Feature-Based Uncertainty Visualization

While uncertainty in scientific data attracts an increasing research interest in the visualization community, two critical issues remain insufficiently studied: (1) visualizing the impact of the uncertainty of a data set on its features and (2) interactively exploring 3D or large 2D data sets with uncertainties. In this study, a suite of feature-based techniques is developed to address these issues. First, a framework of feature-level uncertainty visualization is presented to study the uncertainty of the features in scalar and vector data. The uncertainty in the number and locations of features such as sinks or sources of vector fields are referred to as feature-level uncertainty while the uncertainty in the numerical values of the data is referred to as data-level uncertainty. The features of different ensemble members are indentified and correlated. The feature-level uncertainties are expressed as the transitions between corresponding features through new elliptical glyphs. Second, an interactive visualization tool for exploring scalar data with data-level and two types of feature-level uncertainties — contour-level and topology-level uncertainties — is developed. To avoid visual cluttering and occlusion, the uncertainty information is attached to a contour tree instead of being integrated with the visualization of the data. An efficient contour tree-based interface is designed to reduce users’ workload in viewing and analyzing complicated data with uncertainties and to facilitate a quick and accurate selection of prominent contours. This thesis advances the current uncertainty studies with an in-depth investigation of the feature-level uncertainties and an exploration of topology tools for effective and interactive uncertainty visualizations. With quantified representation and interactive capability, feature-based visualization helps people gain new insights into the uncertainties of their data, especially the uncertainties of extracted features which otherwise would remain unknown with the visualization of only data-level uncertainties

Visual Analysis of Variability and Features of Climate Simulation Ensembles

This PhD thesis is concerned with the visual analysis of time-dependent scalar field ensembles as occur in climate simulations. Modern climate projections consist of multiple simulation runs (ensemble members) that vary in parameter settings and/or initial values, which leads to variations in the resulting simulation data. The goal of ensemble simulations is to sample the space of possible futures under the given climate model and provide quantitative information about uncertainty in the results. The analysis of such data is challenging because apart from the spatiotemporal data, also variability has to be analyzed and communicated. This thesis presents novel techniques to analyze climate simulation ensembles visually. A central question is how the data can be aggregated under minimized information loss. To address this question, a key technique applied in several places in this work is clustering. The first part of the thesis addresses the challenge of finding clusters in the ensemble simulation data. Various distance metrics lend themselves for the comparison of scalar fields which are explored theoretically and practically. A visual analytics interface allows the user to interactively explore and compare multiple parameter settings for the clustering and investigate the resulting clusters, i.e. prototypical climate phenomena. A central contribution here is the development of design principles for analyzing variability in decadal climate simulations, which has lead to a visualization system centered around the new Clustering Timeline. This is a variant of a Sankey diagram that utilizes clustering results to communicate climatic states over time coupled with ensemble member agreement. It can reveal several interesting properties of the dataset, such as: into how many inherently similar groups the ensemble can be divided at any given time, whether the ensemble diverges in general, whether there are different phases in the time lapse, maybe periodicity, or outliers. The Clustering Timeline is also used to compare multiple climate simulation models and assess their performance. The Hierarchical Clustering Timeline is an advanced version of the above. It introduces the concept of a cluster hierarchy that may group the whole dataset down to the individual static scalar fields into clusters of various sizes and densities recording the nesting relationship between them. One more contribution of this work in terms of visualization research is, that ways are investigated how to practically utilize a hierarchical clustering of time-dependent scalar fields to analyze the data. To this end, a system of different views is proposed which are linked through various interaction possibilities. The main advantage of the system is that a dataset can now be inspected at an arbitrary level of detail without having to recompute a clustering with different parameters. Interesting branches of the simulation can be expanded to reveal smaller differences in critical clusters or folded to show only a coarse representation of the less interesting parts of the dataset. The last building block of the suit of visual analysis methods developed for this thesis aims at a robust, (largely) automatic detection and tracking of certain features in a scalar field ensemble. Techniques are presented that I found can identify and track super- and sub-levelsets. And I derive “centers of action” from these sets which mark the location of extremal climate phenomena that govern the weather (e.g. Icelandic Low and Azores High). The thesis also presents visual and quantitative techniques to evaluate the temporal change of the positions of these centers; such a displacement would be likely to manifest in changes in weather. In a preliminary analysis with my collaborators, we indeed observed changes in the loci of the centers of action in a simulation with increased greenhouse gas concentration as compared to pre-industrial concentration levels

Reducing Occlusion in Cinema Databases through Feature-Centric Visualizations

In modern supercomputer architectures, the I/O capabilities do not keep up with the computational speed. Image-based techniques are one very promising approach to a scalable output format for visual analysis, in which a reduced output that corresponds to the visible state of the simulation is rendered in-situ and stored to disk. These techniques can support interactive exploration of the data through image compositing and other methods, but automatic methods of highlighting data and reducing clutter can make these methods more effective. In this paper, we suggest a method of assisted exploration through the combination of feature-centric analysis with image space techniques and show how the reduction of the data to features of interest reduces occlusion in the output for a set of example applications

