Tim McGraw

Fiber tract mapping from diffusion tensor MRI

To understand evolving pathology in the central nervous system (CNS) and develop effective treatments, it is essential to correlate the nerve fiber connectivity with the visualization of function. Diffusion tensor imaging (DTI) can provide the fundamental information required for viewing structural connectivity. We present a novel algorithm for automatic fiber tract mapping in the CNS specifically, the spinal cord. The automatic fiber tract mapping problem is solved in two phases, namely a data smoothing phase and a fiber tract mapping phase. In the former, smoothing is achieved via a new weighted total variation (TV)-norm minimization (for vector-valued data) which strives to smooth while retaining all relevant detail. For the fiber tract mapping, a smooth 3D vector field indicating the dominant anisotropic direction at each spatial location is computed from the smoothed data. Fiber tracts are then determined as the smooth integral curves of this vector field in a variational framework.

DT-MRI denoising and neuronal fiber tracking.

Diffusion tensor imaging can provide the fundamental information required for viewing structural connectivity. However, robust and accurate acquisition and processing algorithms are needed to accurately map the nerve connectivity. In this paper, we present a novel algorithm for extracting and visualizing the fiber tracts in the CNS, specifically in the brain. The automatic fiber tract mapping problem will be solved in two phases, namely a data smoothing phase and a fiber tract mapping phase. In the former, smoothing of the diffusion-weighted data (prior to tensor calculation) is achieved via a weighted TV-norm minimization, which strives to smooth while retaining all relevant detail. For the fiber tract mapping, a smooth 3D vector field indicating the dominant anisotropic direction at each spatial location is computed from the smoothed data. Neuronal fibers are then traced by calculating the integral curves of this vector field. Results are expressed using three modes of visualization: (1) Line integral convolution produces an oriented texture which shows fiber pathways in a planar slice of the data. (2) A streamtube map is generated to present a 3D view of fiber tracts. Additional information, such as degree of anisotropy, can be encoded in the tube radius, or by using color. (3) A particle system form of visualization is also presented. This mode of display allows for interactive exploration of fiber connectivity with no additional preprocessing.

von Mises-Fisher mixture model of the diffusion ODF

High angular resolution diffusion imaging (HARDI) permits the computation of water molecule displacement probabilities over the sphere. This probability is often referred to as the orientation distribution function (ODF). In this paper we present a novel model for representing this diffusion ODF namely, 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

Segmentation of high angular resolution diffusion MRI modeled as a field of von mises-fisher mixtures

High angular resolution diffusion imaging (HARDI) permits the computation of water molecule displacement probabilities over a sphere of possible displacement directions. This probability is often referred to as the orientation distribution function (ODF). In this paper we present a novel model for the diffusion ODF namely, a mixture of von Mises-Fisher (vMF) distributions. Our model is compact in that it requires very few variables to model complicated ODF geometries which occur specifically in the presence of heterogeneous nerve fiber orientation. We also present a Riemannian geometric framework for computing intrinsic distances, in closed-form, and performing interpolation between ODFs represented by vMF mixtures. As an example, we apply the intrinsic distance within a hidden Markov measure field segmentation scheme. We present results of this segmentation for HARDI images of rat spinal cords – which show distinct regions within both the white and gray matter. It should be noted that such a fine level of parcellation of the gray and white matter cannot be obtained either from contrast MRI scans or Diffusion Tensor MRI scans. We validate the segmentation algorithm by applying it to synthetic data sets where the ground truth is known.

Line Integral Convolution for Visualization of Fiber Tract Maps from DTI

Diffusion tensor imaging (DTI) can provide the fundamental information required for viewing structural connectivity. However, robust and accurate acquisition and processing algorithms are needed to accurately map the nerve connectivity. In this paper, we present a novel algorithm for extracting and visualizing the fiber tracts in the CNS specifically, the spinal cord. The automatic fiber tract mapping problem will be solved in two phases, namely a data smoothing phase and a fiber tract mapping phase. In the former, smoothing is achieved via a weighted TV-norm minimization which strives to smooth while retaining all relevant detail. For the fiber tract mapping, a smooth 3D vector field indicating the dominant anisotropic direction at each spatial location is computed from the smoothed data. Visualization of the fiber tracts is achieved by adapting a known Computer Graphics technique called the line integral convolution, which has the advantage of being able to cope with singularities in the vector field and is a resolution independent way of visualizing the 3D vector field corresponding to the dominant eigen vectors of the diffusion tensor field. Examples are presented to depict the performance of the visualization scheme on three DT-MR data sets, one from a normal and another from an injured rat spinal cord and a third from a rat brain.

