Canonical and principal components of shape

Abstract

Canonical components of shape, discriminant functions of shape and principal components of shape are defined from log shape vectors. Several results relate these components to the corresponding components of log measurement and to a particular size variable referred to as residual log size. The latter variable accounts for the variation which cannot be attributed to shape. Canonical components of shape are determined for Anderson's data for three species of iris, as well as for data on red-winged blackbirds in Florida. While the three species differ strongly in shape as well as in size, male and female blackbirds differ strongly in size but not much in shape. Principal components of shape are illustrated with the blackbird data and the most constant principal component is found to be interesting.