Fourier Analysis of Cephalometric Shapes

Abstract

Craniofacial growth and development involve both size and shape variations. Shape variations can be assessed independently from size using mathematical methods such as the Fourier series. A method for the reconstruction of outlines starting from selected landmarks and for their Fourier analysis has been developed and applied to analyze the age differences in shape in the tracings of the Bolton standards (lateral view) from 1 to 18 years of age. The size-independent shape of the Bolton standard at 18 years was larger at the chin, at the gonion, and in the anterior cranial base than the shape at 1 year of age. Conversely, the younger shape was larger in the middle part of face, corresponding roughly to the maxillary bone, than the older shape. When standardized for size, growth thus seemed to modify craniofacial shape with progressive lengthening and narrowing. This shape effect was largely overwhelmed by the very evident size increments, and it could be measured only using the proper mathematical methods.