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

arXiv: https://arxiv.org/abs/1704.07072 · HTML: https://mlsanity.com/paper/1704.07072/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2017.

## Built on by (most cited first, 8 of 8)

- [ZebraPose: Coarse to Fine Surface Encoding for 6DoF Object Pose Estimation](https://mlsanity.com/paper/2203.09418/) (2022)
- [Attention meets Geometry: Geometry Guided Spatial-Temporal Attention for Consistent Self-Supervised Monocular Depth Estimation](https://mlsanity.com/paper/2110.08192/) (2021)
- [The Unreasonable Effectiveness of Pre-Trained Features for Camera Pose Refinement](https://mlsanity.com/paper/2404.10438/) (2024)
- [Chordal Averaging on Flag Manifolds and Its Applications](https://mlsanity.com/paper/2303.13501/) (2023)
- [Fun with Flags: Robust Principal Directions via Flag Manifolds](https://mlsanity.com/paper/2401.04071/) (2024)
- [Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)](https://mlsanity.com/paper/2508.07775/) (2025)
- [Alignist: CAD-Informed Orientation Distribution Estimation by Fusing Shape and Correspondences](https://mlsanity.com/paper/2409.06683/) (2024)
- [Continuous-Time SO(3) Forecasting with Savitzky--Golay Neural Controlled Differential Equations](https://mlsanity.com/paper/2506.06780/) (2025)

## Abstract (arXiv)

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 mathbbD mathbbH1. 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 SOleft(3right) of rotation matrices or the hypersphere mathbbH1 of quaternions, we treat the orientation and translation jointly on the dual quaternion quadric in the 7-dimensional real projective space ℝmathbbP7. We provide an outlier-robust IRLS algorithm for generic pose filtering exploiting this manifold structure. Besides our theoretical analysis, our experiments on synthetic and real data show the practical advantages of the manifold aware filtering on pose tracking and smoothing.