Raphael Fuchs

Visualization of Multi-Variate Scientific Data

In this state‐of‐the‐art report we discuss relevant research works related to the visualization of complex, multi‐variate 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.

World Lines

In this paper we present World Lines as a novel interactive visualization that provides complete control over multiple heterogeneous simulation runs. In many application areas, decisions can only be made by exploring alternative scenarios. The goal of the suggested approach is to support users in this decision making process. In this setting, the data domain is extended to a set of alternative worlds where only one outcome will actually happen. World Lines integrate simulation, visualization and computational steering into a single unified system that is capable of dealing with the extended solution space. World Lines represent simulation runs as causally connected tracks that share a common time axis. This setup enables users to interfere and add new information quickly. A World Line is introduced as a visual combination of user events and their effects in order to present a possible future. To quickly find the most attractive outcome, we suggest World Lines as the governing component in a system of multiple linked views and a simulation component. World Lines employ linking and brushing to enable comparative visual analysis of multiple simulations in linked views. Analysis results can be mapped to various visual variables that World Lines provide in order to highlight the most compelling solutions. To demonstrate this technique we present a flooding scenario and show the usefulness of the integrated approach to support informed decision making.

The State of the Art in Topology-Based Visualization of Unsteady Flow

Vector fields are a common concept for the representation of many different kinds of flow phenomena in science and engineering. Methods based on vector field topology are known for their convenience for visualizing and analysing steady flows, but a counterpart for unsteady flows is still missing. However, a lot of good and relevant work aiming at such a solution is available. We give an overview of previous research leading towards topology‐based and topology‐inspired 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 multifield approaches. Furthermore, we illustrate our review with practical examples for the different approaches.

Visual Human+Machine Learning

In this paper we describe a novel method to integrate interactive visual analysis and machine learning to support the insight generation of the user. The suggested approach combines the vast search and processing power of the computer with the superior reasoning and pattern recognition capabilities of the human user. An evolutionary search algorithm has been adapted to assist in the fuzzy logic formalization of hypotheses that aim at explaining features inside multivariate, volumetric data. Up to now, users solely rely on their knowledge and expertise when looking for explanatory theories. However, it often remains unclear whether the selected attribute ranges represent the real explanation for the feature of interest. Other selections hidden in the large number of data variables could potentially lead to similar features. Moreover, as simulation complexity grows, users are confronted with huge multidimensional data sets making it almost impossible to find meaningful hypotheses at all. We propose an interactive cycle of knowledge-based analysis and automatic hypothesis generation. Starting from initial hypotheses, created with linking and brushing, the user steers a heuristic search algorithm to look for alternative or related hypotheses. The results are analyzed in information visualization views that are linked to the volume rendering. Individual properties as well as global aggregates are visually presented to provide insight into the most relevant aspects of the generated hypotheses. This novel approach becomes computationally feasible due to a GPU implementation of the time-critical parts in the algorithm. A thorough evaluation of search times and noise sensitivity as well as a case study on data from the automotive domain substantiate the usefulness of the suggested approach.

Topological Methods in Data Analysis and Visualization II: Theory, Algorithms, and Applications

We propose a method for visualizing two-dimensional symmetric tensor fields using the Heat Kernel Signature (HKS). The HKS is derived from the heat kernel and was originally introduced as an isometry invariant shape signature. The time parameter of the heat kernel allows a multiscale analysis in a natural way. By considering a positive definite tensor field as a Riemannian metric the definition of the HKS can be applied directly. To investigate how this measure can be used to visualize more general tensor fields we apply mappings to obtain positive definite tensor fields. The resulting scalar quantity is used for the visualization of tensor fields. For short times it is closely related to Gaussian curvature, i. e. it is quite different to usual tensor invariants like the trace or the determinant.When scientists analyze datasets in a search for underlying phenomena, patterns or causal factors, their first step is often an automatic or semi-automatic search for structures in the data. Of these feature-extraction methods, topological ones stand out due to their solid mathematical foundation. Topologically defined structuresas found in scalar, vector and tensor fieldshave proven their merit in a wide range of scientific domains, and scientists have found them to be revealing in subjects such as physics, engineering, and medicine. Full of state-of-the-art research and contemporary hot topics in the subject, this volume is a selection of peer-reviewed papers originally presented at the fourth Workshop on Topology-Based Methods in Data Analysis and Visualization, TopoInVis 2011, held in Zurich, Switzerland. The workshop brought together many of the leading lights in the field for a mixture of formal presentations and discussion. One topic currently generating a great deal of interest, and explored in several chapters here, is the search for topological structures in time-dependent flows, and their relationship with Lagrangian coherent structures. Contributors also focus on discrete topologies of scalar and vector fields, and on persistence-based simplification, among other issues of note. The new research results included in this volume relate to all three key areas in data analysistheory, algorithms and applications.

Parallel Vectors Criteria for Unsteady Flow Vortices

Feature-based flow visualization is naturally dependent on feature extraction. To extract flow features, often higher order properties of the flow data are used such as the Jacobian or curvature properties, implicitly describing the flow features in terms of their inherent flow characteristics (for example, collinear flow and vorticity vectors). In this paper, we present recent research that leads to the (not really surprising) conclusion that feature extraction algorithms need to be extended to a time-dependent analysis framework (in terms of time derivatives) when dealing with unsteady flow data. Accordingly, we present two extensions of the parallel-vectors-based vortex extraction criteria to the time-dependent domain and show the improvements of feature-based flow visualization in comparison to the steady versions of this extraction algorithm both in the context of a high-resolution data set, that is, a simulation specifically designed to evaluate our new approach and for a real-world data set from a concrete application.

Ridge Concepts for the Visualization of Lagrangian Coherent Structures

The popularity of vector field topology in the visualization community is due mainly to the topological skeleton which captures the essential information on a vector field in a set of lines or surfaces separating regions of different flow behavior. Unfortunately, vector field topology has no straightforward extension to unsteady flow, and the concept probably most closely related to the topological skeleton are the so-called Lagrangian coherent structures (LCS). LCS are material lines or material surfaces that separate regions of different flow behavior. Ideally, such structures are material lines (or surfaces) in an exact sense and at the same time maximally attracting or repelling, but practical realizations such as height ridges of the finite-time Lyapunov exponent (FTLE) fulfill these two requirements only in an approximate sense. In this paper, we quantify the deviation from exact material lines/surfaces for several FTLE-based concepts, and we propose a numerically simpler variants of FTLE ridges that has equal or better error characteristics than classical FTLE height ridges.

Visual Analysis and Steering of Flooding Simulations

We present a visualization tool for the real-time analysis of interactively steered ensemble-simulation runs, and apply it to flooding simulations. Simulations are performed on-the-fly, generating large quantities of data. The user wants to make sense of the data as it is created. The tool facilitates understanding of what happens in all scenarios, where important events occur, and how simulation runs are related. We combine different approaches to achieve this goal. To maintain an overview, data are aggregated and embedded into the simulation rendering, showing trends, outliers, and robustness. For a detailed view, we use information-visualization views and interactive visual analysis techniques. A selection mechanism connects the two approaches. Points of interest are selected by clicking on aggregates, supplying data for visual analysis. This allows the user to maintain an overview of the ensemble and perform analysis even as new data are supplied through simulation steering. Unexpected or unwanted developments are detected easily, and the user can focus the exploration on them. The solution was evaluated with two case studies focusing on placing and testing flood defense measures. Both were evaluated by a consortium of flood simulation and defense experts, who found the system to be both intuitive and relevant.

Nodes on Ropes: A Comprehensive Data and Control Flow for Steering Ensemble Simulations

Flood disasters are the most common natural risk and tremendous efforts are spent to improve their simulation and management. However, simulation-based investigation of actions that can be taken in case of flood emergencies is rarely done. This is in part due to the lack of a comprehensive framework which integrates and facilitates these efforts. In this paper, we tackle several problems which are related to steering a flood simulation. One issue is related to uncertainty. We need to account for uncertain knowledge about the environment, such as levee-breach locations. Furthermore, the steering process has to reveal how these uncertainties in the boundary conditions affect the confidence in the simulation outcome. Another important problem is that the simulation setup is often hidden in a black-box. We expose system internals and show that simulation steering can be comprehensible at the same time. This is important because the domain expert needs to be able to modify the simulation setup in order to include local knowledge and experience. In the proposed solution, users steer parameter studies through the World Lines interface to account for input uncertainties. The transport of steering information to the underlying data-flow components is handled by a novel meta-flow. The meta-flow is an extension to a standard data-flow network, comprising additional nodes and ropes to abstract parameter control. The meta-flow has a visual representation to inform the user about which control operations happen. Finally, we present the idea to use the data-flow diagram itself for visualizing steering information and simulation results. We discuss a case-study in collaboration with a domain expert who proposes different actions to protect a virtual city from imminent flooding. The key to choosing the best response strategy is the ability to compare different regions of the parameter space while retaining an understanding of what is happening inside the data-flow system.

Smart Transparency for Illustrative Visualization of Complex Flow Surfaces

The perception of transparency and the underlying neural mechanisms have been subject to extensive research in the cognitive sciences. However, we have yet to develop visualization techniques that optimally convey the inner structure of complex transparent shapes. In this paper, we apply the findings of perception research to develop a novel illustrative rendering method that enhances surface transparency nonlocally. Rendering of transparent geometry is computationally expensive since many optimizations, such as visibility culling, are not applicable and fragments have to be sorted by depth for correct blending. In order to overcome these difficulties efficiently, we propose the illustration buffer. This novel data structure combines the ideas of the A and G-buffers to store a list of all surface layers for each pixel. A set of local and nonlocal operators is then used to process these depth-lists to generate the final image. Our technique is interactive on current graphics hardware and is only limited by the available graphics memory. Based on this framework, we present an efficient algorithm for a nonlocal transparency enhancement that creates expressive renderings of transparent surfaces. A controlled quantitative double blind user study shows that the presented approach improves the understanding of complex transparent surfaces significantly.