  Camera motion estimation from observed scene features is an important task in
image processing to increase the accuracy of many methods, e.g. optical flow
and structure-from-motion. Due to the curved geometry of the state space SE(3)
and the non-linear relation to the observed optical flow, many recent filtering
approaches use a first-order approximation and assume a Gaussian a posteriori
distribution or restrict the state to Euclidean geometry. The physical model is
usually also limited to uniform motions.
  We propose a second-order minimum energy filter with a generalized kinematic
model that copes with the full geometry of SE(3) as well as with the nonlinear
dependencies between the state space and observations. The derived filter
enables reconstructing motions correctly for synthetic and real scenes, e.g.
from the KITTI benchmark. Our experiments confirm that the derived minimum
energy filter with higher-order state differential equation copes with
higher-order kinematics and is also able to minimize model noise. We also show
that the proposed filter is superior to state-of-the-art extended Kalman
filters on Lie groups in the case of linear observations and that our method
reaches the accuracy of modern visual odometry methods.
