Bridging geometric morphometrics to medical anatomy: An example from an experimental study of the human smile

The method of Cartesian transformations introduced by D’Arcy Thompson a century ago in his celebrated book On Growth and Form precipitated an important development in 20th-century biometrics: a fusion of the geometrical and biological approaches to morphology. Some decades later this fusion, in turn, spun off another multidisciplinary focus, statistical shape analysis, that bridges between biostatistics and biomedical imaging. Our article is intended to seed a complementary focus: a bridge between biostatistics and medical anatomy, a field that has to this day remained mainly verbal rather than quantitative. Specifically, we are proposing a novel methodology for arriving at anatomical interpretations of statistical findings about large-scale contrasts of organismal morphology or its dynamics by combining two toolkits hitherto separate in their notation and their disciplinary housing: morphometrics and psychometrics. A contemporary morphometric analysis deals with patterns of shape coordinate covariation in terms of their geometric adjacency; psychometric factor analysis, the same patterns of covariation in terms of simplicity of interpretation. By combining these tools we account for the dynamics of a facial expression in terms of the actions of the underlying muscles, thereby realizing Thompson’s original metaphor, the “origins of form in force,” for systems that “vary in a more or less uniform manner.”

This paper reviews the history of Thompson’s metaphor and then the current literature quantifying smiles, in order to set the stage for the combination of scaling analysis and factor analysis that we are putting forward. We demonstrate the new approach by reanalyzing a data set of ten landmarks around the vermilion borders of the human lip contrasting the dynamics of two socially stereotyped physiological cycles, the open-lip smile and the closed-lip smile, over a sample of 14 normal faces. Our analysis centers on just two dimensions of statistical shape space, those of largest geometrical scale, which can be identified with the action of two different muscles, orbicularis oris and zygomaticus major. The two smiles differ radically in their achieved deformations. Furthermore, while the closed-lip smiles arrived at their final forms along similar shape trajectories, the open-lip smiles did not. Our closing discussion explores some aspects of morphodynamics that are illuminated by the example here.