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We propose the first general and scalable framework to design certifiable algorithms for robust geometric perception in the presence of outliers.
Random sample consensus: a paradigm for model fitting with application to image analysis and automated cartography
M. Fischler and R. Bolles · 1981
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Robust Statistics
P. Huber · 1981
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Visual reconstruction
A. Blake and A. Zisserman · 1987
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Closed-form solution of absolute orientation using unit quaternions
B. K. P. Horn · 1987
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On the unification of line processes, outlier rejection, and robust statistics with applications in early vision
M. J. Black and A. Rangarajan · 1996
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A volumetric method for building complex models from range images
B. Curless and M. Levoy · 1996
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Complementarity and nondegeneracy in semidefinite programming
F. Alizadeh, J. Haeberly, and M. Overton · 1997
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Primal-dual interior-point methods for semidefinite programming: Convergence rates, stability and numerical results
F. Alizadeh, J.-P. A. Haeberly, and M. L. Overton · 1998
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On the nesterov–todd direction in semidefinite programming
M. J. Todd, K.-C. Toh, and R. H. Tütüncü · 1998
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Nonlinear Programming
D. Bertsekas · 1999
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A nonlinear conjugate gradient method with a strong global convergence property
Y.-H. Dai and Y. Yuan · 1999
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An algorithmic overview of surface registration techniques for medical imaging
M. A. Audette, F. P. Ferrie, and T. M. Peters · 2000
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Global optimization with polynomials and the problem of moments
J. B. Lasserre · 2001
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A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
Burer, Samuel and Monteiro, Renato D C · 2003
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Locally optimized ransac
O. Chum, J. Matas, and J. Kittler · 2003
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Solving semidefinite-quadratic-linear programs using SDPT3
R. H. Tütüncü, K.-C. Toh, and M. J. Todd · 2003
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Convex optimization
S. Boyd and L. Vandenberghe · 2004
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Convergent sdp-relaxations in polynomial optimization with sparsity
J. B. Lasserre · 2006
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Numerical optimization
J. Nocedal and S. Wright · 2006
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Fast and globally convergent structure and motion estimation for general camera models
G. Schweighofer and A. Pinz · 2006
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Sums of squares and semidefinite program relaxations for polynomial optimization problems with structured sparsity
H. Waki, S. Kim, M. Kojima, and M. Muramatsu · 2006
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Optimization Algorithms on Matrix Manifolds
P.-A. Absil, R. Mahony, and R. Sepulchre · 2007
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Globally optimal estimates for geometric reconstruction problems
F. Kahl and D. Henrion · 2007
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Parallel tracking and mapping for small ar workspaces
G. Klein and D. Murray · 2007
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The 3D-3D registration problem revisited
H. Li and R. Hartley · 2007
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Automatic generator of minimal problem solvers
Z. Kukelova, M. Bujnak, and T. Pajdla · 2008
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Globally optimal O(n) solution to the PnP problem for general camera models
G. Schweighofer and A. Pinz · 2008
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A fast iterative shrinkage-thresholding algorithm for linear inverse problems
A. Beck and M. Teboulle · 2009
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Consensus set maximization with guaranteed global optimality for robust geometry estimation
