Second-order recursive filtering on the rigid-motion Lie group SE3 based on nonlinear observations

• Verfasst von: Berger, Johannes Peter [VerfasserIn]
• Verfasst von: Lenzen, Frank [VerfasserIn]
• Verfasst von: Becker, Florian [VerfasserIn]
• Verfasst von: Neufeld, Andreas [VerfasserIn]
• Verfasst von: Schnörr, Christoph [VerfasserIn]
• Titel: Second-order recursive filtering on the rigid-motion Lie group SE3 based on nonlinear observations
• Verf.angabe: Johannes Berger, Frank Lenzen, Florian Becker, Andreas Neufeld, Christoph Schnörr
• Umfang: 28 S.
• Fussnoten: Gesehen am 26.04.2018
• Titel Quelle: Enthalten in: Journal of mathematical imaging and vision
• Jahr Quelle: 2016
• Band/Heft Quelle: 58(2017), 1, S. 102-129
• ISSN Quelle: 1573-7683
• DOI: doi:10.1007/s10851-016-0693-1
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1572395400

Abstract

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 SE3SE3{\text {SE}}_{3} and the nonlinear 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 optimal minimum energy filter that copes with the full geometry of SE3SE3{\text {SE}}_{3} as well as with the nonlinear dependencies between the state space and observations., which results in a recursive description of the optimal state and the corresponding second-order operator. The derived filter enables reconstructing motions correctly for synthetic and real scenes, e.g., from the KITTI benchmark. Our experiments confirm thatthe 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.