From intrinsic optimization to iterated extended Kalman filtering on Lie groups

DOI10.1007/s10851-015-0622-8zbMath1368.94007OpenAlexW2232226837WikidataQ115383728 ScholiaQ115383728MaRDI QIDQ294399

Yannick Berthoumieu, Guillaume Bourmaud, Audrey Giremus, Rémi Mégret

Publication date: 16 June 2016

Published in: Journal of Mathematical Imaging and Vision (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10851-015-0622-8

zbMATH Keywords

optimizationmanifoldsLie groupsfilteringmotionmatrix transformations3D similaritycamera poseGauss-NewtonhomographyKalman

Mathematics Subject Classification ID

Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Machine vision and scene understanding (68T45)

Related Items (6)

From intrinsic optimization to iterated extended Kalman filtering on Lie groups ⋮ Synchronization problems in computer vision with closed-form solutions ⋮ Barankin, McAulay-Seidman and Cramér-Rao bounds on matrix Lie groups ⋮ Recursive posterior Cramér-Rao lower bound on Lie groups ⋮ A bundle framework for observer design on smooth manifolds with symmetry ⋮ Continuous-discrete extended Kalman filter on matrix Lie groups using concentrated Gaussian distributions

Uses Software

• MonoSLAM
• iSAM2

Cites Work

• From intrinsic optimization to iterated extended Kalman filtering on Lie groups
• Rotation averaging
• Stochastic models, information theory, and Lie groups. II: Analytic methods and modern applications
• Second-order recursive filtering on the rigid-motion Lie group \(\mathrm{SE}_3\) based on nonlinear observations
• Twisted product of Lie groups
• Continuous-discrete extended Kalman filter on matrix Lie groups using concentrated Gaussian distributions
• Bayesian Fusion on Lie Groups
• Optimization Methods on Riemannian Manifolds and Their Application to Shape Space
• Three-Dimensional Structure Determination from Common Lines in Cryo-EM by Eigenvectors and Semidefinite Programming
• Incremental Least Squares Methods and the Extended Kalman Filter
• Exact and stable recovery of rotations for robust synchronization
• Cramer-Rao bounds for synchronization of rotations
• The iterated Kalman filter update as a Gauss-Newton method
• A Cheeger Inequality for the Graph Connection Laplacian
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