Title: Means and Averaging in the Group of Rotations
Abstract:In this paper we give precise definitions of different, properly invariant notions of mean or average rotation. Each mean is associated with a metric in SO(3). The metric induced from the Frobenius in...In this paper we give precise definitions of different, properly invariant notions of mean or average rotation. Each mean is associated with a metric in SO(3). The metric induced from the Frobenius inner product gives rise to a mean rotation that is given by the closest special orthogonal matrix to the usual arithmetic mean of the given rotation matrices. The mean rotation associated with the intrinsic metric on SO(3) is the Riemannian center of mass of the given rotation matrices. We show that the Riemannian mean rotation shares many common features with the geometric mean of positive numbers and the geometric mean of positive Hermitian operators. We give some examples with closed-form solutions of both notions of mean.Read More
Publication Year: 2002
Publication Date: 2002-01-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 424
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot