Riemannian Lp Averaging on Lie Group of Nonzero Quaternions

This paper discusses quaternion Lp geometric weighting averaging working on the multiplicative Lie group of nonzero quaternions H∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{H}^{*}}$$\end{document}, endowed with its natural bi-invariant Riemannian metric. Algorithms for computing the Riemannian Lp center of mass of a set of points, with 1≤p≤∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${1 \leq p \leq \infty}$$\end{document} (i.e., median, mean, Lp barycenter and minimax center), are particularized to the case of H∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{H}^{*}}$$\end{document}.