Riemannian Time Warping: Multiple Sequence Alignment in Curved Spaces

TL;DR

This paper introduces Riemannian Time Warping (RTW), a novel method for aligning multiple signals on Riemannian manifolds, outperforming existing Euclidean-based techniques in robotics and signal processing applications.

Contribution

The paper extends time warping techniques to Riemannian manifolds, enabling more accurate alignment of data in curved spaces, which was previously limited to Euclidean settings.

Findings

RTW outperforms state-of-the-art baselines in synthetic data tasks.

RTW achieves superior results in real-world robot motion data.

The method effectively handles data on curved Riemannian spaces.

Abstract

Temporal alignment of multiple signals through time warping is crucial in many fields, such as classification within speech recognition or robot motion learning. Almost all related works are limited to data in Euclidean space. Although an attempt was made in 2011 to adapt this concept to unit quaternions, a general extension to Riemannian manifolds remains absent. Given its importance for numerous applications in robotics and beyond, we introduce Riemannian Time Warping (RTW). This novel approach efficiently aligns multiple signals by considering the geometric structure of the Riemannian manifold in which the data is embedded. Extensive experiments on synthetic and real-world data, including tests with an LBR iiwa robot, demonstrate that RTW consistently outperforms state-of-the-art baselines in both averaging and classification tasks.