Growth Models for Shape Data

• Activity Number: 286
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): John Kent*+ and Kanti Mardia and Richard Morris and Robert Aykroyd
• Affiliation(s): University of Leeds and University of Leeds and University of Leeds and University of Leeds
• Keywords: shape ; landmarks ; growth ; Procrustes ; principal warps

Abstract

We consider strategies to model the evolution of landmark-based shapes though time. In some ways this problem falls within the framework of longitudinal analysis for multivariate data. However, there are two extra features. Firstly, the shape of an object is invariant under changes in location, scale, and rotation, and this property must be incorporated into any models. Secondly, the landmarks lie in a Euclidean space (usually of dimension two or three), and any model of landmark evolution should be capable of being interpolated to yield a dynamic deformation of space. The most successful strategy has been to linearize the problem in Procrustes tangent space-to-shape-space and to use vector spaces of functions of space and time, respectively, to construct low-rank tensor product models. These vector spaces are generally built from either principal warps or polynomials in space and time. Assuming normal errors, these models can be easily fitted using maximum likelihood estimation.