H. Li · 2009
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Dualize it: software for automatic primal and dual conversions of conic programs
J. Löfberg · 2009
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Regularization methods for semidefinite programming
J. Malick, J. Povh, F. Rendl, and A. Wiegele · 2009
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Branch-and-bound methods for euclidean registration problems
C. Olsson, F. Kahl, and M. Oskarsson · 2009
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Fast point feature histograms (fpfh) for 3d registration
R. Rusu, N. Blodow, and M. Beetz · 2009
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Bundle adjustment in the large
S. Agarwal, N. Snavely, I. Simon, S. M. Seitz, and R. Szeliski · 2010
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Moments, positive polynomials and their applications
J.-B. Lasserre · 2010
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A newton-cg augmented lagrangian method for semidefinite programming
X.-Y. Zhao, D. Sun, and K.-C. Toh · 2010
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Proximal splitting methods in signal processing
P. L. Combettes and J.-C. Pesquet · 2011
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A qcqp approach to triangulation
C. Aholt, S. Agarwal, and R. Thomas · 2012
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Globally optimal consensus set maximization through rotation search
J. C. Bazin, Y. Seo, and M. Pollefeys · 2012
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Semidefinite optimization and convex algebraic geometry
G. Blekherman, P. A. Parrilo, and R. R. Thomas · 2012
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Simultaneous multiple rotation averaging using lagrangian duality
J. Fredriksson and C. Olsson · 2012
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An inexact accelerated proximal gradient method for large scale linearly constrained convex sdp
K. Jiang, D. Sun, and K.-C. Toh · 2012
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Robust map optimization using dynamic covariance scaling
P. Agarwal, G. D. Tipaldi, L. Spinello, C. Stachniss, and W. Burgard · 2013
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Rotation averaging
R. Hartley, J. Trumpf, Y. Dai, and H. Li · 2013
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Approximation algorithms
V. V. Vazirani · 2013
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Exact and stable recovery of rotations for robust synchronization
L. Wang and A. Singer · 2013
Cited alongside, same era.
Manopt, a Matlab toolbox for optimization on manifolds
N. Boumal, B. Mishra, P.-A. Absil, and R. Sepulchre · 2014
Cited alongside, same era.
Convex relaxations for pose graph optimization with outliers
L. Carlone and G. C. Calafiore · 2018
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Robust fitting in computer vision: Easy or hard?
T.-J. Chin, Z. Cai, and F. Neumann · 2018
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Rotation averaging and strong duality
A. Eriksson, C. Olsson, F. Kahl, and T.-J. Chin · 2018
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Lectures on convex optimization
Y. Nesterov · 2018
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Guaranteed outlier removal for point cloud registration with correspondences
Á. Parra Bustos and T. J. Chin · 2018
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S. Agostinho, J. Gomes, and A. Del Bue · 2019
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Hand-eye and robot-world calibration by global polynomial optimization
J. Heller, D. Henrion, and T. Pajdla · 2014
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UPnP: An optimal o(n) solution to the absolute pose problem with universal applicability
L. Kneip, H. Li, and Y. Seo · 2014
Cited alongside, same era.
Optimality conditions and finite convergence of lasserre’s hierarchy
J. Nie · 2014
Cited alongside, same era.
Beyond pascal: A benchmark for 3d object detection in the wild
Y. Xiang, R. Mottaghi, and S. Savarese · 2014
Cited alongside, same era.
Beyond PASCAL: A benchmark for 3d object detection in the wild
Y. Xiang, R. Mottaghi, and S. Savarese · 2014
Cited alongside, same era.
Optimal essential matrix estimation via inlier-set maximization
J. Yang, H. Li, and Y. Jia · 2014
Cited alongside, same era.
