This paper describes an effort to create new visualizations by exploiting hierarchical scalar topology. First, we build a hierarchical topology through synchronously constructing and simplifying Contour Tree (CT) and Morse-Smale (MS) complex of scalar fields. We then introduce three algorithms based on the hierarchical topology: (1) topology-based multi-resolution contouring — an overview provided for a scalar field by extracting iso-values from the simplified CT and tracing approximate contours across the MS complex cells; (2) topology based spaghetti plots for uncertainty — a seeding scheme based on the hierarchical topology for visualizing uncertainty among ensemble scalar data; (3) virtual ribbons — a new scheme for visualizing multivariate data invented by overlapping visual ribbons which encode the scalar variation of a region covered by uniform contours. We compare the new approaches with current alternatives.

Abstract Precipitation forecast verification is essential to the quality of a forecast. The Gaussian mixture model (GMM) can be used to approximate the precipitation of several rain bands and provide a concise view of the data, which is especially useful for comparing forecast and observation data. The robustness of such comparison mainly depends on the consistency of and the correspondence between the extracted rain bands in the forecast and observation data. We propose a novel co‐estimation approach based on GMM in which forecast and observation data are analysed simultaneously. This approach naturally increases the consistency of and correspondence between the extracted rain bands by exploiting the similarity between both forecast and observation data. Moreover, a novel visualization and exploration framework is implemented to help the meteorologists gain insight from the forecast. The proposed approach was applied to the forecast and observation data provided by the China Meteorological Administration. The results are evaluated by meteorologists and novel insight has been gained.

This paper presents an efficient visualization and exploration approach for modeling and characterizing the relationships and uncertainties in the context of a multidimensional ensemble dataset. Its core is a novel dissimilarity-preserving projection technique that characterizes not only the relationships among the mean values of the ensemble data objects but also the relationships among the distributions of ensemble members. This uncertainty-aware projection scheme leads to an improved understanding of the intrinsic structure in an ensemble dataset. The analysis of the ensemble dataset is further augmented by a suite of visual encoding and exploration tools. Experimental results on both artificial and real-world datasets demonstrate the effectiveness of our approach.

Numerical weather prediction ensembles are routinely used for operational weather forecasting. The members of these ensembles are individual simulations with either slightly perturbed initial conditions or different model parameterizations, or occasionally both. Multi-member ensemble output is usually large, multivariate, and challenging to interpret interactively. Forecast meteorologists are interested in understanding the uncertainties associated with numerical weather prediction; specifically variability between the ensemble members. Currently, visualization of ensemble members is mostly accomplished through spaghetti plots of a single mid-troposphere pressure surface height contour. In order to explore new uncertainty visualization methods, the Weather Research and Forecasting (WRF) model was used to create a 48-hour, 18 member parameterization ensemble of the 13 March 1993 "Superstorm". A tool was designed to interactively explore the ensemble uncertainty of three important weather variables: water-vapor mixing ratio, perturbation potential temperature, and perturbation pressure. Uncertainty was quantified using individual ensemble member standard deviation, inter-quartile range, and the width of the 95% confidence interval. Bootstrapping was employed to overcome the dependence on normality in the uncertainty metrics. A coordinated view of ribbon and glyph-based uncertainty visualization, spaghetti plots, iso-pressure colormaps, and data transect plots was provided to two meteorologists for expert evaluation. They found it useful in assessing uncertainty in the data, especially in finding outliers in the ensemble run and therefore avoiding the WRF parameterizations that lead to these outliers. Additionally, the meteorologists could identify spatial regions where the uncertainty was significantly high, allowing for identification of poorly simulated storm environments and physical interpretation of these model issues.

This paper presents a new streamline placement algorithm that produces evenly spaced long streamlines while preserving topological features of a flow field. Singularities and separatrices are extracted to decompose the flow field into topological regions. In each region, a seeding path is selected from a set of streamlines integrated in the orthogonal flow field. The uniform sample points on this path are then used as seeds to generate streamlines in the original flow field. Additional seeds are placed where a large gap between adjacent streamlines occurs. The number of short streamlines is significantly reduced as evenly spaced long streamlines spawned along the seeding paths can fill the topological regions very well. Several metrics for evaluating streamline placement quality are discussed and applied to our method as well as some other approaches. Compared to previous work in uniform streamline placement, our method is more effective in creating evenly spaced long streamlines and preserving topological features. It has the potential to provide both intuitive perception of important flow characteristics and detail reconstruction across visually pleasing streamlines.

Diffusion tensor fields reveal the underlying anatomical structures in biological tissues such as neural fibers in the brain. Most current methods for visualizing the diffusion tensor field can be categorized into two classes: integral curves and glyphs. Integral curves are continuous and represent the underlying fiber structures, but are prone to integration error and loss of local information. Glyphs are useful for representing local tensor information, but do not convey the connectivity in the anatomical structures well. We introduce a simple yet effective visualization technique that extends the streamball method in flow visualization to tensor ellipsoids. Each tensor ellipsoid represents a local tensor, and either blends with neighboring tensors or breaks away from them depending on their orientations and anisotropies. The resulting visualization shows the connectivity information in the underlying anatomy while characterizing the local tenors in detail. By interactively changing an iso-value parameter, users can examine the diffusion tensor field in the entire spectrum between the continuous integral curves and the discrete glyphs. Expert evaluation indicates that this method conveys very useful visual information about local anisotropy in white matter fibers. Such information was previously unavailable in tractography models. Our method provides a visual tool for assessing variability in DTI fiber tract integrity and its relation to function.

