B.M. ter Haar Romeny

Parameter Sensitivity Visualization for DTI Fiber Tracking

Fiber tracking of diffusion tensor imaging (DTI) data offers a unique insight into the three-dimensional organisation of white matter structures in the living brain. However, fiber tracking algorithms require a number of user-defined input parameters that strongly affect the output results. Usually the fiber tracking parameters are set once and are then re-used for several patient datasets. However, the stability of the chosen parameters is not evaluated and a small change in the parameter values can give very different results. The user remains completely unaware of such effects. Furthermore, it is difficult to reproduce output results between different users. We propose a visualization tool that allows the user to visually explore how small variations in parameter values affect the output of fiber tracking. With this knowledge the user cannot only assess the stability of commonly used parameter values but also evaluate in a more reliable way the output results between different patients. Existing tools do not provide such information. A small user evaluation of our tool has been done to show the potential of the technique.

Top-points as interest points for image matching

We consider the use of top-points for object retrieval. These points are based on scale-space and catastrophe theory, and are invariant under gray value scaling and offset as well as scale-Euclidean transformations. The differential properties and noise characteristics of these points are mathematically well understood. It is possible to retrieve the exact location of a top-point from any coarse estimation through a closed-form vector equation which only depends on local derivatives in the estimated point. All these properties make top-points highly suitable as anchor points for invariant matching schemes. By means of a set of repeatability experiments and receiver-operator-curves we demonstrate the performance of top-points and differential invariant features as image descriptors.

Analysis of distance/similarity measures for diffusion tensor imaging

Many different measures have been proposed to compute similarities and distances between diffusion tensors. These measures are commonly used for algorithms such as segmentation, registration, and quantitative analysis of Diffusion Tensor Imaging data sets. The results obtained from these algorithms are extremely dependent on the chosen measure. The measures presented in literature can be of complete different nature, and it is often difficult to predict the behavior of a given measure for a specific application. In this chapter, we classify and summarize the different measures that have been presented in literature. We also present a framework to analyze and compare the behavior of the measures according to several selected properties. We expect that this framework will help in the initial selection of a measure for a given application and to identify when the generation of a new measure is needed. This framework will also allow the comparison of new measures with existing ones.

Visualization of 4D Blood-Flow Fields by Spatiotemporal Hierarchical Clustering

Advancements in the acquisition and modeling of flow fields result in unsteady volumetric flow fields of unprecedented quality. An important example is found in the analysis of unsteady blood‐flow data. Preclinical research strives for a better understanding of correlations between the hemodynamics and the progression of cardiovascular diseases. Modern‐day computer models and MRI acquisition provide time‐resolved volumetric blood‐flow velocity fields. Unfortunately, these fields often remain unexplored, as high‐dimensional data are difficult to conceive. We present a spatiotemporal, i.e., four‐dimensional, hierarchical clustering, yielding a sparse representation of the velocity data. The clustering results underpin an illustrative visualization approach, facilitating visual analysis. The hierarchy allows an intuitive level‐of‐detail selection, largely retaining important flow patterns. The clustering employs dissimilarity measures to construct the hierarchy. We have adapted two existing measures for steady vector fields for use in the spacetime domain. Because of the inherent computational complexity of the multidimensional clustering, we introduce a coarse hierarchical clustering approach, which closely approximates the full hierarchy generation, and considerably improves the performance. The resulting clusters are visualized by representative patharrows, in combination with an illustrative anatomical context. We present various seeding approaches and visualization styles, providing sparse overviews of the unsteady behavior of volumetric flow fields.

A novel 3D multi-scale lineness filter for vessel detection

The branching pattern and geometry of coronary microvessels are of high interest to understand and model the blood flow distribution and the processes of contrast invasion, ischemic changes and repair in the heart in detail. Analysis is performed on high resolution, 3D volumes of the arterial microvasculature of entire goat hearts, which are acquired with an imaging cryomicrotome. Multi-scale vessel detection is an important step required for a detailed quantitative analysis of the coronary microvasculature. Based on visual inspection, the derived lineness filter shows promising results on real data and digital phantoms, on the way towards accurate computerized reconstructions of entire coronary trees. The novel lineness filter exploits the local first and second order multi-scale derivatives in order to give an intensity-independent response to line centers and to suppress unwanted responses to steep edges.

