Online Variational Bayesian Motion Averaging

Bourmaud, Guillaume

doi:10.1007/978-3-319-46484-8_8

Cited by 12 publications

(9 citation statements)

References 30 publications

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“…If a triplet contains one or more outlier edges, it is most likely to be inconsistent and fail to meet (7). • Number of triplet supports: Suppose that a base node has several non-family neighbors, including node i.…”

Section: Preliminaries and Notationmentioning

confidence: 99%

“…The simplified algorithm described in the previous section constructs a spanning tree by adding the most supported edges first. In the full version, we consider two more aspects: the loop threshold in (7), and optionally, the number of valid 2D-2D correspondences. We highlight the differences between the two versions in Alg.…”

Section: Hierarchical Initialization (Full Version)mentioning

confidence: 99%

“…We consider the problem of multiple rotation averaging in the presence of outliers, i.e., finding multiple absolute rotations R i given a partial set of noisy, outlier-contaminated constraints on relative rotations R ij = R i R j [35]. This problem has direct application to structure-from-motion (SfM) [1,13,15,17,18,20,44,47,62,65,67], multiple point cloud registration [3-5, 28, 32, 36, 46, 56] and simultaneous localization and mapping (SLAM) [7,8,10,66].…”

Section: Introductionmentioning

confidence: 99%

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HARA: A Hierarchical Approach for Robust Rotation Averaging

Lee¹,

Civera²

2021

Preprint

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We propose a novel hierarchical approach for multiple rotation averaging, dubbed HARA. Our method incrementally initializes the rotation graph based on a hierarchy of triplet support. The key idea is to build a spanning tree by prioritizing the edges with many strong triplet supports and gradually adding those with weaker and fewer supports. This reduces the risk of adding outliers in the spanning tree. As a result, we obtain a robust initial solution that enables us to filter outliers prior to nonlinear optimization. With minimal modification, our approach can also integrate the knowledge of the number of valid 2D-2D correspondences. We perform extensive evaluations on both synthetic and real datasets, demonstrating state-of-the-art results.

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Section: Preliminaries and Notationmentioning

confidence: 99%

Section: Hierarchical Initialization (Full Version)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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HARA: A Hierarchical Approach for Robust Rotation Averaging

Lee¹,

Civera²

2021

Preprint

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“…While the recursive methods are fundamentally important, here we concern ourselves with problems that require batch Gaussian inference. In robotics, some canonical problems are batch trajectory estimation, pose-graph relaxation (Bourmaud 2016), and BA/SLAM. However, we can also pose control/planning (Dong et al 2016; Mukadam et al 2018), calibration (Pradeep et al 2014), and three-dimensional modelling problems (Li et al 2011) as Gaussian inference, such that the number of commonplace applications is quite large.…”

Section: Related Workmentioning

confidence: 99%

Exactly sparse Gaussian variational inference with application to derivative-free batch nonlinear state estimation

Barfoot

Forbes

Yoon

2020

The International Journal of Robotics Research

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We present a Gaussian variational inference (GVI) technique that can be applied to large-scale nonlinear batch state estimation problems. The main contribution is to show how to fit both the mean and (inverse) covariance of a Gaussian to the posterior efficiently, by exploiting factorization of the joint likelihood of the state and data, as is common in practical problems. This is different than maximum a posteriori (MAP) estimation, which seeks the point estimate for the state that maximizes the posterior (i.e., the mode). The proposed exactly sparse Gaussian variational inference (ESGVI) technique stores the inverse covariance matrix, which is typically very sparse (e.g., block-tridiagonal for classic state estimation). We show that the only blocks of the (dense) covariance matrix that are required during the calculations correspond to the non-zero blocks of the inverse covariance matrix, and further show how to calculate these blocks efficiently in the general GVI problem. ESGVI operates iteratively, and while we can use analytical derivatives at each iteration, Gaussian cubature can be substituted, thereby producing an efficient derivative-free batch formulation. ESGVI simplifies to precisely the Rauch–Tung–Striebel (RTS) smoother in the batch linear estimation case, but goes beyond the ‘extended’ RTS smoother in the nonlinear case because it finds the best-fit Gaussian (mean and covariance), not the MAP point estimate. We demonstrate the technique on controlled simulation problems and a batch nonlinear simultaneous localization and mapping problem with an experimental dataset.

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“…The synchronization problem is also related to simultaneous localization and mapping (SLAM), where the goal is to orient a robot moving in an unknown environment, while building a map of the environment (Carlone et al, 2015;Rosen et al, 2015;Bourmaud, 2016). This task can be reduced to a synchronization in SE(3), if measures of relative poses are available.…”

Section: Other Applicationsmentioning

confidence: 99%

Robust synchronization in SO(3) and SE(3) via low-rank and sparse matrix decomposition

Arrigoni

Fusiello

Rossi

et al. 2018

Computer Vision and Image Understanding

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This paper deals with the synchronization problem, which arises in multiple 3D point-set registration and in structure-from-motion. The problem is formulated as a low-rank and sparse matrix decomposition that caters for missing data, outliers and noise, and it benefits from a wealth of available decomposition algorithms that can be plugged-in. A minimization strategy, dubbed R-GoDec, is also proposed. Experimental results on simulated and real data show that this approach o↵ers a good trade-o↵ between resistance to outliers and speed.

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Online Variational Bayesian Motion Averaging

Cited by 12 publications

References 30 publications

HARA: A Hierarchical Approach for Robust Rotation Averaging

HARA: A Hierarchical Approach for Robust Rotation Averaging

Exactly sparse Gaussian variational inference with application to derivative-free batch nonlinear state estimation

Robust synchronization in SO(3) and SE(3) via low-rank and sparse matrix decomposition

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