https://www.semortho.com/article/S1073-8746(95)80097-2/pdf

Selected aspects of the art and science of facial esthetics

Distance from symmetry: A three-dimensional evaluation of facial asymmetry

Perception of head orientation.

The effect of sex and age on facial asymmetry in healthy subjects: A cross-sectional study from adolescence to mid-adulthood

Soft-tissue facial asymmetry was studied in a group of 80 young healthy white Caucasian adults (40 men, 40 women) with no craniofacial, dental or mandibular disorders. For each subject, the 3-dimensional coordinates of 16 standardised soft-tissue facial landmarks (trichion, nasion, pronasale, subnasale, B point, pogonion, eye lateral canthi, nasal alae, labial commissures, tragi, gonia) were measured by infrared photogrammetry by an automated instrument. The form of the right and left hemifaces was assessed by calculating all the possible linear distances between pairs of landmarks within side. Side differences were tested by using euclidean distance matrix analysis. The mean faces of both groups were significantly asymmetric, i.e. the 2 sides of face showed significant differences in shape, but no differences in size.

A three-dimensional evaluation of human facial asymmetry.

Three-cycled Fourier equations are used in representing the frontal and lateral views of the human face. Fourier equations representing the general pattern of a group of individuals can also be obtained. The group pattern then represents the pattern characteristics common to all individuals. Difference in patterns may be represented by the difference between two Fourier equations. In the frontal view, the cosine terms measure the form of symmetry and the sine terms measure the form of asymmetry.

Lu Kh

Papers

Harmonic analysis of the human face.