scholarly journals Clustering of Gaussian Random Vector Fields in Multiple Trajectory Modelling

2018 ◽  
Author(s):  
Miguel Barao ◽  
Jorge S. Marques
Keyword(s):  
Random Vector ◽  
Vector Fields ◽  
Gaussian Random Vector ◽  
Trajectory Modelling

On the Geometry and Shape of Brain Sub-Manifolds

1997 ◽  
Vol 11 (08) ◽  
pp. 1317-1343 ◽  
Author(s):  
Sarang C. Joshi ◽  
Michael I. Miller ◽  
Ulf Grenander
Keyword(s):  
Random Vector ◽  
Vector Fields ◽  
Anatomical Variation ◽  
Principal Component ◽  
Brain Images ◽  
Quadratic Mean ◽  
Orthonormal Bases ◽  
Gaussian Random Vector ◽  
Brain Data ◽  
The Brain

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 on 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.

Randomized Spectral and Fourier-Wavelet Methods for multidimensional Gaussian random vector fields

2013 ◽  
Vol 245 ◽  
pp. 218-234 ◽  
Author(s):  
Orazgeldi Kurbanmuradov ◽  
Karl Sabelfeld ◽  
Peter R. Kramer
Keyword(s):  
Random Vector ◽  
Vector Fields ◽  
Gaussian Random Vector ◽  
Wavelet Methods

A Lévy Based Approach to Random Vector Fields: With a View Towards Turbulence

2014 ◽  
Vol 15 (7-8) ◽  
Author(s):  
Emil Hedevang ◽  
Jürgen Schmiegel
Keyword(s):  
Random Vector ◽  
Vector Fields ◽  
Vector Valued ◽  
Deterministic Matrix

AbstractUsing integration of deterministic, matrix-valued functions with respect to vector-valued, volatility modulated Lévy bases, we construct random vector fields on

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