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Camera motion estimation from observed scene features is an important task inimage processing to increase the accuracy of many methods, e.g. optical flowand 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 filteringapproaches use a first-order approximation and assume a Gaussian a posterioridistribution or restrict the state to Euclidean geometry. The physical model isusually also limited to uniform motions.  We propose a second-order minimum energy filter with a generalized kinematicmodel that copes with the full geometry of SE(3) as well as with the nonlineardependencies between the state space and observations. The derived filterenables reconstructing motions correctly for synthetic and real scenes, e.g.from the KITTI benchmark. Our experiments confirm that the derived minimumenergy filter with higher-order state differential equation copes withhigher-order kinematics and is also able to minimize model noise. We also showthat the proposed filter is superior to state-of-the-art extended Kalmanfilters on Lie groups in the case of linear observations and that our methodreaches the accuracy of modern visual odometry methods.

Second-Order Recursive Filtering on the Rigid-Motion Lie Group SE(3) Based on Nonlinear Observations