Dye advection is an intuitive and versatile technique to visualize both steady and unsteady flow. Dye can be easily combined with noise-based dense vector field representations and is an important element in user-centric visual exploration processes. However, fast texture-based implementations of dye advection rely on linear interpolation operations that lead to severe diffusion artifacts. In this paper, a novel approach for dye advection is proposed to avoid this blurring and to achieve long and clearly defined streaklines or extended streak-like patterns. The interface between dye and background is modeled as a level-set within a signed distance field. The level-set evolution is governed by the underlying flow field and is computed by a semi-Lagrangian method. A reinitialization technique is used to counteract the distortions introduced by the level-set evolution and to maintain a levelset function that represents a local distance field. This approach works for 2D and 3D flow fields alike. It is demonstrated how the texture-based level-set representation lends itself to an efficient GPU implementation and therefore facilitates interactive visualization.

In this state-of-the-art report we discuss relevant research works related to the visualization of complex, multivariate data. We discuss how different techniques take effect at specific stages of the visualization pipeline and how they apply to multi-variate data sets being composed of scalars, vectors and tensors. We also provide a categorization of these techniques with the aim for a better overview of related approaches. Based on this classification we highlight combinable and hybrid approaches and focus on techniques that potentially lead towards new directions in visualization research. In the second part of this paper we take a look at recent techniques that are useful for the visualization of complex data sets either because they are general purpose or because they can be adapted to specific problems.

Abstract—The gradient of a velocity vector field is an asymmetric tensor field which can provide critical insight that is difficult to infer from traditional trajectory-based vector field visualization techniques. We describe the structures in the eigenvalue and eigenvector fields of the gradient tensor and how these structures can be used to infer the behaviors of the velocity field that can represent either a 2D compressible flow or the projection of a 3D compressible or incompressible flow onto a 2D manifold. To illustrate the structures in asymmetric tensor fields, we introduce the notions of eigenvalue manifold and eigenvector manifold. These concepts afford a number of theoretical results that clarify the connections between symmetric and antisymmetric components in tensor fields. In addition, these manifolds naturally lead to partitions of tensor fields, which we use to design effective visualization strategies. Moreover, we extend eigenvectors continuously into the complex domains which we refer to as pseudoeigenvectors. We make use of evenly spaced tensor lines following pseudoeigenvectors to illustrate the local linearization of tensors everywhere inside complex domains simultaneously. Both eigenvalue manifold and eigenvector manifold are supported by a tensor reparameterization with physical meaning. This allows us to relate our tensor analysis to physical quantities such as rotation, angular deformation, and dilation, which provide a physical interpretation of our tensor-driven vector field analysis in the context of fluid mechanics. To demonstrate the utility of our approach, we have applied our visualization techniques and interpretation to the study of the Sullivan Vortex as well as computational fluid dynamics simulation data. Index Terms—Tensor field visualization, flow analysis, asymmetric tensors, flow segmentation, tensor field topology, surfaces. Ç 1

Abstract — Video visualization is a computation process that extracts meaningful information from original video data sets and conveys the extracted information to users in appropriate visual representations. This paper presents a broad treatment of the subject, following a typical research pipeline involving concept formulation, system development, a path-finding user study, and a field trial with real application data. In particular, we have conducted a fundamental study on the visualization of motion events in videos. We have, for the first time, deployed flow visualization techniques in video visualization. We have compared the effectiveness of different abstract visual representations of videos. We have conducted a user study to examine whether users are able to learn to recognize visual signatures of motions, and to assist in the evaluation of different visualization techniques. We have applied our understanding and the developed techniques to a set of application video clips. Our study has demonstrated that video visualization is both technically feasible and cost-effective. It has provided the first set of evidence confirming that ordinary users can be accustomed to the visual features depicted in video visualizations, and can learn to recognize visual signatures of a variety of motion events. Index Terms—Video visualization, volume visualization, flow visualization, human factors, user study, visual signatures, video processing, optical flow, GPU rendering. 1

