Flow visualization research has made rapid advances in recent years, especially in the area of topology-based flow visualization. The ever increasing size of scientific data sets favors algorithms that are capable of extracting important subsets of the data, leaving the scientist with a more manageable representation that may be visualized interactively. Extracting the topology of a flow achieves the goal of obtaining a compact representation of a vector or tensor field while simultaneously retaining its most important features. We present the state of the art in topology-based flow visualization techniques. We outline numerous topology-based algorithms categorized according to the type and dimensionality of data on which they operate and according to the goal-oriented nature of each method. Topology tracking algorithms are also discussed. The result serves as a useful introduction and overview to research literature concerned with the study of topology-based flow visualization.

The study of stress and strains in soils and structures (solids) help us gain a better understanding of events such as failure of bridges, dams and buildings, or accumulated stresses and strains in geological subduction zones that could trigger earthquakes and subsequently tsunamis. In such domains, the key feature of interest is the location and orientation of maximal shearing planes. This paper describes a method that highlights this feature in stress tensor fields. It uses a plane-in-a-box glyph which provides a global perspective of shearing planes based on local analysis of tensors. The analysis can be performed over the entire domain, or the user can interactively specify where to introduce these glyphs. Alternatively, they can also be placed depending on the threshold level of several physical relevant parameters such as double couple and compensated linear vector dipole. Both methods are tested on stress tensor fields from geomechanics.

Vector fields are a common concept for the representation of many different kinds of flow phenomena in science and engineering. Topology-based methods have shown their convenience for visualizing and analyzing steady flow but a counterpart for unsteady flow is still missing. However, a lot of good and relevant work has been done aiming at such a solution. We give an overview of the research done on the way towards topology-based visualization of unsteady flow, pointing out the different approaches and methodologies involved as well as their relation to each other, taking classical (i.e. steady) vector field topology as our starting point. Particularly, we focus on Lagrangian Methods, Space-Time Domain Approaches, Local Methods, and Stochastic and Multi-Field Approaches. Furthermore, we illustrated our review with practical examples for the different approaches.

Abstract—Feature Flow Fields are a well-accepted approach for extracting and tracking features. In particular, they are often used to track critical points in time-dependent vector fields and to extract and track vortex core lines. The general idea is to extract the feature or its temporal evolution using a stream line integration in a derived vector field – the so-called Feature Flow Field (FFF). Hence, the desired feature line is a stream line of the FFF. As we will carefully analyze in this paper, the stream lines around this feature line may diverge from it. This creates an unstable situation: if the integration moves slightly off the feature line due to numerical errors, then it will be captured by the diverging neighborhood and carried away from the real feature line. The goal of this paper is to define a new FFF with the guarantee that the neighborhood of a feature line has always converging behavior. This way, we have an automatic correction of numerical errors: if the integration moves slightly off the feature line, it automatically moves back to it during the ongoing integration. This yields results which are an order of magnitude more accurate than the results from previous schemes. We present new stable FFF formulations for the main applications of tracking critical points and solving the Parallel Vectors operator. We apply our method to a number of data sets. 1

By measuring the anisotropic self-diffusion rates of water, Diffusion Weighted Magnetic Resonance Imaging (DW-MRI) provides a unique noninvasive probe of fibrous tissue. In particular, it has been explored widely for imaging nerve fiber tracts in the human brain. Geometric features provide a quick visual overview of the complex datasets that arise from DW-MRI. At the same time, they build a bridge towards quantitative analysis, by extracting explicit representations of structures in the data that are relevant to specific research questions. Therefore, features in DW-MRI data are an active research topic not only within scientific visualization, but have received considerable interest from the medical image analysis, neuroimaging, and computer vision communities. It is the goal of this paper to survey contributions from all these fields, concentrating on streamline clustering, edge detection and segmentation, topological methods, and extraction of anisotropy creases. We point out interrelations between these topics and make suggestions for future research.

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