Statistical Shape Analysis, 2nd Edition

18 Object data and manifolds

This final chapter contains some extensions to shape analysis, especially applications to object data and more general manifolds.

18.1 Object oriented data analysis

The techniques of shape analysis have natural extensions to other application areas. The very broad field of object oriented data analysis (OODA) is concerned with analysing different types of data objects compared with the conventional univariate or multivariate data. The concept of OODA was proposed by J.S. Marron. Examples of object data include functions, images, shapes, manifolds, dynamical systems, and trees. The main aims of shape analysis extend more generally to object data, for example defining a distance between objects, estimation of a mean, summarizing variability, reducing dimension to important components, specifying distributions of objects and carrying out hypothesis tests. From Marron and Alonso (2014) in any study an important consideration is to decide what are the atoms (most basic parts) of the data. A key question is ‘what should be the data objects?’, and the answer will then lead to appropriate methodology for statistical analysis. The subject is fast developing following initial definitions in Wang and Marron (2007), and a recent summary with discussion is given by Marron and Alonso (2014) with applications to Spanish human mortality functional data, shapes, trees and medical images.

One of the key aspects of object data analysis is that registration of the ...