A new dynamical model for solving rotation averaging problem

TL;DR

This paper introduces a novel dynamical system approach, generalizing the Kuramoto model on SO(3), to solve the rotation averaging problem efficiently, with validation against geometric averages on real and synthetic data.

Contribution

The paper proposes a new dynamical model for rotation averaging, extending the Kuramoto model to SO(3), and introduces algorithms that match geometric averages in accuracy.

Findings

The proposed method approximates geometric averages closely.

Validation on real and synthetic data confirms the method's effectiveness.

The model generalizes the Kuramoto model to non-Abelian groups.

Abstract

The paper analyzes the rotation averaging problem as a minimization problem for a potential function of the corresponding gradient system. This dynamical system is one generalization of the famous Kuramoto model on special orthogonal group SO(3), which is known as the non-Abelian Kuramoto model. We have proposed a novel method for finding weighted and unweighted rotation average. In order to verify the correctness of our algorithms, we have compared the simulation results with geometric and projected average using real and random data sets. In particular, we have discovered that our method gives approximately the same results as geometric average.