Johannes Berger

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Projects

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

In this project we investigated, how to set up a mathematica rigorous recursive filter that respects the curved geometry of the Lie group SE(3) as well as copes with the nonlinear dependence of the unknown state variable (i.e. the camera motion on SE(3)) and the observations in terms of optical flow and depth maps. To approach this problem, we used the recently introduced Minimum Energy Filters by Saccon et al. In [1] we derived the corresponding second order filtering equations and showed experimentally, that our approach is on par with state-of-the-art.

state and observation equation
State and observation equations for constant velocity model


Second-Order Recursive Filtering on the Rigid-Motion Lie Group SE(3) with a Generalized Kinematic Model

Camera track reconstructions

In [2] we generalized our approach from a constant velocity model to a constant acceleration model that is able to reconstruct higher order information about the camera's motion. We also showed how to derive the Minimum Energy Filter for a generalized kinematic model that respects temporal derivatives of the motion of any order.

state and observation equation
State and observation equations for constant acceleration model

Code of this algorithm is available on github: https://github.com/johberger/MEF_Odometry

Joint Recursive Monocular Filtering of Camera Motion and Depth Map

In this project we expand our previous work that requires optical flow and depth map from a stereo setting to a monocular approach for which the true depth map is unknown. We derive the corresponding filtering equations to obtain a filter that estimates jointly the camera motion and the scene's depth map from monocular optical flow observations.


References