Shape Analysis with Multivariate Tensor-based Morphometry and Holomorphic Differentials

Yalin Wang, Tony F. Chan, Arthur W. Toga and Paul M. Thompson

Abstract

Here we introduce multivariate tensor-based surface morphometry using holomorphic one-forms to study brain anatomy. We computed new statistics from the Riemannian metric tensors that retain the full information in the deformation tensor fields. We introduce two different holomorphic one-forms that induce different surface conformal parameterizations. We applied this framework to 3D MRI data to analyze hippocampal surface morphometry in Alzheimer's Disease (AD; 26 subjects), lateral ventricular surface morphometry in HIV/AIDS (19 subjects) and cortical surface morphometry in Williams Syndrome (WS; 80 subjects). Experimental results demonstrated that our method powerfully detected brain surface abnormalities. Multivariate statistics on the local tensors outperformed other TBM methods including analysis of the Jacobian determinant, the largest eigenvalue, or the pair of eigenvalues, of the surface Jacobian matrix.

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Related Publications

Wang Y, Zhang J, Gutman B, Chan TF, Becker JT, Aizenstein HJ, Lopez OL, Tamburo RJ, Toga AW, Thompson PM, Multivariate Tensor-based Morphometry on Surfaces: Application to Mapping Ventricular Abnormalities in HIV/AIDS, NeuroImage, 49, February 2010, pp. 2141-2157
Wang Y, Chan TF, Toga AW, Thompson PM, "Multivariate Tensor-based Brain Anatomical Surface Morphometry via Holomorphic One-Forms", 12th International Conference on Medical Image Computing and Computer Assisted Intervention - MICCAI 2009, London, UK, Sep. 2009, pp. 337-344