Geometric morphometrics and the analysis of variations in facial form: robusticity of biological findings in relation to bilateral versus unilateral and missing landmarks

Abstract

This paper reviews some recent advances in the analysis of form variability amongst objects described in terms of landmark configurations. Emphasis is given to the methods of geometric morphometrics that utilise the geometry of Kendall's shape space. This space has well understood and desirable statistical properties. Geometric morphometric methods preserve the geometry of the landmark configurations at every step of analysis and so enable ready visualisation of statistical findings. The methods are illustrated by reference to two example analyses of biological shape variability within growth series of facial skeletons. The first is a study of growth and sexual dimorphism in monkeys and the second is a study of human facial growth. Since the material is biological it is to be expected that its morphogenesis generates correlations amongst landmarks. Thus, the face is bilateral symmetrical, with bilateral as opposed to unilateral landmarks likely contributing little new information about underlying patterns of growth. Further, any one landmark is unlikely to be sited on a region that shows a completely uncorrelated pattern of a variation with the regions on which the other landmarks are sited. This paper investigates the effects of using bilateral as opposed to unilateral landmarks, and of missing landmarks, on the ultimate biological interpretation of analyses. Our empirical findings in these studies to indeed indicate considerable stability of biological findings when diverse landmark sets are chosen. These findings reflect on the degree of morphological integration amongst diverse anatomical regions in the face.