title: Fourier analysis of human soft tissue facial shape: sex differences in normal adults.
abstract: Sexual dimorphism in human facial form involves both size and shape variations of the soft tissue structures. These variations are conventionally appreciated using linear and angular measurements, as well as ratios, taken from photographs or radiographs. Unfortunately this metric approach provides adequate quantitative information about size only, eluding the problems of shape definition. Mathematical methods such as the Fourier series allow a correct quantitative analysis of shape and of its changes. A method for the reconstruction of outlines starting from selected landmarks and for their Fourier analysis has been developed, and applied to analyse sex differences in shape of the soft tissue facial contour in a group of healthy young adults. When standardised for size, no sex differences were found between both cosine and sine coefficients of the Fourier series expansion. This shape similarity was largely overwhelmed by the very evident size differences and it could be measured only using the proper mathematical methods.
authors.affiliation: Laboratorio di Anatomia Funzionale dell'Apparato Stomatognatico, Istituto di Anatomia Umana Normale, Facoltà di Medicina e Chirurgia, Università degli Studi di Milano, Italy.
authors.forename: V F
authors.initials: VF
authors.lastname: Ferrario
authors.forename: C
authors.initials: C
authors.lastname: Sforza
authors.forename: J H
authors.initials: JH
authors.lastname: Schmitz
authors.forename: A
authors.initials: A
authors.lastname: Miani
authors.forename: G
authors.initials: G
authors.lastname: Taroni
mesh_terms: D000328:Adult; D001699:Biometry; D003238:Connective Tissue / Q000033:anatomy & histology*; D005145:Face / Q000033:anatomy & histology*; D005260:Female; D005583:Fourier Analysis; D006801:Humans; D008297:Male; D012727:Sex Characteristics