Functional approximation of scattered data is a popular technique for compactly representing various types of datasets in computer graphics, including surface, volume, and vector datasets. Typically, sums of Gaussians or similar radial basis functions are used in the functional approximation and PC graphics hardware is used to quickly evaluate and render these datasets. Previously, researchers presented techniques for spatially-limited spherical Gaussian radial basis function encoding and visualization of volumetric scalar, vector, and multifield datasets. While truncated radially symmetric basis functions are quick to evaluate and simple for encoding optimization, they are not the most appropriate choice for data that is not radially symmetric and are especially problematic for representing linear, planar, and many non-spherical structures. Therefore, we have developed a volumetric approximation and visualization system using ellipsoidal Gaussian functions which provides greater compression, and visually more accurate encodings of volumetric scattered datasets. In this paper, we extend previous work to use ellipsoidal Gaussians as basis functions, create a rendering system to adapt these basis functions to graphics hardware rendering, and evaluate the encoding effectiveness and performance for both spherical Gaussians and ellipsoidal Gaussians. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Scientific Visualization,

This paper presents an interactive technique for the dense texture-based visualization of unsteady 3D flow, taking into account issues of computational efficiency and visual perception. High efficiency is achieved by a novel 3D GPU-based texture advection mechanism that implements logical 3D grid structures by physical memory in the form of 2D textures. This approach results in fast read and write access to physical memory, independent of GPU architecture. Slice-based direct volume rendering is used for the final display. A real-time computation of gradients is employed to achieve volume illumination. Perception-guided volume shading methods are included, such as halos, cool/warm shading, or color-based depth cueing. The problems of clutter and occlusion are addressed by supporting a volumetric importance function that enhances features of the flow and reduces visual complexity in less interesting regions.

We propose a hybrid particle and texture based approach for the visualization of time-dependent vector fields. The underlying spacetime framework builds a dense vector field representation in a twostep process: 1) particle-based forward integration of trajectories in spacetime for temporal coherence, and 2) texture-based convolution along another set of paths through the spacetime for spatially correlated patterns. Particle density is controlled by stochastically injecting and removing particles, taking into account the divergence of the vector field. Alternatively, a uniform density can be maintained by placing exactly one particle in each cell of a uniform grid, which leads to particle-in-cell forward advection. Moreover, we discuss strategies of previous visualization methods for unsteady flow and show how they address issues of spatiotemporal coherence and dense visual representations. We demonstrate how our framework is capable of realizing several of these strategies. Finally, we present an efficient GPU implementation that facilitates an interactive visualization of unsteady 2D flow on Shader Model 3 compliant graphics hardware.

Figure 1: Visualization of the flow field of a tornado with: (left) a point-based stream surface; (right) the combination of a stream surface and texture-based flow visualization to show the vector field within the surface. Each stream surface is seeded along a straight line in the center of the respective image. We introduce a point-based algorithm for computing and rendering stream surfaces and path surfaces of a 3D flow. The points are generated by particle tracing, and an even distribution of those particles on the surfaces is achieved by selective particle removal and creation. Texture-based surface flow visualization is added to show inner flow structure on those surfaces. We demonstrate that our visualization method is designed for steady and unsteady flow alike: both the path surface component and the texture-based flow representation are capable of processing time-dependent data. Finally, we show that our algorithms lend themselves to an efficient GPU implementation that allows the user to interactively visualize and explore stream surfaces and path surfaces, even when seed curves are modified and even for time-dependent vector fields.

Although luminance contrast plays a predominant role in motion perception, significant additional effects are introduced by chromatic contrasts. In this paper, relevant results from psychophysical and physiological research are described to clarify the role of color in motion detection. Interpreting these psychophysical experiments, we propose guidelines for the design of animated visualizations, and a calibration procedure that improves the reliability of visual motion representation. The guidelines are applied to examples from texture-based flow visualization, as well as graph and tree visualization.

This work introduces a novel streamline seeding technique based on dual streamlines that are orthogonal to the vector field, instead of tangential. The greedy algorithm presented here produces a net of orthogonal streamlines that is iteratively refined resulting in good domain coverage and a high degree of continuity and uniformity. The algorithm is easy to implement and efficient, and it naturally extends to curved surfaces.