Abstract: Described here are a system and method for generating uniform antipodally symmetric point sets that define diffusion-weighting directions or three-dimensional radial k-space trajectories for magnetic resonance imaging. The point sets are generated robustly and efficiently using a constrained centroidal Voronoi tessellation endowed with a pseudometric. This pseudometric is derived from a measure of the electrostatic energy of points distributed on a hemispherical surface.

Abstract: Described here are a system and method for generating uniform antipodally symmetric point sets that define diffusion-weighting directions or three-dimensional radial k-space trajectories for magnetic resonance imaging. The point sets are generated robustly and efficiently using a constrained centroidal Voronoi tessellation endowed with a pseudometric. This pseudometric is derived from a measure of the electrostatic energy of points distributed on a hemispherical surface.

Abstract: A system and method for determining and ordering magnetic resonance imaging (MRI) acquisition parameters, such as k-space views or diffusion-weighting gradient directions, are provided. The MRI acquisition parameters are defined by generated points that are uniformly distributed on the surface of a sphere. These points may also be antipodally symmetric. The points are ordered by minimizing the electrostatic potential energy of different configurations of the points.

Abstract: A system and method for determining and ordering magnetic resonance imaging (MRI) acquisition parameters, such as k-space views or diffusion-weighting gradient directions, are provided. The MRI acquisition parameters are defined by generated points that are uniformly distributed on the surface of a sphere. These points may also be antipodally symmetric. The points are ordered by minimizing the electrostatic potential energy of different configurations of the points.

Abstract: A magnetic resonance imaging scanner acquires diffusion-weighted imaging data. A reconstruction engine reconstructs the acquired diffusion-weighted imaging data into diffusion-weighted image representations. A diffusion tensor engine constructs a diffusion tensor map of an area of an interest of a subject. An eigenvalue/eigenvector ordering engine obtains and orders eigenvectors and eigenvalues at each voxel. A covariance matrix determining engine constructs a covariance matrix of a major eigenvector of each voxel. A first normalized measure determining engine computes a first normalized measure. A second normalized measure determining engine computes a second normalized measure. A rendering engine generates a human-viewable display of an image representation.

Abstract: A magnetic resonance imaging scanner acquires diffusion-weighted imaging data. A reconstruction engine reconstructs the acquired diffusion-weighted imaging data into diffusion-weighted image representations. A diffusion tensor engine constructs a diffusion tensor map of an area of an interest of a subject. An eigenvalue/eigenvector ordering engine obtains and orders eigenvectors and eigenvalues at each voxel. A covariance matrix determining engine constructs a covariance matrix of a major eigenvector of each voxel. A first normalized measure determining engine computes a first normalized measure. A second normalized measure determining engine computes a second normalized measure. A rendering engine generates a human-viewable display of an image representation.