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Time-varying, smooth trajectory estimation is of great interest to the visioncommunity for accurate and well behaving 3D systems. In this paper, we proposea novel principal component local regression filter acting directly on theRiemannian manifold of unit dual quaternions $\mathbb{D} \mathbb{H}_1$. We usea numerically stable Lie algebra of the dual quaternions together with $\exp$and $\log$ operators to locally linearize the 6D pose space. Unlike state ofthe art path smoothing methods which either operate on $SO\left(3\right)$ ofrotation matrices or the hypersphere $\mathbb{H}_1$ of quaternions, we treatthe orientation and translation jointly on the dual quaternion quadric in the7-dimensional real projective space $\mathbb{R}\mathbb{P}^7$. We provide anoutlier-robust IRLS algorithm for generic pose filtering exploiting thismanifold structure. Besides our theoretical analysis, our experiments onsynthetic and real data show the practical advantages of the manifold awarefiltering on pose tracking and smoothing.

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