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IEEE Trans Med Imaging. 2007 Apr;26(4):566-81.

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

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Department of Statistics, Biostatistics, and Medical Informatics, and the Waisman Laboratory for Brain Imaging and Behavior, University of Wisconsin, Madison, WI 53706, USA.


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 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.

[Indexed for MEDLINE]

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