Anchored Spectral Estimator for Rigid Motion Synchronization

TL;DR

This paper introduces the anchored spectral estimator (ASE), a novel spectral method for rigid motion synchronization that outperforms existing approaches in accuracy and robustness across applications in signal processing, robotics, and computer vision.

Contribution

The paper develops ASE, a new spectral approach with theoretical error bounds, demonstrating improved performance over traditional two-stage methods in rigid motion synchronization.

Findings

ASE provides uniform estimation error bounds.

ASE outperforms two-stage approaches in experiments.

Numerical results show ASE's superiority in point-set registration.

Abstract

A rigid motion in $\mathbb{R}^d$ consists of a proper rotation and a translation, and it can be represented as a matrix in $\mathbb{R}^{(d+1)\times (d+1)}$. The problem of rigid motion synchronization aims to estimate a collection of rigid motions $G^*_1, \dots, G^*_n$ from noisy observations of their comparisons ${G^*_i}^{-1} G^*_j$. Such problems naturally arise in diverse applications across signal processing, robotics, and computer vision, and have thus attracted intense research attention in recent years. Motivated by geometric considerations, this paper develops a novel spectral approach for rigid motion synchronization, called the anchored spectral estimator (ASE). Theoretically, we establish uniform estimation error bounds for the estimators produced by ASE. Empirically, we show that ASE outperforms the widely used two-stage approach, which first estimates the rotations and then the translations. Further numerical experiments on the multiple point-set registration problem are presented to demonstrate the superiority of ASE over state-of-the-art methods.