Visual exploration is essential to the visualization and analysis of densely sampled 3D DTI fibers in biological specimens, due to the high geometric, spatial, and anatomical complexity of fiber tracts. Previous methods for DTI fiber visualization use zooming, color-mapping, selection, and abstraction to deliver the characteristics of the fibers. However, these schemes mainly focus on the optimization of visualization in the 3D space where cluttering and occlusion make grasping even a few thousand fibers difficult. This paper introduces a novel interaction method that augments the 3D visualization with a 2D representation containing a low-dimensional embedding of the DTI fibers. This embedding preserves the relationship between the fibers and removes the visual clutter that is inherent in 3D renderings of the fibers. This new interface allows the user to manipulate the DTI fibers as both 3D curves and 2D embedded points and easily compare or validate his or her results in both domains. The implementation of the framework is GPU based to achieve real-time interaction. The framework was applied to several tasks, and the results show that our method reduces the user's workload in recognizing 3D DTI fibers and permits quick and accurate DTI fiber selection.

Medical illustration has demonstrated its effectiveness to depict salient anatomical features while hiding the irrelevant details. Current solutions are ineffective for visualizing fibrous structures such as muscle, because typical datasets (CT or MRI) do not contain directional details. In this paper, we introduce a new muscle illustration approach that leverages diffusion tensor imaging (DTI) data and example-based texture synthesis techniques. Beginning with a volumetric diffusion tensor image, we reformulate it into a scalar field and an auxiliary guidance vector field to represent the structure and orientation of a muscle bundle. A muscle mask derived from the input diffusion tensor image is used to classify the muscle structure. The guidance vector field is further refined to remove noise and clarify structure. To simulate the internal appearance of the muscle, we propose a new two-dimensional example based solid texture synthesis algorithm that builds a solid texture constrained by the guidance vector field. Illustrating the constructed scalar field and solid texture efficiently highlights the global appearance of the muscle as well as the local shape and structure of the muscle fibers in an illustrative fashion. We have applied the proposed approach to five example datasets (four pig hearts and a pig leg), demonstrating plausible illustration and expressiveness.

Many techniques have been proposed to show uncertainty in data visualizations. However, very little is known about their effectiveness in conveying meaningful information. In this paper, we present a user study that evaluates the perception of uncertainty amongst four of the most commonly used techniques for visualizing uncertainty in one-dimensional and two-dimensional data. The techniques evaluated are traditional errorbars, scaled size of glyphs, color-mapping on glyphs, and color-mapping of uncertainty on the data surface. The study uses generated data that was designed to represent the systematic and random uncertainty components. Twenty-seven users performed two types of search tasks and two types of counting tasks on 1D and 2D datasets. The search tasks involved finding data points that were least or most uncertain. The counting tasks involved counting data features or uncertainty features. A 4x4 full-factorial ANOVA indicated a significant interaction between the techniques used and the type of tasks assigned for both datasets indicating that differences in performance between the four techniques depended on the type of task performed. Several one-way ANOVAs were computed to explore the simple main effects. Bonferronni's correction was used to control for the family-wise error rate for alpha-inflation. Although we did not find a consistent order among the four techniques for all the tasks, there are several findings from the study that we think are useful for uncertainty visualization design. We found a significant difference in user performance between searching for locations of high and searching for locations of low uncertainty. Errorbars consistently underperformed throughout the experiment. Scaling the size of glyphs and color-mapping of the surface performed reasonably well. The efficiency of most of these techniques were highly dependent on the tasks performed. We believe that these findings can be used in future uncertainty visualization design. In addition, the framework developed in this user study presents a structured approach to evaluate uncertainty visualization techniques, as well as provides a basis for future research in uncertainty visualization.

Abstract Diffusion tensor imaging (DTI) has been used to generate fibrous structures in both brain white matter and muscles. Fiber clustering groups the DTI fibers into spatially and anatomically related tracts. As an increasing number of fiber clustering methods have been recently developed, it is important to display, compare, and explore the clustering results efficiently and effectively. In this paper, we present an anatomical visualization technique that reduces the geometric complexity of the fiber tracts and emphasizes the high‐level structures. Beginning with a volumetric diffusion tensor image, we first construct a hierarchical clustering representation of the fiber bundles. These bundles are then reformulated into a 3D multi‐valued volume data. We then build a set of geometric hulls and principal fibers to approximate the shape and orientation of each fiber bundle. By simultaneously visualizing the geometric hulls, individual fibers, and other data sets such as fractional anisotropy, the overall shape of the fiber tracts are highlighted, while preserving the fibrous details. A rater with expert knowledge of white matter structure has evaluated the resulting interactive illustration and confirmed the improvement over straightforward DTI fiber tract visualization.

