Statistical analysis of shape through triangulation of landmarks: A study of sexual dimorphism in hominids

Two objects with homologous landmarks are said to be of the same shape if the configuration of landmarks of one object can be exactly matched with that of the other by translation, rotation/reflection, and scaling. In an earlier paper, the authors proposed statistical analysis of shape by considering logarithmic differences of all possible Euclidean distances between landmarks. Tests of significance for differences in the shape of objects and methods of discrimination between populations were developed with such data. In the present paper, the corresponding statistical methodology is developed by triangulation of the landmarks and by considering the angles as natural measurements of shape. This method is applied to the study of sexual dimorphism in hominids.