A functional spatio-temporal model for geometric shape analysis

Abstract

In this chapter we consider a functional spatio-temporal model for shape objects represented by landmark data. The model describes a time-varying deformation of the ambient space in which the objects of interest lie. The use of basis functions, defined by principal warps in space and time, facilitates both the model specification and the fitting of the data in Procrustes tangent coordinates. The fitted model can be interpreted either just in terms of the finite set of landmarks at the given set of time points, or in terms of a deformation of the space which varies continuously in time. The method is illustrated on a facial expression dataset.