B1381
Title: Analysis of variability in three-dimensional curves: Development of a generative model
Authors: Perrine Chassat - LaMME, Université Paris-Saclay, CNRS (France) [presenting]
Juhyun Park - ENSIIE (France)
Nicolas Brunel - ENSIIE (France)
Abstract: Current advanced signal recording techniques offer new data as multidimensional functional observations, such as human motion trajectories. Developing generative models for multidimensional curves is an important task in statistical functional analysis. These models must consider the geometric characteristics inherent to these multidimensional curves and thus differ from classical approaches developed for scalar functional data. Two types of variation play a key role in characterizing multidimensional curves: parametrisation (or time) variability and shape variability. We identify these two variations using a method based on the geometric representation of curves by the Frenet-Serret equations, defining the mean and variations within a set of curves through the mean of functional parameters characterising geometry, velocity, and their non-linear transformations. Inspired by generative models of scalar functional data considering phase and amplitude variations, we analyse the non-linear variations in time and geometry by functional PCA. Completing with classical PCA of the curves' initial positions in Euclidean space and an extended PCA on manifolds of the initial orientations, we develop a generative model by imposing a joint probability model on the principal coefficients of these PCA components. We apply this method to develop a realistic generative model of three-dimensional wrist movement trajectories in sign language from a real data set.
