Reduces covariance tracking error by 30x by reformulating the problem as rigid-body motion on Lie groups.
March 23, 2026
Original Paper
K-GMRF: Kinetic Gauss-Markov Random Field for First-Principles Covariance Tracking on Lie Groups
arXiv · 2603.19601
The Takeaway
By using second-order dynamics and symplectic integrators instead of standard first-order updates, this method eliminates the phase lag typical of existing estimators. It is a plug-and-play geometric prior that significantly improves tracking fidelity in high-speed or data-constrained vision and robotics tasks.
From the abstract
Tracking non-stationary covariance matrices is fundamental to vision yet hindered by existing estimators that either neglect manifold constraints or rely on first-order updates, incurring inevitable phase lag during rapid evolution. We propose K-GMRF, an online, training-free framework for covariance tracking that reformulates the problem as forced rigid-body motion on Lie groups. Derived from the Euler-Poincaré equations, our method interprets observations as torques driving a latent angular ve