Alexander Wiebel

Multifield Visualization Using Local Statistical Complexity

Modern unsteady (multi-)field visualizations require an effective reduction of the data to be displayed. From a huge amount of information the most informative parts have to be extracted. Instead of the fuzzy application dependent notion of feature, a new approach based on information theoretic concepts is introduced in this paper to detect important regions. This is accomplished by extending the concept of local statistical complexity from finite state cellular automata to discretized (multi-)fields. Thus, informative parts of the data can be highlighted in an application-independent, purely mathematical sense. The new measure can be applied to unsteady multifields on regular grids in any application domain. The ability to detect and visualize important parts is demonstrated using diffusion, flow, and weather simulations.

Interactive Comparison of Scalar Fields Based on Largest Contours with Applications to Flow Visualization

Understanding fluid flow data, especially vortices, is still a challenging task. Sophisticated visualization tools help to gain insight. In this paper, we present a novel approach for the interactive comparison of scalar fields using isosurfaces, and its application to fluid flow datasets. Features in two scalar fields are defined by largest contour segmentation after topological simplification. These features are matched using a volumetric similarity measure based on spatial overlap of individual features. The relationships defined by this similarity measure are ranked and presented in a thumbnail gallery of feature pairs and a graph representation showing all relationships between individual contours. Additionally, linked views of the contour trees are provided to ease navigation. The main render view shows the selected features overlapping each other. Thus, by displaying individual features and their relationships in a structured fashion, we enable exploratory visualization of correlations between similar structures in two scalar fields. We demonstrate the utility of our approach by applying it to a number of complex fluid flow datasets, where the emphasis is put on the comparison of vortex related scalar quantities.

Illustrative Stream Surfaces

Stream surfaces are an intuitive approach to represent 3D vector fields. In many cases, however, they are challenging objects to visualize and to understand, due to a high degree of self-occlusion. Despite the need for adequate rendering methods, little work has been done so far in this important research area. In this paper, we present an illustrative rendering strategy for stream surfaces. In our approach, we apply various rendering techniques, which are inspired by the traditional flow illustrations drawn by Dallmann and Abraham & Shaw in the early 1980s. Among these techniques are contour lines and halftoning to show the overall surface shape. Flow direction as well as singularities on the stream surface are depicted by illustrative surface streamlines. ;To go beyond reproducing static text book images, we provide several interaction features, such as movable cuts and slabs allowing an interactive exploration of the flow and insights into subjacent structures, e.g., the inner windings of vortex breakdown bubbles. These methods take only the parameterized stream surface as input, require no further preprocessing, and can be freely combined by the user. We explain the design, GPU-implementation, and combination of the different illustrative rendering and interaction methods and demonstrate the potential of our approach by applying it to stream surfaces from various flow simulations.

Generalized Streak Lines: Analysis and Visualization of Boundary Induced Vortices

We present a method to extract and visualize vortices that originate from bounding walls of three-dimensional time- dependent flows. These vortices can be detected using their footprint on the boundary, which consists of critical points in the wall shear stress vector field. In order to follow these critical points and detect their transformations, affected regions of the surface are parameterized. Thus, an existing singularity tracking algorithm devised for planar settings can be applied. The trajectories of the singularities are used as a basis for seeding particles. This leads to a new type of streak line visualization, in which particles are released from a moving source. These generalized streak lines visualize the particles that are ejected from the wall. We demonstrate the usefulness of our method on several transient fluid flow datasets from computational fluid dynamics simulations.

Computational modeling for assessment of IBD: To be or not to be?

The grading of inflammatory bowel disease (IBD) severity is important to determine the proper treatment strategy and to quantify the response to treatment. Traditionally, ileocolonoscopy is considered the reference standard for assessment of IBD. However, the procedure is invasive and requires extensive bowel preparation. Magnetic resonance imaging (MRI) has become an important tool for determining the presence of disease activity. Unfortunately, only moderate interobserver agreement is reported for most of the radiological severity measures. There is a clear demand for automated evaluation of MR images in Crohns disease (CD). This paper aims to introduce a preliminary suite of fundamental tools for assessment of CD severity. It involves procedures for image analysis, classification and visualization to predict the colonoscopy disease scores.

WYSIWYP: What You See Is What You Pick

Scientists, engineers and physicians are used to analyze 3D data with slice-based visualizations. Radiologists for example are trained to read slices of medical imaging data. Despite the numerous examples of sophisticated 3D rendering techniques, domain experts, who still prefer slice-based visualization do not consider these to be very useful. Since 3D renderings have the advantage of providing an overview at a glance, while 2D depictions better serve detailed analyses, it is of general interest to better combine these methods. Recently there have been attempts to bridge this gap between 2D and 3D renderings. These attempts include specialized techniques for volume picking in medical imaging data that result in repositioning slices. In this paper, we present a new volume picking technique called WYSIWYP (“what you see is what you pick”) that, in contrast to previous work, does not require pre-segmented data or metadata and thus is more generally applicable. The positions picked by our method are solely based on the data itself, the transfer function, and the way the volumetric rendering is perceived by the user. To demonstrate the utility of the proposed method, we apply it to automated positioning of slices in volumetric scalar fields from various application areas. Finally, we present results of a user study in which 3D locations selected by users are compared to those resulting from WYSIWYP. The user study confirms our claim that the resulting positions correlate well with those perceived by the user.

Lagrangian visualization of flow-embedded surface structures

The notions of Finite‐Time Lyapunov Exponent (FTLE) and Lagrangian Coherent Structures provide a strong framework for the analysis and visualization of complex technical flows. Their definition is simple and intuitive, and they are built on a deep theoretical foundation. We apply these concepts to enable the analysis of flows in the immediate vicinity of the boundaries of flow‐embedded objects by limiting the Lagrangian analysis to surfaces closely neighboring these boundaries. To this purpose, we present an approach to approximate FTLE fields over such surfaces. Furthermore, we achieve an effective depiction of boundary‐related flow structures such as separation and attachment over object boundaries and specific insight into the surrounding flow using several specifically chosen visualization techniques. We document the applicability of our methods by presenting a number of application examples.

Smooth stream surfaces of fourth order precision

We introduce a novel technique for the construction of smooth stream surfaces of 4th order precision. While common stream surface techniques use linear interpolation for generating seed points for new streamlines in the refinement phase, we use Hermite interpolation. The derivatives needed for Hermite interpolation are obtained by integration along the streamlines. This yields stream surfaces of4th order precision. Additionally, we analyse the accuracy ofthe well known Hultquist approach and our new algorithm and proof that Hultquists method is exact for linear vector fields. We compare both methods using the well known distance based and a novel error based refinement strategy. Our resulting surface is C1 ‐continuous, enabling improved rendering among other benefits.

Topological Flow Structures in a Mathematical Model for Rotation-Mediated Cell Aggregation

In this paper we applyvector field topology methods to amathematical model for the fluid dynamics of reaggregation processes in tissue engineering. The experimental background are dispersed embryonic retinal cells, which reaggregate in a rotation culture on a gyratory shaker, according to defined rotation and culture conditions. Under optimal conditions, finally complex 3D spheres result. In order to optimize high throughput drug testing systems of biological cell and tissue models, a major aim is to understand the role which the fluid dynamics plays in this process. To allow for a mathematical analysis, an experimental model system was set up, using micro-beads instead of spheres within the culture dish. The qualitative behavior of this artificial model was monitored in time by using a camera. For this experimental setup amathematical model for the bead-fluid dynamics was derived, analyzed and simulated. The simulations showed that the beads form distinctive clusters in a layer close to the bottom of the petri dish. To analyze these patterns further, we perform a topological analysis of thevelocity field within this layer of the fluid. We find that traditional two-dimensional visualization techniques like path lines, streak lines and currenttime-dependent topology approaches are not able to answer the posed questions, for example they do not allow to find the location of clusters. We discuss the problems of these techniques and develop a new approach that measures thedensity of advected particles in the flow to find the moving point of particleaggregation. Using thedensity field the path of the movingaggregation point is extracted.

Topology aware stream surfaces

We present an algorithm that allows stream surfaces to recognize and adapt to vector field topology. Standard stream surface algorithms either refine the surface uncontrolled near critical points which slows down the computation considerably and may lead to a poor surface approximation. Alternatively, the concerned region is omitted from the stream surface by severing it into two parts thus generating an incomplete stream surface. Our algorithm utilizes topological information to provide a fast, accurate, and complete triangulation of the stream surface near critical points. The required topological information is calculated in a preprocessing step. We compare our algorithm against the standard approach both visually and in performance.