New scalar measures for diffusion-weighted MRI visualization are described which are based on operations of tensor calculus and have a connection to topological visualization. These operators are generalizations of the familiar divergence and curl operations in vector calculus, and
apply to tensors of arbitrary order. The computation is based on a generalization of the Helmholtz decomposition.
A novel variational formulation for restoring high angular resolution diffusion imaging (HARDI) data is described. The restoration formulation involves smoothing signal measurements over the spherical domain and across the 3D image lattice.
By exploiting the programmable vertex and fragment processors in modern GPUs the computation of ambient occlusion maps can be greatly accelerated.
Feature preserving continuous level-of-detail for terrain rendering.
Terrain features such as peaks, ridges, and valleys are preserved while terrain patches transition between levels-of-detail. Continuity along patch edges is enforced. The technique is accelerated on the GPU.
An efficient scheme for tensor field interpolation which is
inspired by subdivision surfaces in computer graphics. The method applies
to Cartesian tensors of all ranks and imposes smoothness on the
interpolated field by constraining the divergence and curl of the tensor
field.
By generalizing the equations governing anisotropic diffusion to obtain a non-Gaussian model a new
reaction-diffusion process can be simulated. The resulting textures are inorganic and feature a controllable
distribution of orientations, even when the diffusion process is homogeneous. A GPU implementation is described and timing results are presented.
A Bayesian formulation of the fiber model is presented
and it is shown that the inversion method can be used to construct plausible connectivity. An implementation
of the fiber model on the graphics processing unit (GPU) is presented. Since the fiber paths can be stochastically generated independently of one another, the algorithm is highly parallelizable. This allows us to exploit the data-parallel nature of the GPU fragment processors. We also present a framework for the connectivity computation
on the GPU.
Animation, color, intensity and texture properties such as frequency and orientation can be used to convey
tensor anisotropy, mean diffusivity and principal diffusion direction.
We present a novel model for representing the diffusion ODF: a mixture of von Mises-Fisher (vMF) distributions. Our model is compact in that it requires very few parameters to represent
complicated ODF geometries which occur specifically in the presence of heterogeneous nerve fiber orientations. We present a Riemannian geometric framework for computing intrinsic distances (in closed-form) and for performing interpolation between ODFs represented by vMF mixtures. We also present closed-form equations for entropy and variance based anisotropy measures that are then computed and illustrated for real HARDI data from a rat brain.
Tractography and visualization of diffusion tensor MRI.
We use line integral convolution, a texture-based visualization technique to visualize the diffusion tensor field.
This involves synthesizing a texture whose orientation is parallel with the dominant direction of diffusion. The hue of
the texture represents the direction of diffusion, and the intensity of the texture represents the fraction anisotropy
of the tensor field.
Also, streamtube, particle, and ellipsoid based visualizations are shown.
This technique works by scaling the control points of the Bezier patches. The scale factor can be computed as a function
of the volume ratio. Here we have used free-form deformations to twist, squeeze and bend the meshes. Based on a preprint
by Dr. Jorg Peters.
