Minimization of a Large-Scale Quadratic Function Subject to a Spherical Constraint
SIAM Journal on Optimization
An Efficient Solution to the Five-Point Relative Pose Problem
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convex Optimization
Robustness in motion averaging
ACCV'06 Proceedings of the 7th Asian conference on Computer Vision - Volume Part II
Rotation averaging with application to camera-rig calibration
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part II
Discrete-continuous optimization for large-scale structure from motion
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
L1 rotation averaging using the Weiszfeld algorithm
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Multiview registration of 3D scenes by minimizing error between coordinate frames
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Multiple rotation averaging is an important problem in computer vision. The problem is challenging because of the nonlinear constraints required to represent the set of rotations. To our knowledge no one has proposed any globally optimal solution for the case of simultaneous updates of the rotations. In this paper we propose a simple procedure based on Lagrangian duality that can be used to verify global optimality of a local solution, by solving a linear system of equations. We show experimentally on real and synthetic data that unless the noise levels are extremely high this procedure always generates the globally optimal solution.