Tensor-Based Cortical Surface Morphometry via Weighted Spherical Harmonic Representation

• Published in: IEEE transactions on medical imaging Vol. 27; no. 8; pp. 1143 - 1151
• Main Authors: Chung, M.K., Dalton, K.M., Davidson, R.J.
• Format: Journal Article
• Language: English
• Published: United States IEEE 01-08-2008; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Atrophy; Autism; Biomedical informatics; Brain; Brain - anatomy & histology; Cortical surface; Humans; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Imaging, Three-Dimensional - methods; Jacobian matrices; Least squares approximation; Magnetic Resonance Imaging - methods; Reproducibility of Results; Sensitivity and Specificity; Shape; spherical harmonic (SPHARM); Surface morphology; Tensile stress; tensor-based morphometry; Thickness measurement; spherical harmonics; tensor-based morphometry; SPHARM; cortical surface
• ISSN: 0278-0062; 1558-254X
• DOI: 10.1109/TMI.2008.918338

We present a new tensor-based morphometric framework that quantifies cortical shape variations using a local area element. The local area element is computed from the Riemannian metric tensors, which are obtained from the smooth functional parametrization of a cortical mesh. For the smooth parametrization, we have developed a novel weighted spherical harmonic (SPHARM) representation, which generalizes the traditional SPHARM as a special case. For a specific choice of weights, the weighted-SPHARM is shown to be the least squares approximation to the solution of an isotropic heat diffusion on a unit sphere. The main aims of this paper are to present the weighted-SPHARM and to show how it can be used in the tensor-based morphometry. As an illustration, the methodology has been applied in the problem of detecting abnormal cortical regions in the group of high functioning autistic subjects.