Efficient, decentralized detection of qualitative spatial events in a dynamic scalar field

This paper describes an efficient, decentralized algorithm to monitor qualitative spatial events in a dynamic scalar field. The events of interest involve changes to the critical points (i.e., peak, pits and passes) and edges of the surface network derived from the field. Four fundamental types of event (appearance, disappearance, movement and switch) are defined. Our algorithm is designed to rely purely on qualitative information about the neighborhoods of nodes in the sensor network and does not require information about nodes' coordinate positions. Experimental investigations confirm that our algorithm is efficient, with O(n) overall communication complexity (where n is the number of nodes in the sensor network), an even load balance and low operational latency. The accuracy of event detection is comparable to established centralized algorithms for the identification of critical points of a surface network. Our algorithm is relevant to a broad range of environmental monitoring applications of sensor networks

Lifted Wasserstein Matcher for Fast and Robust Topology Tracking

This paper presents a robust and efficient method for tracking topological features in time-varying scalar data. Structures are tracked based on the optimal matching between persistence diagrams with respect to the Wasserstein metric. This fundamentally relies on solving the assignment problem, a special case of optimal transport, for all consecutive timesteps. Our approach relies on two main contributions. First, we revisit the seminal assignment algorithm by Kuhn and Munkres which we specifically adapt to the problem of matching persistence diagrams in an efficient way. Second, we propose an extension of the Wasserstein metric that significantly improves the geometrical stability of the matching of domain-embedded persistence pairs. We show that this geometrical lifting has the additional positive side-effect of improving the assignment matrix sparsity and therefore computing time. The global framework implements a coarse-grained parallelism by computing persistence diagrams and finding optimal matchings in parallel for every couple of consecutive timesteps. Critical trajectories are constructed by associating successively matched persistence pairs over time. Merging and splitting events are detected with a geometrical threshold in a post-processing stage. Extensive experiments on real-life datasets show that our matching approach is an order of magnitude faster than the seminal Munkres algorithm. Moreover, compared to a modern approximation method, our method provides competitive runtimes while yielding exact results. We demonstrate the utility of our global framework by extracting critical point trajectories from various simulated time-varying datasets and compare it to the existing methods based on associated overlaps of volumes. Robustness to noise and temporal resolution downsampling is empirically demonstrated

Computing and Visualizing Time-Varying Merge Trees for High-Dimensional Data

We introduce a new method that identifies and tracks features in arbitrary dimensions using the merge tree—a structure for identifying topological features based on thresholding in scalar fields. This method analyzes the evolution of features of the function by tracking changes in the merge tree and relates features by matching subtrees between consecutive time steps. Using the time-varying merge tree, we present a structural visualization of the changing function that illustrates both features and their temporal evolution. We demonstrate the utility of our approach by applying it to temporal cluster analysis of high-dimensional point clouds

A Content Analysis-Based Approach to Explore Simulation Verification and Identify Its Current Challenges

Verification is a crucial process to facilitate the identification and removal of errors within simulations. This study explores semantic changes to the concept of simulation verification over the past six decades using a data-supported, automated content analysis approach. We collect and utilize a corpus of 4,047 peer-reviewed Modeling and Simulation (M&S) publications dealing with a wide range of studies of simulation verification from 1963 to 2015. We group the selected papers by decade of publication to provide insights and explore the corpus from four perspectives: (i) the positioning of prominent concepts across the corpus as a whole; (ii) a comparison of the prominence of verification, validation, and Verification and Validation (V&V) as separate concepts; (iii) the positioning of the concepts specifically associated with verification; and (iv) an evaluation of verification\u27s defining characteristics within each decade. Our analysis reveals unique characterizations of verification in each decade. The insights gathered helped to identify and discuss three categories of verification challenges as avenues of future research, awareness, and understanding for researchers, students, and practitioners. These categories include conveying confidence and maintaining ease of use; techniques\u27 coverage abilities for handling increasing simulation complexities; and new ways to provide error feedback to model users

Generalized Framework and Algorithms for Illustrative Visualization of Time-Varying Data on Unstructured Meshes

