We consider a space-time finite element discretization of a time-dependent nonlinear hyperbolic conservation law in one space dimension (Burgers' equation). The finite element method is higher-order accurate and is a Petrov-Galerkin method based on the so-called streamline diffusion modification of the test functions giving added stability. We first prove that if a sequence of finite element so...

Introduction A great deal of recent research in diffusion MRI has focussed on improved modelling and reconstruction of multiple white matter fibre orientations within single image voxels. These methods are typically used to create an orientation distribution function (ODF) at each voxel, which represents the orientations of each fibre population crossing the voxel. However, very little attentio...

Many computer aided diagnosis (CAD) schemes have been developed for colon cancer detection using Virtual Colonoscopy (VC). In earlier work, we developed an automatic polyp detection method integrating flow visualization techniques, that forms part of the CAD functionality of an existing Virtual Colonoscopy pipeline. Curvature streamlines were used to characterize polyp surface shape. Features d...

We propose a new clustering algorithm. This algorithm performs clustering and manifold learning simultaneously by using a graph-theoretical approach to manifold learning. We apply this algorithm in order to cluster white matter fiber tracts obtained from Diffusion Tensor MRI (DT-MRI) through streamline tractography. Our algorithm is able perform clustering of these fiber tracts incorporating in...

We present a fiber tractography approach based on a random forest classification and voting process, guiding each step of the streamline progression by directly processing raw diffusion-weighted signal intensities. For comparison to the state-of-the-art, i.e. tractography pipelines that rely on mathematical modeling, we performed a quantitative and qualitative evaluation with multiple phantom a...

The radiative transfer equation can be utilized in optical tomography in situations in which the more commonly applied diffusion approximation is not valid. In this paper, an image reconstruction method based on a frequency domain radiative transfer equation is developed. The approach is based on a total variation output regularized least squares method which is solved with a Gauss–Newton algor...

We present a Fourier analysis of multigrid for the two-dimensional discrete convection-diffusion equation. For constant coefficient problems with grid-aligned flow and semi-periodic boundary conditions, we show that the two-grid iteration matrix can be reduced via a set of orthogonal transformations to a matrix containing individual 4×4 blocks. This enables a trivial computation of the norm of ...

Streamline visualization can be formulated as the problem of streamline placement or streamline selection. In this paper, we present an importance-driven approach to view-dependent streamline selection that guarantees coherent streamline update when the view changes gradually. Given a large number of randomly or uniformly seeded and traced streamlines and sample viewpoints, our approach evaluat...

The aim of this article is to shows that hierarchical matrices (H-matrices) provide a means to efficiently precondition linear systems arising from the streamline diffusion finite-element method applied to convection-dominated problems. Approximate inverses and approximate LU decompositions can be computed with logarithmic-linear complexity in the standard Hmatrix format. Neither the complexity...