Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree

The contour tree is an abstraction of a scalar field that encodes the nesting relationships of isosurfaces. We show how to use the contour tree to represent individual contours of a scalar field, how to simplify both the contour tree and the topology of the scalar field, how to compute and store geometric properties for all possible contours in the contour tree, and how to use the simplified contour tree as an interface for exploratory visualization

Subdomain Aware Contour Trees and Contour Evolution in Time-Dependent Scalar Fields

For time-dependent scalar fields, one is often interested in topology changes of contours in time. In this paper, we focus on describing how contours split and merge over a certain time interval. Rather than attempting to describe all individual contour splitting and merging events, we focus on the simpler and therefore more tractable in practice problem: describing and querying the cumulative effect of the splitting and merging events over a user-specified time interval. Using our system one can, for example, find all contours at time tº that continue to two contours at time t¹ without hitting the boundary of the domain. For any such contour, there has to be a bifurcation happening to it somewhere between the two times, but, in addition to that, many other events may possibly happen without changing the cumulative outcome (e.g. merging with several contours born after tº or splitting off several contours that disappear before t¹). Our approach is flexible enough to enable other types of queries, if they can be cast as counting queries for numbers of connected components of intersections of contours with certain simply connected domains. Examples of such queries include finding contours with large life spans, contours avoiding certain subset of the domain over a given time interval or contours that continue to two at a later time and then merge back to one some time later. Experimental results show that our method can handle large 3D (2 space dimensions plus time) and 4D (3D+time) datasets. Both preprocessing and query algorithms can easily be parallelized

Time-varying volume visualization

Volume rendering is a very active research field in Computer Graphics because of its wide range of applications in various sciences, from medicine to flow mechanics. In this report, we survey a state-of-the-art on time-varying volume rendering. We state several basic concepts and then we establish several criteria to classify the studied works: IVR versus DVR, 4D versus 3D+time, compression techniques, involved architectures, use of parallelism and image-space versus object-space coherence. We also address other related problems as transfer functions and 2D cross-sections computation of time-varying volume data. All the papers reviewed are classified into several tables based on the mentioned classification and, finally, several conclusions are presented.Preprin

Comparative Uncertainty Visualization for High-Level Analysis of Scalar- and Vector-Valued Ensembles

With this thesis, I contribute to the research field of uncertainty visualization, considering parameter dependencies in multi valued fields and the uncertainty of automated data analysis. Like uncertainty visualization in general, both of these fields are becoming more and more important due to increasing computational power, growing importance and availability of complex models and collected data, and progress in artificial intelligence. I contribute in the following application areas: Uncertain Topology of Scalar Field Ensembles. The generalization of topology-based visualizations to multi valued data involves many challenges. An example is the comparative visualization of multiple contour trees, complicated by the random nature of prevalent contour tree layout algorithms. I present a novel approach for the comparative visualization of contour trees - the Fuzzy Contour Tree. Uncertain Topological Features in Time-Dependent Scalar Fields. Tracking features in time-dependent scalar fields is an active field of research, where most approaches rely on the comparison of consecutive time steps. I created a more holistic visualization for time-varying scalar field topology by adapting Fuzzy Contour Trees to the time-dependent setting. Uncertain Trajectories in Vector Field Ensembles. Visitation maps are an intuitive and well-known visualization of uncertain trajectories in vector field ensembles. For large ensembles, visitation maps are not applicable, or only with extensive time requirements. I developed Visitation Graphs, a new representation and data reduction method for vector field ensembles that can be calculated in situ and is an optimal basis for the efficient generation of visitation maps. This is accomplished by bringing forward calculation times to the pre-processing. Visually Supported Anomaly Detection in Cyber Security. Numerous cyber attacks and the increasing complexity of networks and their protection necessitate the application of automated data analysis in cyber security. Due to uncertainty in automated anomaly detection, the results need to be communicated to analysts to ensure appropriate reactions. I introduce a visualization system combining device readings and anomaly detection results: the Security in Process System. To further support analysts I developed an application agnostic framework that supports the integration of knowledge assistance and applied it to the Security in Process System. I present this Knowledge Rocks Framework, its application and the results of evaluations for both, the original and the knowledge assisted Security in Process System. For all presented systems, I provide implementation details, illustrations and applications

