The Morphometric Synthesis for landmarks and edge-elements in images

Abstract

Over the last decade, techniques from mathematical statistics, multivariate biometrics, non-Euclidean geometry, and computer graphics have been combined in a coherent new system of tools for the biometric analysis of landmarks , or labelled points, along with the biological images in which they are seen. Multivariate analyses of samples for all the usual scientific purposes - description of mean shapes, of shape variation, and of the covariation of shape with size, group, or other causes or effects - may be carried out very effectively in the tangent space to David Kendall's shape space at the Procrustes average shape. For biometric interpretation of such analyses, we need a basis for the tangent space that is Procrustes-orthonormal, and we need graphics for visualizing mean shape differences and other segments and vectors there; both of these needs are managed by the thin-plate spline. The spline also links the biometrics of landmarks to deformation analysis of curves in the images from which the landmarks originally arose. This article reviews the principal tools of this synthesis in a typical study design involving landmarks and edge information from a microfossil.