Fetching the paper…
Reading the bibliography…
Why is it that semidefinite relaxations have been so successful in numerous applications in computer vision and robotics for solving non-convex optimization problems involving rotations? In studying the empirical performance we note that there are few failure cases reported in the literature, in particular for estimation problems with a single rotation, motivating us to gain further theoretical understanding.
J. Opt. Soc. America A 4
Horn, B.K.P.: Closed-form solution of absolute orientation using unit quaternions · 1987
Earlier work this paper cites.
IEEE Trans. Pattern Analysis and Machine Intelligence 14
Besl, P., McKay, N.: A method for registration two 3-d shapes · 1992
Earlier work this paper cites.
Int. J. Robotics Research 14
Horaud, R., Dornaika, F.: Hand-eye calibration · 1995
Earlier work this paper cites.
In: Computer Vision and Pattern Recognition (2001)
Govindu, V.: Combining two-view constraints for motion estimation · 2001
Earlier work this paper cites.
SIAM J. on Opt. 11
Lasserre, J.B.: Global optimization with polynomials and the problem of moments · 2001
Earlier work this paper cites.
Cambridge University Press (2004)
Boyd, S., Vandenberghe, L.: Convex Optimization · 2004
Earlier work this paper cites.
In: Computer Vision and Pattern Recognition (2006)
Olsson, C., Kahl, F., Oskarsson, M.: The registration problem revisited: Optimal solutions from points, lines and planes · 2006
Earlier work this paper cites.
Int. J. Computer Vision (IJCV) 74
Kahl, F., Henrion, D.: Globally optimal estimates for geometric reconstruction problems · 2007
Earlier work this paper cites.
IEEE Trans. Pattern Analysis and Machine Intelligence 31
Olsson, C., Kahl, F., Oskarsson, M.: Branch-and-bound methods for Euclidean registration problems · 2009
Earlier work this paper cites.
In: IEEE Conference on Computer Vision and Pattern Recognition (2011)
Hartley, R., Aftab, K., Trumpf, J.: L 1 L_{1} rotation averaging using the Weiszfeld algorithm · 2011
Earlier work this paper cites.
Mathematika 57
Sanyal, R., Sottile, F., Sturmfels, B.: Orbitopes · 2011
Earlier work this paper cites.
SIAM J. on Opt. (2012)
Blekherman, G., Parrilo, P., Thomas, R.: Semidefinite Optimization and Convex Algebraic Geometry · 2012
Earlier work this paper cites.
In: Asian Conf. Computer Vision (ACCV) (2012)
Fredriksson, J., Olsson, C.: Simultaneous multiple rotation averaging using Lagrangian duality · 2012
Earlier work this paper cites.
In: International Conference on Computer Vision (2013)
Chatterjee, A., Govindu, V.: Efficient and robust large-scale rotation averaging · 2013
Earlier work this paper cites.
Int. J. Computer Vision (IJCV) 103
Hartley, R., Trumpf, J., Dai, Y., Li, H.: Rotation averaging · 2013
Cited alongside, same era.
In: Int. Conf. Computer Vision (ICCV) (2013)
Zheng, Y., Kuang, Y., Sugimoto, S., Astrom, K., Okutomi, M.: Revisiting the PnP problem: A fast, general and optimal solution · 2013
Cited alongside, same era.
In: International Conference on 3D Vision (2014)
Arrigoni, F., Magri, L., Rossi, B., Fragneto, P., Fusiello, A.: Robust absolute rotation estimation via low-rank and sparse matrix decomposition · 2014
Cited alongside, same era.
In: Eur. Conf. Computer Vision (ECCV) (2014)
Sweeney, C., Fragoso, V., Höllerer, T., Turk, M.: gDLS: A scalable solution to the generalized pose and scale problem · 2014
Cited alongside, same era.
arXiv preprint arXiv:1506.00575 (2015)
Boumal, N.: A riemannian low-rank method for optimization over semidefinite matrices with block-diagonal constraints · 2015
Cited alongside, same era.
Springer (2017)
Brandt, M., Bruce, J., Brysiewicz, T., Krone, R., Robeva, E.: The Degree of SO ( n , ℂ ) \mathrm{SO}(n,\mathbb{C}) · 2017
Later among the works it cites.