Photo- and physically-realistic techniques are often insufficient for visualization of simulation results, especially for 3D and time-varying datasets. Substantial research efforts have been dedicated to the development of non-photorealistic and illustration-inspired visualization techniques for compact and intuitive presentation of such complex datasets. While these efforts have yielded valuable visualization results, a great deal of work has been reproduced in studies as individual research groups often develop purpose-built platforms. Additionally, interoperability between illustrative visualization software is limited due to specialized processing and rendering architectures employed in different studies. In this investigation, a generalized framework for illustrative visualization is proposed, and implemented in marmotViz, a ParaView plugin, enabling its use on variety of computing platforms with various data file formats and mesh geometries. Detailed descriptions of the region-of-interest identification and feature-tracking algorithms incorporated into this tool are provided. Additionally, implementations of multiple illustrative effect algorithms are presented to demonstrate the use and flexibility of this framework. By providing a framework and useful underlying functionality, the marmotViz tool can act as a springboard for future research in the field of illustrative visualization

Visual Analysis of High-Dimensional Point Clouds using Topological Abstraction

This thesis is about visualizing a kind of data that is trivial to process by computers but difficult to imagine by humans because nature does not allow for intuition with this type of information: high-dimensional data. Such data often result from representing observations of objects under various aspects or with different properties. In many applications, a typical, laborious task is to find related objects or to group those that are similar to each other. One classic solution for this task is to imagine the data as vectors in a Euclidean space with object variables as dimensions. Utilizing Euclidean distance as a measure of similarity, objects with similar properties and values accumulate to groups, so-called clusters, that are exposed by cluster analysis on the high-dimensional point cloud. Because similar vectors can be thought of as objects that are alike in terms of their attributes, the point cloud\''s structure and individual cluster properties, like their size or compactness, summarize data categories and their relative importance. The contribution of this thesis is a novel analysis approach for visual exploration of high-dimensional point clouds without suffering from structural occlusion. The work is based on implementing two key concepts: The first idea is to discard those geometric properties that cannot be preserved and, thus, lead to the typical artifacts. Topological concepts are used instead to shift away the focus from a point-centered view on the data to a more structure-centered perspective. The advantage is that topology-driven clustering information can be extracted in the data\''s original domain and be preserved without loss in low dimensions. The second idea is to split the analysis into a topology-based global overview and a subsequent geometric local refinement. The occlusion-free overview enables the analyst to identify features and to link them to other visualizations that permit analysis of those properties not captured by the topological abstraction, e.g. cluster shape or value distributions in particular dimensions or subspaces. The advantage of separating structure from data point analysis is that restricting local analysis only to data subsets significantly reduces artifacts and the visual complexity of standard techniques. That is, the additional topological layer enables the analyst to identify structure that was hidden before and to focus on particular features by suppressing irrelevant points during local feature analysis. This thesis addresses the topology-based visual analysis of high-dimensional point clouds for both the time-invariant and the time-varying case. Time-invariant means that the points do not change in their number or positions. That is, the analyst explores the clustering of a fixed and constant set of points. The extension to the time-varying case implies the analysis of a varying clustering, where clusters appear as new, merge or split, or vanish. Especially for high-dimensional data, both tracking---which means to relate features over time---but also visualizing changing structure are difficult problems to solve

Contributions to the cornerstones of interaction in visualization: strengthening the interaction of visualization

Visualization has become an accepted means for data exploration and analysis. Although interaction is an important component of visualization approaches, current visualization research pays less attention to interaction than to aspects of the graphical representation. Therefore, the goal of this work is to strengthen the interaction side of visualization. To this end, we establish a unified view on interaction in visualization. This unified view covers four cornerstones: the data, the tasks, the technology, and the human.Visualisierung hat sich zu einem unverzichtbaren Werkzeug für die Exploration und Analyse von Daten entwickelt. Obwohl Interaktion ein wichtiger Bestandteil solcher Werkzeuge ist, wird der Interaktion in der aktuellen Visualisierungsforschung weniger Aufmerksamkeit gewidmet als Aspekten der graphischen Repräsentation. Daher ist es das Ziel dieser Arbeit, die Interaktion im Bereich der Visualisierung zu stärken. Hierzu wird eine einheitliche Sicht auf Interaktion in der Visualisierung entwickelt