Time-varying Reeb graphs: a topological framework supporting the analysis of continuous time-varying data

I present time-varying Reeb graphs as a topological framework to support the analysis of continuous time-varying data. Such data is captured in many studies, including computational fluid dynamics, oceanography, medical imaging, and climate modeling, by measuring physical processes over time, or by modeling and simulating them on a computer. Analysis tools are applied to these data sets by scientists and engineers who seek to understand the underlying physical processes. A popular tool for analyzing scientific datasets is level sets, which are the points in space with a fixed data value s. Displaying level sets allows the user to study their geometry, their topological features such as connected components, handles, and voids, and to study the evolution of these features for varying s. For static data, the Reeb graph encodes the evolution of topological features and compactly represents topological information of all level sets. The Reeb graph essentially contracts each level set component to a point. It can be computed efficiently, and it has several uses: as a succinct summary of the data, as an interface to select meaningful level sets, as a data structure to accelerate level set extraction, and as a guide to remove noise. I extend these uses of Reeb graphs to time-varying data. I characterize the changes to Reeb graphs over time, and develop an algorithm that can maintain a Reeb graph data structure by tracking these changes over time. I store this sequence of Reeb graphs compactly, and call it a time-varying Reeb graph. I augment the time-varying Reeb graph with information that records the topology of level sets of all level values at all times, that maintains the correspondence of level set components over time, and that accelerates the extraction of level sets for a chosen level value and time. Scientific data sampled in space-time must be extended everywhere in this domain using an interpolant. A poor choice of interpolant can create degeneracies that are difficult to resolve, making construction of time-varying Reeb graphs impractical. I investigate piecewise-linear, piecewise-trilinear, and piecewise-prismatic interpolants, and conclude that piecewise-prismatic is the best choice for computing time-varying Reeb graphs. Large Reeb graphs must be simplified for an effective presentation in a visualization system. I extend an algorithm for simplifying static Reeb graphs to compute simplifications of time-varying Reeb graphs as a first step towards building a visualization system to support the analysis of time-varying data

A contour tree based spatio-temporal data model for oceanographic applications

To present the spatio/temporal data from oceanographic modeling in GIS has been a challenging task due to the highly dynamic characteristic and complex pattern of variables, in relation to time and space. This dissertation focuses the research on spatio-temporal GIS data model applied to oceanographic model data, especially to homogeneous iso-surface data. The available spatio-temporal data models are carefully reviewed and characteristics in spatial and temporal issues from oceanographic model data are discussed in detail. As an important tool for data modeling, ontology is introduced to categorize oceanographic model data and further set up fundamental software components in the new data model. The proposed data model is based on the concept of contour tree. By adding temporal information to each node and arc of the contour tree, and using multiple contour trees to represent different time steps in the temporal domain, the changes can be stored and tracked by the data model. In order to reduce the data volume and increase the data quality, the new data model integrates spatial and temporal interpolation methods within it. The spatial interpolation calculates the data that fall between neighboring contours at a single time step. The Inverse Distance Weighting (IDW) is applied as the main algorithm and the Minimum Bounding Rectangle (MBR) is used to enhance the spatial interpolation performance. The temporal interpolation calculates the data that are not recorded, which fall between neighboring contour trees for adjacent time steps. The “linear interpolation” algorithm is preferred to the “nearest neighbor’s value” and “spline” interpolation methods, for its modest accuracy and the simple implementation scheme. In order to evaluate the support functions of the new data model, a case study is presented with the motivation to show how this data model supports complicated spatio-temporal queries in forecasting applications. This dissertation also showcases some work in contour tree simplification. A new simplification algorithm is introduced to reduce the data complexity. This algorithm is based on the branch decomposition method and supports temporal information integrated into contour trees. Three types of criteria parameters are introduced to run different simplification methods for various applications