We present a method for clustering diffusion tensor imaging (DTI) integral curves into anatomically plausible bundles. An expert rater evaluated the anatomical accuracy of the bundles. We also evaluated the method by applying an experimental cross-subject labeling method to the clustering results. We first employ a sampling and culling strategy for generating DTI integral curves and then constrain the curves so that they terminate in gray matter. We then employ a clustering method based on a proximity measure calculated between every pair of curves. We interactively selected a proximity threshold to achieve visually optimal clustering in models from four DTI datasets. An expert rater then assigned a confidence rating about bundle presence and accuracy for each of 12 target fiber bundles of varying calibers and type in each dataset. We then created a fiber bundle template to cluster and label the fiber bundles automatically in new datasets. According to expert evaluation, the automated proximity-based clustering and labeling algorithm consistently yields anatomically plausible fiber bundles on large and coherent clusters. This work has the potential to provide an automatic and robust way to find and study neural fiber bundles within DTI.

We present the results from a qualitative and quantitative user study comparing fishtank virtual-reality (VR) and CAVE displays. The results of the qualitative study show that users preferred the fishtank VR display to the CAVE system for our scientific visualization application because of perceived higher resolution, brightness and crispness of imagery, and comfort of use. The results of the quantitative study show that users performed an abstract visual search task significantly more quickly and more accurately on the fishtank VR display system than in the CAVE. The same study also showed that visual context had no significant effect on task performance for either of the platforms. We suggest that fishtank VR displays are more effective than CAVEs for applications in which the task occurs outside the user's reference frame, the user views and manipulates the virtual world from the outside in, and the size of the virtual object that the user interacts with is smaller than the user's body and fits into the fishtank VR display. The results of both studies support this proposition.

Researchers in computational condensed matter physics deal with complex data sets consisting of time varying 3D tensor, vector, and scalar quantities. Particularly, in the research of topological defects in nematic liquid crystals (LC) displaying the results of the computer simulation of molecular dynamics presents a challenge. Combining existing immersive and interactive visualization methods we developed new methods that attempt to provide a clear, efficient, and intuitive way to visualize and explore LC data. In addition, the visualization of the data has presented us with a novel method of obtaining the locations of the topological defects present in a liquid crystal system.

Figure 1: Top view of the streamline clusters on the whole brain. Streamlines within the same cluster share the same color. From the picture, the cingulum bundles can be easily identified in two clusters. Neural fibers along the corpus callosum are clustered into coherent bundles. Some of the U-fibers also form clusters.

Multiple sclerosis (MS) is a chronic disease of the central nervous system that predominantly affects young adults during their most productive years. Pathologically, MS is characterized by the presence of areas of demyelination and T-cell predominant perivascular

We present a threads and halos representation for interactive volume rendering of vector-field structure and describe a number of additional components that combine to create effective visualizations of multivalued 3D scientific data. After filtering linear structures, such as flow lines, into a volume representation, we use a multilayer volume rendering approach to simultaneously display this derived volume along with other data values. We demonstrate the utility of threads and halos in clarifying depth relationships within dense renderings and we present results from two scientific applications: visualization of second-order tensor valued magnetic resonance imaging (MRI) data and simulated 3D fluid flow data. In both application areas, the interactivity of the visualizations proved to be important to the domain scientists. Finally, we describe a PC-based implementation of our framework along with domain specific transfer functions, including an exploratory data culling tool, that enable fast data exploration.

We present a new method for visualizing 3D volumetric diffusion tensor MR images. We distinguish between linear anisotropy and planar anisotropy and represent values in the two regimes using streamtubes and streamsurfaces, respectively. Streamtubes represent structures with primarily linear diffusion, typically fiber tracts; streamtube direction correlates with tract orientation. The cross-sectional shape and color of each streamtube represent additional information from the diffusion tensor at each point. Streamsurfaces represent structures in which diffusion is primarily planar. Our algorithm chooses a very small representative subset of the streamtubes and streamsurfaces for display. We describe the set of metrics used for the culling process, which reduces visual clutter and improves interactivity. We also generate anatomical landmarks to identify the locations of such structures as the eyes, skull surface, and ventricles. The final models are complex surface geometries that can be imported into many interactive graphics software environments. We describe a virtual environment to interact with these models. Expert feedback from doctors studying changes in white-matter structures after gamma-knife capsulotomy and preoperative planning for brain tumor surgery shows that streamtubes correlate well with major neural structures, the 2D section and geometric landmarks are important in understanding the visualization, and the stereo and interactivity from the virtual environment aid in understanding the complex geometric models.

We describe a virtual reality environment for visualizing tensor-valued volumetric datasets acquired with diffusion tensor magnetic resonance imaging (DT-MRI). We have prototyped a virtual environment that displays geometric representations of the volumetric second-order diffusion tensor data and are developing interaction and visualization techniques for two application areas: studying changes in white-matter structures after gamma-knife capsulotomy and pre-operative planning for brain tumor surgery. Our feedback shows that compared to desktop displays, our system helps the user better interpret the large and complex geometric models, and facilitates communication among a group of users.