Abstract-Any sufficiently smooth, positive, real-valued function ψ : S(2) → K+ on a sphere S(2) 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.

High-angular resolution diffusion imaging (HARDI) is a diffusion weighted MRI technique that overcomes some of the decisive limitations of its predecessor, diffusion tensor imaging (DTI), in the areas of composite nerve fiber structure. Despite its advantages, HARDI raises several issues: complex modeling of the data, nonintuitive and computationally demanding visualization, inability to interactively explore and transform the data, etc. To overcome these drawbacks, we present a novel, multifield visualization framework that adopts the benefits of both DTI and HARDI. By applying a classification scheme based on HARDI anisotropy measures, the most suitable model per imaging voxel is automatically chosen. This classification allows simplification of the data in areas with single fiber bundle coherence. To accomplish fast and interactive visualization for both HARDI and DTI modalities, we exploit the capabilities of modern GPUs for glyph rendering and adopt DTI fiber tracking in suitable regions. The resulting framework, allows user-friendly data exploration of fused HARDI and DTI data. Many incorporated features such as sharpening, normalization, maxima enhancement and different types of color coding of the HARDI glyphs, simplify the data and enhance its features. We provide a qualitative user evaluation that shows the potentials of our visualization tools in several HARDI applications.

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.