Flow visualization has been a very active subfield of scientific visualization in recent years. From the resulting large variety of methods this paper discusses partition-based techniques. The aim of these approaches is to partition the flow in areas of common structure. Based on this partitioning, subsequent visualization techniques can be applied. A classification is suggested and advantages/disadvantages of the different techniques are discussed as well. 1

Abstract. Visualization of glyphs has a long history in medical imaging but gains much more power when the glyphs are properly placed to fill the screen. Glyph packing is often performed via an iterative approach to improve the location of glyphs. We present an alternative implementation of glyph packing based on a Delaunay triangulation to speed up the clustering process and reduce costs for neighborhood searches. Our approach does not require a re–computation of acceleration structures when a plane is moved through a volume, which can be done interactively. We provide two methods for initial placement of glyphs to improve the convergence of our algorithm for glyphs larger and glyphs smaller than the data set’s voxel size. The main contribution of this paper is a novel approach to glyph packing that supports simpler parameterization and can be used easily for highly efficient interactive data exploration, in contrast to previous methods. 1

We present the design of a scalable parallel pathline construction method for visualizing large time-varying 3D vector fields. A 4D (i.e., time and the 3D spatial domain) representation of the vector field is introduced to make a timeaccurate depiction of the flow field. This representation also allows us to obtain pathlines through streamline tracing in the 4D space. Furthermore, a hierarchical representation of the 4D vector field, constructed by clustering the 4D field, makes possible interactive visualization of the flow field at different levels of abstraction. Based on this hierarchical representation, a data partitioning scheme is designed to achieve high parallel efficiency. We demonstrate the performance of parallel pathline visualization using data sets obtained from terascale flow simulations. This new capability will enable scientists to study their time-varying vector fields at the resolution and interactivity previously unavailable to them. 1.

Scientific computing is an increasingly crucial component of research in various disciplines. Despite its potential, exploration of the results is an often laborious task, owing to excessively large and verbose datasets output by these simulation runs. Several approaches have been proposed to analyze, classify, and simplify such data to facilitate an informative visualization and deeper understanding of the underlying system. However, traditional methods leave much room for improvement. In this article we investigate the visualization of large vector fields, departing from accustomed processing algorithms by casting vector field simplification as a variational partitioning problem. Adopting an iterative strategy, we introduce the notion of vector “proxies ” to minimize the distortion error of our simplification by clustering the dataset into multiple best-fitting characteristic regions. This error driven approach can be performed with respect to various similarity metrics, offering a convenient set of tools to design clear and succinct representations of high dimensional datasets. We illustrate the benefits of such tools through visualization experiments of three-dimensional vector fields. Categories and Subject Descriptors (according to ACM CCS): I.3.0 [Computer Graphics]: Flow Visualization 1.

Mathematical methods for time series analysis and digital image processing

Many problems in imaging are actually inverse problems. One reason for this is that conditions and parameters of the physical processes underlying the actual image acquisition are usually not known. Examples for this are the inhomogeneities of the magnet field in magnetic resonance images leading to

The visualization of stationary and time-dependent flow is an important and challenging topic in scientific visualization. Its aim is to represent transport phenomena governed by vector fields in an intuitively understandable way. In this paper, we review the use of methods based on partial differential equations (PDEs) to postprocess flow datasets for the purpose of visualization. This connects flow visualization with image processing and mathematical multi-scale models. We introduce the concepts of flow operators and scale-space and explain their use in modeling post processing methods for flow data. Based on this framework, we present several classes of PDE-based visualization methods: anisotropic linear diffusion for stationary flow; transport and diffusion for non-stationary flow; continuous clustering based on phase-separation; and an algebraic clustering of a matrix-encoded flow operator. We illustrate the presented classes of methods with results obtained from concrete flow applications, using datasets in 2D, flows on curved surfaces, and volumetric 3D fields. 1

Extreme simplification and rendering of point sets

Large, heterogeneous volumes of simulation data are calculated and stored in many disciplines, e.g. in climate and climate impact research. To gain insight, current climate analysis applies statistical methods and model sensitivity analyzes in combination with standard visualization techniques. However, there are some obstacles for researchers in applying the full functionality of sophisticated visualization, exploiting the available interaction and visualization functionality in order to go beyond data presentation tasks. In particular, there is a gap between available and actually applied multi-variate visualization techniques. Furthermore, visual data comparison of simulation (and measured) data is still a challenging task. Consequently, this paper introduces a library of visualization techniques, tailored to support exploration and evaluation of climate simulation data. These techniques are integrated into the easy-to-use visualization framework SimEnvVis- designed as a front-end user interface to a simulation environment- which provides a high level of user support generating visual representations. 1

In this paper, we present a novel approach for efficiently evolving meshes using mean-curvature flow. We use a finite-elements hierarchy that supports an efficient multigrid solver for performing the semi-implicit time-stepping. Though expensive to compute, we show that it is possible to track this hierarchy through the process of surface evolution. As a result, we provide a way to efficiently flow the surface through the evolution, without requiring a costly initialization at the beginning of each time-step. Using our approach, we demonstrate a factor of nearly seven-fold improvement over the non-tracking implementation, supporting the evolution of surfaces consisting of 1M triangles at a rate of just a few seconds per update.