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Camera Pose Filtering with Local Regression Geodesicsc on the Riemannian Manifold of Dual Quaternions

Abstract · Apr 24, 2017 07:52 ·

aided manifold trajectory pose smoothing quaternions quaternion dual procedures cs-cv

Arxiv Abstract

  • Benjamin Busam
  • Tolga Birdal
  • Nassir Navab

Time-varying, smooth trajectory estimation is of great interest to the vision community for accurate and well behaving 3D systems. In this paper, we propose a novel principal component local regression filter acting directly on the Riemannian manifold of unit dual quaternions $\mathbb{D} \mathbb{H}_1$. We first present a numerically stable Lie algebra of the dual quaternions. Then, we introduce $\exp$ and $\log$ operators. Unlike state of the art path smoothing methods which either operate on $SE\left(3\right)$ of rotation matrices or the hypersphere $\mathbb{H}_1$ of quaternions, we treat the orientation and translation jointly on the dual quaternion quadric in the 7-dimensional real projective space $\mathbb{R}\mathbb{P}^7$. In the end, we provide an outlier-robust IRLS algorithm for generic pose filtering exploiting this manifold structure. Besides our theoretical contributions, our experiments on synthetic and real data show the advantages of the manifold aware filtering on pose tracking and smoothing.

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