Tracking linear features through tensor field datasets is an open research problem with widespread utility in medical and engineering disciplines. Existing tracking methods, which consider only the preferred local diffusion direction as they propagate, fail to accurately follow features as they enter regions of local complexity. This shortcoming is a result of partial voluming; that is, voxels in these regions often contain contributions from multiple features. These combined contributions result in ambiguities when deciding local primary feature orientation based solely on the preferred diffusion direction. In this paper, we introduce a novel feature extraction method, which we term tensorline propagation. Our method resolves the above ambiguity by incorporating information about the nearby orientation of the feature, as well as the anisotropic classification of the local tensor. The nearby orientation information is added in the spirit of an advection term in a standard diffusionbased propagation technique, and has the effect of stabilizing the tracking. To demonstrate the efficacy of tensorlines, we apply this method to the neuroscience problem of tracking white-matter bundles within the brain.

Most direct volume renderings produced today employ onedimensional transfer functions, which assign color and opacity to the volume based solely on the single scalar quantity which comprises the dataset. Though they have not received widespread attention, multi-dimensional transfer functions are a very effective way to extract specific material boundaries and convey subtle surface properties. However, identifying good transfer functions is difficult enough in one dimension, let alone two or three dimensions. This paper demonstrates an important class of three-dimensional transfer functions for scalar data (based on data value, gradient magnitude, and a second directional derivative), and describes a set of direct manipulation widgets which make specifying such transfer functions intuitive and convenient. We also describe how to use modern graphics hardware to interactively render with multi-dimensional transfer functions. The transfer functions, widgets, and hardware combine to form a powerful system for interactive volume exploration.

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With the development of magnetic resonance imaging techniques for acquiring diffusion tensor data from biological tissue, visualization of tensor data has become a new research focus. The diffusion tensor describes the directional dependence of water molecules' diffusion and can be represented by a three-by-three symmetric matrix. Visualization of second-order tensor fields is difficult because the data values have many degrees of freedom. Existing visualization techniques are best at portraying the tensor's properties over a two-dimensional field, or over a small subset of locations within a three-dimensional field. A means of visualizing the global structure in measured diffusion tensor data is needed. We propose the use of direct volume rendering, with novel approaches for the tensors' coloring, lighting, and opacity assignment. Hueballs use a two-dimensional colormap on the unit sphere to illustrate the tensor's action as a linear operator. Lit-tensors provide a lighting model for tensors which includes as special cases both lit-lines (from streamline vector visualization) and standard Phong surface lighting. Together with an opacity assignment based on a novel two-dimensional barycentric space of anisotropy, these methods are shown to produce informative renderings of measured diffusion tensor data from the human brain.

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