Camera Pose Filtering With Local Regression Geodesics on the Riemannian Manifold of Dual Quaternions

Benjamin Busam, Tolga Birdal, Nassir Navab; Proceedings of the IEEE International Conference on Computer Vision (ICCV), 2017, pp. 2436-2445

Abstract


Time-varying, smooth trajectory estimation is of great interest to the vision community for accurate 3D systems. In this paper, we propose a novel principal component local regression filter acting on the Riemannian manifold of unit dual quaternions DH_1 We use a numerically stable Lie algebra of the dual quaternions together with exp and log operators to locally linearize the 6D pose space. Unlike state of the art path smoothing methods which either operate on SE(3) of rotation matrices or the hypersphere H_1 of quaternions, we treat orientation and translation jointly on the dual quaternion quadric in 7-dimensional real projective space RP^7. We provide an outlier-robust IRLS algorithm for generic pose filtering exploiting this manifold structure. Besides our theoretical analysis, experiments on synthetic and real data show the practical advantages of the manifold aware filtering on pose tracking and smoothing.

Related Material


[pdf] [arXiv]
[bibtex]
@InProceedings{Busam_2017_ICCV,
author = {Busam, Benjamin and Birdal, Tolga and Navab, Nassir},
title = {Camera Pose Filtering With Local Regression Geodesics on the Riemannian Manifold of Dual Quaternions},
booktitle = {Proceedings of the IEEE International Conference on Computer Vision (ICCV) Workshops},
month = {Oct},
year = {2017}
}