Smiles and factor analysis: geometric morphometrics of some dynamic soft-tissue data

Fred Bookstein, University of Washington & University of Vienna. Part of the statistics seminars series.

As Charles Darwin himself knew, smiling is as fundamental an expression of emotion as anything observable across the higher primates.  Several recent papers from the applied anatomical and craniofacial literature apply geometric morphometrics to configurations of landmark points observed on the human face during the muscular cycle of ordinary smiling.  But hitherto these studies have not exploited the more advanced tools of this toolkit that combine Procrustes analysis with two other particularly powerful techniques of dynamic biometrical modeling.  One of these, the analysis of morphometric scaling, is previously known mainly from applications to evolutionary biology; the other, factor analysis, is borrowed here from a related methodology, psychometrics. Morphometric scaling deals with patterns of shape coordinate covariation in terms of their geometric adjacency; factor analysis, the same patterns of covariation in terms of simplicity of interpretation.  By combining these tools we can model the dynamics of a facial expression in terms of the actions of the otherwise unmeasured underlying muscles.  This paper reviews the current literature of Procrustes analysis of smiles and introduces the combination of scaling analysis and factor analysis that we are putting forward to replace it.  We demonstrate the new approach by reanalyzing a data set contrasting the dynamics of two socially stereotyped physiological cycles, the maximal (open-lip) smile and the closed-lip smile, over a sample of 14 normal faces.  A closing discussion focuses on some aspects of quantitative anatomical methodology that are illuminated by the example here.

This work in progress is joint with Kanti Mardia, John Kent, and Balvinder Khambay

Fred Bookstein, University of Washington & University of Vienna