title: Weighted fourier series representation and its application to quantifying the amount of gray matter.
abstract: 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 i n quantifying the amount ofgray matter in a group of high functioning autistic subjects. Within the WFS framework, cortical thickness and gray matter density are computed and compared.
authors.affiliation: Department of Statistics, Biostatistics, and Medical Informatics, and the Waisman Laboratory for Brain Imaging and Behavior, University of Wisconsin, Madison, WI 53706, USA. mchung@stat.wisc.edu
authors.forename: Moo K
authors.initials: MK
authors.lastname: Chung
authors.forename: Kim M
authors.initials: KM
authors.lastname: Dalton
authors.forename: Li
authors.initials: L
authors.lastname: Shen
authors.forename: Alan C
authors.initials: AC
authors.lastname: Evans
authors.forename: Richard J
authors.initials: RJ
authors.lastname: Davidson
mesh_terms: D000465:Algorithms; D001321:Autistic Disorder / Q000175:diagnosis*; D001921:Brain / Q000473:pathology*; D005583:Fourier Analysis; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D009474:Neurons / Q000473:pathology*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity