Statistical Shape Analysis, 2nd Edition

7 Procrustes analysis

7.1 Introduction

This chapter outlines various methods based on Procrustes methods, which are very practical tools for analysing landmark data. Procrustes methods have earlier been seen to be useful for assessing distances between shapes in Chapter 3. In this chapter we provide a more comprehensive treatment of Procrustes methods suitable for two and higher dimensional shape analysis.

Procrustes methods are useful for estimating an average shape and for exploring the structure of shape variability in a dataset. The techniques described in this chapter are generally of a descriptive nature and more explicit emphasis on shape models and inference will be considered in Chapters 9 and 10.

Procrustes analysis involves matching configurations with similarity transformations to be as close as possible according to Euclidean distance, using least squares techniques. Procrustes analysis using orthogonal (rotation/reflection) matrices was developed initially for applications in psychology, and early papers on the topic appeared in the journal Psychometrika. The technique can be traced back to Boas (1905) and Mosier (1939) and later principal references include Green (1952); Cliff (1966); Schönemann (1966, 1968); Gruvaeus (1970); Schönemann and Carroll (1970); Gower (1971, 1975); Ten Berge (1977); Sibson (1978, 1979); Langron and Collins (1985); and Goodall (1991). In addition, Sneath (1967) considered a similar least squares matching procedure, with applications ...