Geometric morphometrics of human facial shape : a deformation perspective

Abstract

Introduction: Geometric morphometrics (GM) is concerned with statistical analysis of shape, which is the information encoded in all landmarks of an object except for location, size, and orientation. Local shape of an object can be quantified by estimating the deformation required to transform a reference configuration to an object. Quantification of facial shape locally contributes to a deeper understanding of the morphological architecture of human face by complementing current facial research which has been confined to analysis of face as an entirety. Aims: The work in this thesis aims to: (1) provide a comprehensive investigation of patterns of facial growth and development of the European and African population; (2) propose a novel measure of local shape incorporating information on both the magnitude and orientation of local deformation; (3) establish an atlas of hierarchical structural organisation of the human face and to investigate morphological and topographic properties of the resulting facial clusters. Methods: Two datasets comprising 3D facial images 2112 and 2874 individuals of European and African ancestry, respectively, were used to constructed facial growth and development trajectories through partial least-squares regression. Developmental changes of facial shape variation were investigated through generalised additive model and relative principal component analysis. A Riemannian distance-based measure of local shape was proposed, validated, and used to construct an atlas of hierarchical structural organisation of the human face. Modularity, integration, connectivity of the resulting clusters, as well as dominant gradients of facial structural connectome, were used to investigate properties of human facial morphology. Results: In Europeans, facial shape developed nonlinearly from 5 to 37 years of age, with the largest sexual dimorphism being the more pronounced nasal growth in males during 12-15 years of age. Variance of facial shape increased nonlinearly with age. In Africans, facial development from 6 to 18 years followed a linear pattern. Characteristic protrusive displacement of nasolabial and zygomatic regions were observed in both sexes. Facial proportions were developmentally constrained whereas nasolabial and mental regions were developmentally diversified. Hierarchical consensus clustering based on the Riemannian distance-based measure of local shape resulted in facial clusters strongly internally integrated and sparsely correlated among each other. An atlas of facial structural organisation containing two levels of hierarchy was established. At level 1, face was divided into four clusters, which were further divided to form nine clusters at level 2. The facial clusters were both modular and integrated. Structurally more complex regions such as the nose, mouth, and orbit exhibited lower levels of within- and between-cluster connectivity than the temporal, cheek, and maxillary region. The dominant gradient of facial structural connectome was anchored along a superior-inferior direction, which likely reflects variations in the degree to which facial structures are influenced by environmental factors. Conclusion: A deformation perspective of shape analysis led to the proposal of a novel measure of local shape. This allows for a topographic perspective to shape analysis and an investigation into the multi-scale architecture of face and other landmark configurations, which sets the stage for a new generation of research in GM.