Paper Info
Title
On The Geometry And Shape Of Brain Sub-Manifolds
Abstract
This paper develops mathematical representations for neuro-anatomically significant substructures of the brain and their variability in a population. The focus of the paper is an the neuro-anatomical variation of the geometry and the "shape" of two-dimensional surfaces in the brain. As examples, we focus on the cortical and hippocampal surfaces in an ensemble of Macaque monkeys and human MRI brains. The "shapes" of the substructures are quantified via the construction of templates; the variations are represented by defining probabilistic deformations of the template. Methods for empirically estimating probability measures on these deformations are developed by representing the deformations as Gaussian random vector fields on the embedded sub-manifolds. The Gaussian random vector fields are constructed as quadratic mean limits using complete orthonormal bases on the sub-manifolds. The complete orthonormal bases are generated using modes of vibrations of the geometries of the brain sub-manifolds. The covariances are empirically estimated from an ensemble of brain data. Principal component analysis is presented for characterizing the "eigen-shape" of the hippocampus in an ensemble of MRI-MPRAGE whole brain images. Clustering based on eigen-shape is presented for two sub-populations of normal and schizophrenic.
Year
DOI
Venue
1997
10.1142/S0218001497000615
INTERNATIONAL JOURNAL OF PATTERN RECOGNITION AND ARTIFICIAL INTELLIGENCE
Keywords
Field
DocType
medical imaging, pattern theory, deformable templates, computational anatomy
Population,Computational anatomy,Pattern theory,Probability measure,Multivariate random variable,Orthonormal basis,Gaussian,Geometry,Mathematics,Manifold
Journal
Volume
Issue
ISSN
11
8
0218-0014
Citations 
PageRank 
References 
62
11.07
4
Authors
3
Name
Order
Citations
PageRank
Sarang Joshi1775114.36
Michael I Miller23123422.82
Ulf Grenander330880.59