Harmonic Analysis of the Human Face

Publisher Website
Google Scholar
Abstract
By appropriate choice of coordinates and plotting technique, the frontal view and profile of the human face may be viewed as single-valued curves defined over closed intervals. Each consists of a set of systematically unequal magnitude with a finite number of extrema and inflexion points. A least-squares fit by Fourier equations with 3 cycles, in the form [image] provides an efficient representation of the face. In the analysis of the frontal view, the matter of symmetry and asymmetry may be conveniently considered as a linear representation of cosine and sine functions. It can be shown that symmetry and asymmetry are orthogonally represented by the cosine and sine terms respectively. The analysis of 24 frontal cephalograms from boys of 4 to 6 years of age showed A, and A2 > 0, and A3 < 0. The magnitudes of the A''s may be used to describe various types of symmetry. The functions of [plus or minus] B1 sin 0 represent left and right asymmetry, and [plus or minus] B2 sin 2 0 represent left and right diagonal asymmetry. The analysis of 100 lateral cephalograms yield a general pattern of the profile as follows: A0, A3 and B1 > 0; A1, A2, B2 and B3 < 0. An individual''s facial changes through time may then be represented by successive sets of Fourier coefficients. The facial characteristic pattern of ethnic groups can also be extracted by computing group Fourier coefficients. The difference between group patterns can be obtained directly by the difference of 2 group Fourier equations. The resultant equation is by definition also a Fourier equation.

This publication has 0 references indexed in Scilit: