Sebastian Kurtek1, Eric Klassen2,
Anuj Srivastava1, Zhaohua Ding3,4, Sandra W. Jacobson5,
Joseph L. Jacobson5, Malcolm J. Avison3,4
1Department of Statistics, Florida
State University, Tallahassee, FL, United States; 2Department of
Mathematics, Florida State University, Tallahassee, FL, United States; 3Institute
of Imaging Science, Vanderbilt University, Nashville, TN, United States; 4Department
of Radiology and Radiological Sciences, Vanderbilt University, Nashville, TN,
United States; 5Department of Psychiatry and Behavioral
Neurosciences, Wayne State University School of Medicine, Detroit, MI, United
States
Shape
analysis of anatomical structures is central to medical diagnosis, especially
when using MRI data. We propose a novel Riemannian framework for analyzing
shapes of 3D brain substructures (e.g. putamen). This framework provides
metrics that are invariant to rigid motion, scaling and most importantly
parameterizations of surfaces (placements of meshes). The metric is evaluated
by a gradient-based alignment of meshes for the surfaces being compared.
Consequently, the distance between identical surfaces with different meshes
is zero. We present results of this methodology applied to comparisons of
left putamens across subjects and to classification of subjects with prenatal
exposure to alcohol.