Automatic fiber tractography from DTI and its validation

To understand evolving pathology in the central nervous system (CNS) and develop effective treatments, it is essential to correlate the nerve fiber connectivity with the visualization of function. Such information is fundamental in CNS processes since anatomical connections determine where information is passed and processed Diffusion tensor imaging (DTI) can provide the fundamental information required for viewing structural connectivity. However robust and accurate acquisition and processing algorithms are needed to accurately map the nerve connectivity. In this paper we present a novel, algorithm for automatic fiber tract mapping in the CNS specifically, a rat spinal cord as well as validate the mapped fibers using ex-vivo fluoro images of the excised rat. The novelty of our work lies in the fiber tract mapping as well as the validation experiment. The automatic fiber tract mapping problem will be solved in two phases, namely a data smoothing phase and a fiber tract mapping phase. In the former smoothing is achieved via a new weighted TV-norm minimization which strives to smooth while retaining all relevant detail. For the fiber tract mapping, a smooth 3D vector field indicating the dominant anisotropic direction at each spatial location is computed from the smoothed data. Fiber tracts are then determined as the smooth integral curves of this vector field in a variational framework Examples are presented for DTI data sets from a normal and injured rat spinal cords respectively.

Fast Bokeh effects using low-rank linear filters

We present a method for faster and more flexible approximation of camera defocus effects given a focused image of a virtual scene and depth map. Our method leverages the advantages of low-rank linear filtering by reducing the problem of 2D convolution to multiple 1D convolutions, which significantly reduces the computational complexity of the filtering operation. In the case of rank 1 filters (e.g., the box filter and Gaussian filter), the kernel is described as ‘separable’ since it can be implemented as a horizontal 1D convolution followed by a 1D vertical convolution. While many filter kernels which result in bokeh effects cannot be approximated closely by separable kernels, they can be effectively approximated by low-rank kernels. We demonstrate the speed and flexibility of low-rank filters by applying them to image blurring, tilt-shift postprocessing, and depth-of-field simulation, and also analyze the approximation error for several aperture shapes.

Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators

The challenge of tensor field visualization is to provide simple and comprehensible representations of data which vary both directionally and spatially. We explore the use of differential operators to extract features from tensor fields. These features can be used to generate skeleton representations of the data that accurately characterize the global field structure. Previously, vector field operators such as gradient, divergence, and curl have previously been used to visualize of flow fields. In this paper, we use generalizations of these operators to locate and classify tensor field degenerate points and to partition the field into regions of homogeneous behavior. We describe the implementation of our feature extraction and demonstrate our new techniques on synthetic data sets of order 2, 3 and 4.

Generalized reaction-diffusion textures

We present a method of synthesizing textures based on a modified reaction-diffusion equation. A non-Gaussian model of diffusion is employed to make a new class of textures possible. Whereas the Gaussian diffusion model is characterized by its covariance matrix (a rank-2 tensor), the generalized model of diffusion is characterized by a sequence of tensors of increasing rank which represent higher-order moments of the diffusion displacement probability. A numerical method of solving the new reaction-diffusion equation is described, as well as representative textures generated by this technique. The resulting patterns are inorganic in nature, often featuring sharp corners. The generalized reaction-diffusion textures display spatial inhomogeneity, even when the diffusion process is homogeneous, making it possible to generate complex textures from few parameters when compared with previous techniques employing inhomogeneous reaction-diffusion. The preferred orientations depend on the tensor sequence, and can be inspected prior to texture generation by plotting the non-Gaussian diffusion propagator.

Graph-Based Visualization of Neuronal Connectivity Using Matrix Block Partitioning and Edge Bundling

Neuronal connectivity matrices contain information vital to the understanding of brain structure and function. In this work we present graph-based visualization techniques for macroscale connectivity matrices that retain anatomical context while reducing the clutter and occlusion problems that plague 2D and 3D node-link diagrams. By partitioning the connectivity matrix into blocks corresponding to brain hemispheres and bundling graph edges we are able to generate intuitive visualizations that permit investigation at multiple scales (hemisphere, lobe, anatomical region). We demonstrate our approach on connectivity matrices computed using tractography of high angular resolution diffusion images acquired as part of a Parkinson’s disease study.