vision problems), and show that graduated nonconvexity (GNC) can be used in conjunction with non-minimal solvers to compute robust solutions, without requiring an initial guess. We demonstrate the resulting robust non-minimal solvers in applications, including point cloud and mesh registration, pose graph optimization, and image-based object pose estimation (also called shape alignment). Our solvers are robust to 70-80% of outliers, outperform RANSAC, are more accurate than specialized local solvers, and faster than specialized global solvers. We also extend the literature on non-minimal solvers by proposing a certifiably optimal SOS solver for shape alignment.

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Section: Introductionmentioning

confidence: 99%

Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection

Yang

Antonante

Tzoumas

et al. 2020

IEEE Robot. Autom. Lett.

Self Cite

222

175

View full text Add to dashboard Cite

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“…In point cloud registration, [55] showed how to build invariant measurements to decouple the estimation of scale, rotation and translation. Therefore, in this section we test QUASAR to solve the rotation-only subproblem.…”

Section: Point Cloud Registrationmentioning

confidence: 99%

A Quaternion-Based Certifiably Optimal Solution to the Wahba Problem With Outliers

Yang

Carlone

2019

2019 IEEE/CVF International Conference on Computer Vision (ICCV)

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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. arXiv:1905.12536v4 [math.OC] 22 Sep 2019 Wahba problem with outliersIn computer vision applications, the vector-to-vector correspondences are typically established through descriptor matching, which may lead to spurious correspondences and outliers [44,15]. This observation triggered research into outlier-robust variants of the Wahba problem.Local Methods. The most widely used method for handling outliers is RANSAC, which is efficient and accurate in the low-noise and low-outlier regime [24,40]. However,

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“…Liu et al [ 28 ] proposed a rotation invariant feature to decompose rigid transformation, but it cannot be used for similarity registration. Yang et al [ 39 , 40 ] estimated scale, rotation and translation separately and proposed a polynomial time method, but putative correspondences between the two point sets to be registered are needed.…”

Section: Related Workmentioning

confidence: 99%

Efficient Similarity Point Set Registration by Transformation Decomposition

Wang

Chen

Wang

2020

Sensors

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Point set registration is one of the basic problems in computer vision. When the overlap ratio between point sets is small or the relative transformation is large, local methods cannot guarantee the accuracy. However, the time complexity of the branch and bound (BnB) optimization used in most existing global methods is exponential in the dimensionality of parameter space. Therefore, seven-Degrees of Freedom (7-DoF) similarity transformation is a big challenge for BnB. In this paper, a novel rotation and scale invariant feature is introduced to decouple the optimization of translation, rotation, and scale in similarity point set registration, so that BnB optimization can be done in two lower dimensional spaces. With the transformation decomposition, the translation is first estimated and then the rotation is optimized by maximizing a robust objective function defined on consensus set. Finally, the scale is estimated according to the potential correspondences in the obtained consensus set. Experiments on synthetic data and clinical data show that our method is approximately two orders of magnitude faster than the state-of-the-art global method and more accurate than a typical local method. When the outlier ratio with respect to the inliers is up to 1.0, our method still achieves accurate registration.

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A Polynomial-time Solution for Robust Registration with Extreme Outlier Rates

Cited by 106 publications

References 56 publications

Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection

Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection

A Quaternion-Based Certifiably Optimal Solution to the Wahba Problem With Outliers

Efficient Similarity Point Set Registration by Transformation Decomposition

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