Elliptic fourier analysis of mandibular shape

Virgilio F. Ferrario, Chiarella Sforza, Marco Guazzi, Graziano Serrao

Research output: Contribution to journalArticlepeer-review


Craniofacial growth and development involve both size and shape variations. Shape variations can be assessed independently from size using mathematical methods such as the elliptic Fourier analysis, which allows a global evaluation of the shape of organs identified by their outlines independently from size, spatial orientation, and relation to reference planes. The mandibular outlines were digitized from the tracings of the Bolton standards (lateral view) from 1 to 18 years of age, and the age differences in shape independently from size were quantified using the elliptic Fourier series. A 'morphologic distance' MD (i.e., a measurement of differences in shape) between each younger mandible and the oldest one was computed using the relevant Fourier coefficients like the cartesian coordinates in standard metric measurements. MD equals 0 when the profiles are identical. MD (Y) between the Bolton standard at 18 years of age and all the other Bolton tracings were significantly correlated (correlation coefficient r = 0.987, P ≤ 0.001) with age (X) (semilogarithmic interpolation Y = -3.87 log(e)̇ X + 13.593). Differences between the size-independent shape of the Bolton standard at 18 years and the relevant plot at 1 year were located at the chin, gonion, coronoid process, anterior border of the ramus. Size differences were measured from the areas enclosed by the mandibular outlines. Mandibular area (Y) increased about 2.58 times from 1 to 18 years of age (X) (Y = -0.071 X2 + 4.917̇X + 35.904, r = 0.997, P ≤ 0.001). The shape effect was largely overwhelmed by the very evident size increments, and it could be measured only using the proper mathematical methods. The method developed could also be applied to the comparison between healthy and diseased individuals.

Original languageEnglish
Pages (from-to)208-217
Number of pages10
JournalJournal of Craniofacial Genetics and Developmental Biology
Issue number4
Publication statusPublished - 1996


  • Cephalometrics
  • Development
  • Fourier series
  • Growth
  • Morphometry
  • Shape analysis

ASJC Scopus subject areas

  • Developmental Biology
  • Genetics


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