A1226
Title: Statistical analysis of trajectories of 3-dimensional object orientations
Authors: Lise Bellanger - Nantes University (France)
Margot Bornet - Nantes University (France)
Klervi Le Gall - Nantes University (France)
Nadia Negab - Nantes University (France)
Manon Simonot - Nantes University (France)
Aymeric Stamm - CNRS (France) [presenting]
Abstract: It is becoming increasingly frequent to measure a collection of trajectories of 3-dimensional object orientations in various fields such as robotics, tracking in video, health, etc. Orientation is mathematically expressed as a 3D rotation matrix. Various other representations can be used: Euler angles, axis-angle pairs and unit quaternions. The latter representation is often preferred as the most compact, avoiding the gimbal lock issue. Trajectories of 3D object orientations are, therefore, typically treated as unit quaternion time series. The aim is to present a comprehensive framework for the analysis of samples of unit quaternion time series, which unlocks the use of traditional statistical methods such as summary statistics, dimensionality reduction, supervised and unsupervised classification, prediction, etc. Specifically, unit quaternions belong to the special unitary group SU(2), which is a Lie group. As such, it is both a group and a differentiable Riemannian manifold. The latter property guarantees the existence of tangent spaces at each point of the manifold, onto which classical Euclidean geometry of vector spaces applies. Metrics are introduced with geometric invariance on tangent spaces and demonstrate the use of the framework to study and compare individual gait patterns.