Fast and sleek glyph rendering for interactive HARDI data exploration

High angular resolution diffusion imaging (HARDI) is an emerging magnetic resonance imaging (MRI) technique that overcomes some decisive limitations of its predecessor diffusion tensor imaging (DTI). HARDI can resolve locally more than one direction in the diffusion pattern of water molecules and thereby opens up the opportunity to display and track crossing fibers. Showing the local structure of the reconstructed, angular probability profiles in a fast, detailed, and interactive way can improve the quality of the research in this area and help to move it into clinical application. In this paper we present a novel approach for HARDI glyph visualization or, more generally, for the visualization of any function that resides on a sphere and that can be expressed by a Laplace series. Our GPU-accelerated glyph rendering improves the performance of the traditional way of HARDI glyph visualization as well as the visual quality of the reconstructed data, thus offering interactive HARDI data exploration of the local structure of the white brain matter in-vivo. In this paper we exploit the capabilities of modern GPUs to overcome the large, processor-intensive and memory-consuming data visualization.

Stability of top-points in scale space

This paper presents an algorithm for computing stability of top-points in scale-space. The potential usefulness of top-points in scale-space has already been shown for a number of applications, such as image reconstruction and image retrieval. In order to improve results only reliable top-points should be used. The algorithm is based on perturbation theory and noise propagation.

GPU-Based Ray-Casting of Spherical Functions Applied to High Angular Resolution Diffusion Imaging

Abstract-Any sufficiently smooth, positive, real-valued function ψ : S2 → K+ on a sphere S2 can be expanded by a Laplace expansion into a sum of spherical harmonics. Given the Laplace expansion coefficients, we provide a CPU and GPU-based algorithm that renders the radial graph of ψ in a fast and efficient way by ray-casting the glyph of ψ in the fragment shader of a GPU. The proposed rendering algorithm has proven highly useful in the visualization of high angular resolution diffusion imaging (HARDI) data. Our implementation of the rendering algorithm can display simultaneously thousands of glyphs depicting the local diffusivity of water. The rendering is fast enough to allow for interactive manipulation of large HARDI data sets.

Multivalued geodesic ray-tracing for computing brain connections using diffusion tensor imaging

Diffusion tensor imaging (DTI) is a magnetic resonance technique used to explore anatomical fibrous structures, like brain white matter. Fiber-tracking methods use the diffusion tensor (DT) field to reconstruct the corresponding fibrous structure. A group of fiber-tracking methods trace geodesics on a Riemannian manifold whose metric is defined as a function of the DT. These methods are more robust to noise than more commonly used methods where just the main eigenvector of the DT is considered. Until now, geodesic-based methods were not able to resolve all geodesics, since they solved the Eikonal equation, and therefore were not able to deal with multivalued solutions. Our algorithm computes multivalued solutions using an Euler–Lagrange form of the geodesic equations. The multivalued solutions become relevant in regions with sharp anisotropy and complex geometries, or when the first arrival time does not describe the geodesic close to the anatomical fibrous structure. In this paper, we compare our algorit...

Using top-points as interest points for image matching

We consider the use of so-called top-points for object retrieval. These points are based on scale-space and catastrophe theory, and are invariant under gray value scaling and offset as well as scale-Euclidean transformations. The differential properties and noise characteristics of these points are mathematically well understood. It is possible to retrieve the exact location of a top-point from any coarse estimation through a closed-form vector equation which only depends on local derivatives in the estimated point. All these properties make top-points highly suitable as anchor points for invariant matching schemes. In a set of examples we show the excellent performance of top-points in an object retrieval task.