Jacobi Fiber Surfaces for Bivariate Reeb Space Computation

This paper presents an efficient algorithm for the computation of the Reeb space of an input bivariate piecewise linear scalar function f defined on a tetrahedral mesh. By extending and generalizing algorithmic concepts from the univariate case to the bivariate one, we report the first practical, output-sensitive algorithm for the exact computation of such a Reeb space. The algorithm starts by identifying the Jacobi set of f , the bivariate analogs of critical points in the univariate case. Next, the Reeb space is computed by segmenting the input mesh along the new notion of Jacobi Fiber Surfaces, the bivariate analog of critical contours in the univariate case. We additionally present a simplification heuristic that enables the progressive coarsening of the Reeb space. Our algorithm is simple to implement and most of its computations can be trivially parallelized. We report performance numbers demonstrating orders of magnitude speedups over previous approaches, enabling for the first time the tractable computation of bivariate Reeb spaces in practice. Moreover, unlike range-based quantization approaches (such as the Joint Contour Net), our algorithm is parameter-free. We demonstrate the utility of our approach by using the Reeb space as a semi-automatic segmentation tool for bivariate data. In particular, we introduce continuous scatterplot peeling, a technique which enables the reduction of the cluttering in the continuous scatterplot, by interactively selecting the features of the Reeb space to project. We provide a VTK-based C++ implementation of our algorithm that can be used for reproduction purposes or for the development of new Reeb space based visualization techniques

Progressive Wasserstein Barycenters of Persistence Diagrams

This paper presents an efficient algorithm for the progressive approximation of Wasserstein barycenters of persistence diagrams, with applications to the visual analysis of ensemble data. Given a set of scalar fields, our approach enables the computation of a persistence diagram which is representative of the set, and which visually conveys the number, data ranges and saliences of the main features of interest found in the set. Such representative diagrams are obtained by computing explicitly the discrete Wasserstein barycenter of the set of persistence diagrams, a notoriously computationally intensive task. In particular, we revisit efficient algorithms for Wasserstein distance approximation [12,51] to extend previous work on barycenter estimation [94]. We present a new fast algorithm, which progressively approximates the barycenter by iteratively increasing the computation accuracy as well as the number of persistent features in the output diagram. Such a progressivity drastically improves convergence in practice and allows to design an interruptible algorithm, capable of respecting computation time constraints. This enables the approximation of Wasserstein barycenters within interactive times. We present an application to ensemble clustering where we revisit the k-means algorithm to exploit our barycenters and compute, within execution time constraints, meaningful clusters of ensemble data along with their barycenter diagram. Extensive experiments on synthetic and real-life data sets report that our algorithm converges to barycenters that are qualitatively meaningful with regard to the applications, and quantitatively comparable to previous techniques, while offering an order of magnitude speedup when run until convergence (without time constraint). Our algorithm can be trivially parallelized to provide additional speedups in practice on standard workstations. [...

Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence

We report the multi-scale geometric analysis of Lagrangian structures in forced isotropic turbulence and also with a frozen turbulent field. A particle backward-tracking method, which is stable and topology preserving, was applied to obtain the Lagrangian scalar field φ governed by the pure advection equation in the Eulerian form ∂_tφ + u · ∇φ = 0. The temporal evolution of Lagrangian structures was first obtained by extracting iso-surfaces of φ with resolution 1024^3 at different times, from t = 0 to t = T_e, where T_e is the eddy turnover time. The surface area growth rate of the Lagrangian structure was quantified and the formation of stretched and rolled-up structures was observed in straining regions and stretched vortex tubes, respectively. The multi-scale geometric analysis of Bermejo-Moreno & Pullin (J. Fluid Mech., vol. 603, 2008, p. 101) has been applied to the evolution of φ to extract structures at different length scales and to characterize their non-local geometry in a space of reduced geometrical parameters. In this multi-scale sense, we observe, for the evolving turbulent velocity field, an evolutionary breakdown of initially large-scale Lagrangian structures that first distort and then either themselves are broken down or stretched laterally into sheets. Moreover, after a finite time, this progression appears to be insensible to the form of the initially smooth Lagrangian field. In comparison with the statistical geometry of instantaneous passive scalar and enstrophy fields in turbulence obtained by Bermejo-Moreno & Pullin (2008) and Bermejo-Moreno et al. (J. Fluid Mech., vol. 620, 2009, p. 121), Lagrangian structures tend to exhibit more prevalent sheet-like shapes at intermediate and small scales. For the frozen flow, the Lagrangian field appears to be attracted onto a stream-surface field and it develops less complex multi-scale geometry than found for the turbulent velocity field. In the latter case, there appears to be a tendency for the Lagrangian field to move towards a vortex-surface field of the evolving turbulent flow but this is mitigated by cumulative viscous effects