Weighted Fourier series representation and its application to quantifying the amount of gray matter

Moo K. Chung, Kim M. Dalton, Li Shen, Alan C. Evans, Richard J. Davidson

Research output: Contribution to journalArticle

122 Scopus citations


We present a novel weighted Fourier series (WFS) representation for cortical surfaces. The WFS representation is a data smoothing technique that provides the explicit smooth functional estimation of unknown cortical boundary as a linear combination of basis functions. The basic properties of the representation are investigated in connection with a self-adjoint partial differential equation and the traditional spherical harmonic (SPHARM) representation. To reduce steep computational requirements, a new iterative residual fitting (IRF) algorithm is developed. Its computational and numerical implementation issues are discussed in detail. The computer codes are also available at http://www.stat.wisc.edu/~mchung/softwares/weighted-SPHARM/ weighted-SPHARM.html. As an illustration, the WFS is applied in quantifying the amount of gray matter in a group of high functioning autistic subjects. Within the WFS framework, cortical thickness and gray matter density are computed and compared.

Original languageEnglish (US)
Pages (from-to)566-581
Number of pages16
JournalIEEE Transactions on Medical Imaging
Issue number4
StatePublished - Apr 1 2007
Externally publishedYes


  • Cortical thickness
  • Diffusion smoothing
  • Gray matter density
  • Iterative residual fitting
  • Spherical harmonics

ASJC Scopus subject areas

  • Software
  • Radiological and Ultrasound Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering

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