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A general and adaptive robust loss function
J. T. Barron · 2019
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Satellite pose estimation with deep landmark regression and nonlinear pose refinement
B. Chen, J. Cao, A. Parra, and T.-J. Chin · 2019
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Rotation averaging with the chordal distance: Global minimizers and strong duality
A. Eriksson, C. Olsson, F. Kahl, and T.-J. Chin · 2019
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Certifiably globally optimal extrinsic calibration from per-sensor egomotion
M. Giamou, Z. Ma, V. Peretroukhin, and J. Kelly · 2019
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Homebreweddb: Rgb-d dataset for 6d pose estimation of 3d objects
R. Kaskman, S. Zakharov, I. Shugurov, and S. Ilic · 2019
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Modeling perceptual aliasing in slam via discrete–continuous graphical models
P.-Y. Lajoie, S. Hu, G. Beltrame, and L. Carlone · 2019
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Deterministic approximate methods for maximum consensus robust fitting
H. M. Le, T.-J. Chin, A. Eriksson, T.-T. Do, and D. Suter · 2019
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Robust statistics: theory and methods (with R)
R. A. Maronna, R. D. Martin, V. J. Yohai, and M. Salibián-Barrera · 2019
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SE-Sync: A certifiably correct algorithm for synchronization over the special euclidean group
D. M. Rosen, L. Carlone, A. S. Bandeira, and J. J. Leonard · 2019
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Pose estimation for non-cooperative rendezvous using neural networks
S. Sharma and S. D’Amico · 2019
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The ApolloScape open dataset for autonomous driving and its application
P. Wang, X. Huang, X. Cheng, D. Zhou, Q. Geng, and R. Yang · 2019
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A polynomial-time solution for robust registration with extreme outlier rates
H. Yang and L. Carlone · 2019
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A quaternion-based certifiably optimal solution to the wahba problem with outliers
H. Yang and L. Carlone · 2019
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Global optimality for point set registration using semidefinite programming
J. P. Iglesias, C. Olsson, and F. Kahl · 2020
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Gsnet: Joint vehicle pose and shape reconstruction with geometrical and scene-aware supervision
L. Ke, S. Li, Y. Sun, Y.-W. Tai, and C.-K. Tang · 2020
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Scalable low-rank semidefinite programming for certifiably correct machine perception
D. M. Rosen · 2020
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Certifiably optimal monocular hand-eye calibration
E. Wise, M. Giamou, S. Khoubyarian, A. Grover, and J. Kelly · 2020
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Graduated non-convexity for robust spatial perception: From non-minimal solvers to global outlier rejection
H. Yang, P. Antonante, V. Tzoumas, and L. Carlone · 2020
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In perfect shape: Certifiably optimal 3d shape reconstruction from 2d landmarks
H. Yang and L. Carlone · 2020
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One ring to rule them all: Certifiably robust geometric perception with outliers
H. Yang and L. Carlone · 2020
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TEASER: Fast and Certifiable Point Cloud Registration
H. Yang, J. Shi, and L. Carlone · 2020
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Sparse semidefinite programs with guaranteed near-linear time complexity via dualized clique tree conversion
R. Y. Zhang and J. Lavaei · 2020
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An efficient solution to non-minimal case essential matrix estimation
J. Zhao · 2020
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Chordal decomposition in operator-splitting methods for sparse semidefinite programs
Y. Zheng, G. Fantuzzi, A. Papachristodoulou, P. Goulart, and A. Wynn · 2020
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Outlier-robust estimation: Hardness, minimally-tuned algorithms, and applications
P. Antonante, V. Tzoumas, H. Yang, and L. Carlone · 2021
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A convex relaxation to compute the nearest structured rank deficient matrix
D. Cifuentes · 2021
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Certifiable relative pose estimation
M. Garcia-Salguero, J. Briales, and J. Gonzalez-Jimenez · 2021
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Optimal pose and shape estimation for category-level 3D object perception
J. Shi, H. Yang, and L. Carlone · 2021
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ROBIN: a graph-theoretic approach to reject outliers in robust estimation using invariants
J. Shi, H. Yang, and L. Carlone · 2021
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Chordal-TSSOS: a moment-SOS hierarchy that exploits term sparsity with chordal extension
J. Wang, V. Magron, and J.-B. Lasserre · 2021
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TSSOS: A Moment-SOS hierarchy that exploits term sparsity
J. Wang, V. Magron, and J.-B. Lasserre · 2021
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Self-supervised geometric perception
H. Yang, W. Dong, L. Carlone, and V. Koltun · 2021
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Dynamical pose estimation
H. Yang, C. Doran, and J.-J. Slotine · 2021
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H. Yang, L. Liang, L. Carlone, and K.-C. Toh · 2021
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