Renderer-Aware Cram\'{e}r--Rao Bounds for Camera Pose on $\mathrm{SE}(3)$

Arun Muthukkumar

Abstract: Pose estimation is essential for many applications within computer vision and robotics. Yet few works provide rigorous uncertainty quantification for poses under dense or learned models, despite their uses. We derive a closed-form lower bound on the covariance of camera pose estimates by treating a differentiable renderer as a measurement function. We linearize image formation with respect to a small pose perturbation on the manifold and yield a \emph{render-aware} Cram'er--Rao bound. Our approach reduces to classical bundle-adjustment uncertainty, ensuring continuity with vision theory. It also naturally extends to multi-agent settings by fusing Fisher information across cameras. Our statistical formulation has downstream applications for tasks such as cooperative perception and novel view synthesis without requiring explicit keypoint correspondences.

Submission Number: 13