Statistics with a human face

Adrian Bowman
School of Mathematics & Statistics, University of Glasgow

Stereo-photogrammetry provides high-resolution data defining the shape of three-dimensional objects. One example of its application is in the study of facial shape, and indeed of other parts of human anatomy. One particular study aims to describe the facial shape and growth of healthy children and to contrast this with the shape and growth of children who have been born with a cleft lip and/or palate and who have subsequently undergone surgical repair. Information can be extracted in a variety of forms. Methods of analysing landmark shape data are well developed but landmarks alone clearly do not adequately represent the very much richer information present in each digitised face. Facial curves with clear anatomical meaning can be identified. In order to exploit the full extent of the information present in the images, standardised meshes, whose nodes correspond across individuals, can also be fitted. Some of the issues involved in identifying and analysing data of these types will be discussed and illustrated in a variety of surgical and other settings. Statistical issues include how to analyse data objects which express shape, how to measure asymmetry and how to conduct longitudinal modelling.