In: Computer Vision and Pattern Recognition (2017)
Briales, J., Gonzalez-Jimenez, J.: Convex global 3D registration with Lagrangian duality · 2017
Later among the works it cites.
arXiv preprint arXiv:1710.04287 (2017)
Cifuentes, D., Agarwal, S., Parrilo, P.A., Thomas, R.R.: On the local stability of semidefinite relaxations · 2017
Later among the works it cites.
Int. J. Robotics Research 38
Rosen, D., Carlone, L., Bandeira, A., Leonard, J.: SE-Sync: A certifiably correct algorithm for synchronization over the special Euclidean group · 2018
Later among the works it cites.
SIAM J. on Opt. 28
Zhong, Y., Boumal, N.: Near-optimal bounds for phase synchronization · 2018
Later among the works it cites.
IEEE Robotics and Automation Letters 4
Giamou, M., Ma, Z., Peretroukhin, V., Kelly, J.: Certifiably globally optimal extrinsic calibration from per-sensor egomotion · 2019
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Carlone, L., Rosen, D.M., Calafiore, G., Leonard, J.J., Dellaert, F.: Lagrangian duality in 3D SLAM: Verification techniques and optimal solutions · 2015
Cited alongside, same era.
SIAM J. on Opt. 25
Chaudhury, K., Khoo, Y., Singer, A.: Global registration of multiple point clouds using semidefinite programming · 2015
Cited alongside, same era.
EURO J. Comput. Opt. 5
Lasserre, J.B., Toh, K.C., Yang, S.: A bounded degree sos hierarchy for polynomial optimization · 2015
Cited alongside, same era.
In: Brit. Mach. Vision Conf. (BMVC) (2015)
Nakano, G.: Globally optimal DLS method for PnP problem with Cayley parameterization · 2015
Cited alongside, same era.
J. American Math. Soc. 29
Blekherman, G., Smith, G., Velasco, M.: Sums of squares and varieties of minimal degree · 2016
Cited alongside, same era.
In: Int. Conf. Intell. Robots and Systems (2016)
Briales, J., Gonzalez-Jimenez, J.: Fast global optimality verification in 3D SLAM · 2016
Cited alongside, same era.
IEEE Trans. Robotics 32
Carlone, L., Calafiore, G.C., Tommolillo, C., Dellaert, F.: Planar pose graph optimization: Duality, optimal solutions, and verification · 2016
Cited alongside, same era.
Later among the works it cites.
In: Int. Conf. Robotics and Automation (2019)
Mangelson, J., Liu, J., Eustice, R., Vasudevan, R.: Guaranteed globally optimal planar pose graph and landmark slam via sparse-bounded sums-of-squares programming · 2019
Later among the works it cites.
In: Brit. Mach. Vision Conf. (BMVC) (2020)
Brynte, L., Kahl, F.: Pose proposal critic: Robust pose refinement by learning reprojection errors · 2020
Later among the works it cites.
Mathematical programming 182
Cifuentes, D., Harris, C., Sturmfels, B.: The geometry of SDP-exactness in quadratic optimization · 2020
Later among the works it cites.
In: Eur. Conf. Computer Vision (ECCV) (2020)
Dellaert, F., Rosen, D., Wu, J., Mahony, R., Carlone, L.: Shonan rotation averaging: Global optimality by surfing S O ( p ) n SO(p)^{n} · 2020
Later among the works it cites.
IEEE Trans. Robotics 36
Fan, T., Wang, H., Rubenstein, M., Murphey, T.: Cpl-slam: Efficient and certifiably correct planar graph-based slam using the complex number representation · 2020
Later among the works it cites.
World Scientific (2020)
Henrion, D., Korda, M., Lasserre, J.B.: The Moment-SOS Hierarchy · 2020
Later among the works it cites.
In: Computer Vision and Pattern Recognition (2020)
Iglesias, J., Olsson, C., Kahl, F.: Global optimality for point set registration using semidefinite programming · 2020
Later among the works it cites.
IEEE Trans. Pattern Analysis and Machine Intelligence 43
Eriksson, A., Olsson, C., Kahl, F., Chin, T.J.: Rotation averaging with the chordal distance: Global minimizers and strong duality · 2021
Closest in time.