Euclidean distance matrix analysis: a coordinate-free approach for comparing biological shapes using landmark data.

For problems of classification and comparison in biological research, the primary focus is on the similarity of forms. A biological form can be conveniently defined as consisting of size and shape. Several approaches for comparing biological shapes using landmark data are available. Lele (1991a) critically discusses these approaches and proposes a new method based on the Euclidean distance matrix representation of the form of an object. The purpose of this paper is to extend this new methodology to the comparison of groups of objects. We develop the statistical versions of various concepts introduced by Lele (1991a) and use them for developing statistical procedures for testing the hypothesis of shape difference between biological forms. We illustrate the use of this method by studying morphological differences between normal children and those affected with Crouzon and Apert syndromes and craniofacial sexual dimorphism in Cebus apella.