Abstract Computer vision increasingly uses synthetic data from physically based rendering to supplement limited real‐world datasets. In industrial inspection, defect data is scarce and the rendering pipeline is explicitly controlled, and synthetic defect generation therefore becomes a dataset design problem. In this setting, building a dataset means choosing points in a rendering parameter space: defect shape, material, illumination, viewpoint, and sampling define the training distribution, but their effect on downstream learning is often hard to judge from images alone. We therefore study how these factors change defect features, where their relation to downstream learning is easier to inspect. Our results show that the rendering factors do not matter equally: defect shape, material, illumination, and viewpoint often affect downstream behavior much more than the number of samples per pixel. Synthetic subsets that transfer better downstream tend to stay close to real defect features, cover the observed defect modes, and stay separated from the defect‐free (OK) region. Based on these observations, we build a simple feature‐space screening heuristic for selecting subsets from large candidate pools. The selected subsets often outperform matched random selection for downstream segmentation on real data.

This paper presents a generalization of the Wasserstein distance for both 0th persistence diagrams and merge trees (Edelsbrunner and Harer 2009), (Pont et al. 2022) that takes advantage of the regions of their topological features in the input domain. Specifically, we redefine the comparison of topological features as a distance between the values of their extrema-aligned regions. It results in a more discriminative metric than the classical Wasserstein distance and generalizes it through an input parameter adjusting the impact of the region properties in the distance. We present two strategies to control both computation time and memory storage of our method by respectively enabling the use of subsets of the regions in the computation, and by compressing the regions' properties to obtain low-memory representations. Extensive experiments on openly available ensemble data demonstrate the efficiency of our method, with running times on the orders of minutes on average. We show the utility of our contributions with two applications. First, we use the assignments between topological features provided by our method to track their evolution in time-varying ensembles and propose the temporal persistence curves to facilitate the understanding of how these features appear, disappear and change over time. Second, our method allows to compute a distance matrix of an ensemble that can be used for dimensionality reduction purposes and visually represent in 2D all its members, we show that such distance matrices also allow to detect key phases in the ensemble. Finally, we provide a C++ implementation that can be used to reproduce our results.

This January 2025 issue of the IEEE Transactions on Visualization and Computer Graphics (TVCG) contains the proceedings of IEEE VIS 2024, held on October 1318 October, 2024 in St. Pete Beach, Florida, USA, with the three General Chairs Paul Rosen (University of Utah), Kristi Potter (U.S. National Renewable Energy Laboratory), and Remco Chang (Tufts University). With IEEE VIS 2024, the conference series is in its 35th year.

In this paper, we present a novel heuristic algorithm for the stable but NP-complete deformation-based edit distance on merge trees. Our key contribution is the introduction of a user-controlled look-ahead parameter that allows to trade off accuracy and computational cost. We achieve a fixed parameter tractable running time that is polynomial in the size of the input but exponential in the look-ahead value. This extension unlocks the potential of the deformation-based edit distance in handling saddle swaps, while maintaining feasible computation times. Experimental results demonstrate the computational efficiency and effectiveness of this approach in handling specific perturbations.

Abstract Scientists working with uncertain data, such as climate simulations, medical images, or ensembles of physical simulations, regularly confront the problem of comparing observations, e.g., to identify similarities, differences, or patterns. Current approaches in comparative visualization of uncertain scalar fields mainly rely on juxtaposition of both data and uncertainties, where each is represented using, e.g., color mapping or volume rendering. While interpretation of uncertain scalar data from visual encodings is already cognitively challenging, comparison of uncertain fields without explicit visualization support adds a further layer of complexity. In this paper, we present a theoretical framework to devise and describe a class of techniques that directly visualize differences between two or more uncertain scalar fields in a single image. We model each such technique as a combination of one or more interpolation stages, with the application of distance measures on random variables to the resulting distributions, and an appropriate visual encoding. Our framework captures existing methods and lends itself well to formulating new comparative visualization techniques for uncertain data for different visualization scenarios. Furthermore, by modeling uncertain scalar field differences as random variables themselves, we enable additional opportunities for comparison. We demonstrate the usefulness of our framework and its properties by applying it to effective comparative visualization techniques for several synthetic and real-world data sets.

Visualization, from simple line plots to complex high-dimensional visual analysis systems, has established itself throughout numerous domains to explore, analyze, and evaluate data. Applying such visualizations in the context of simulation science where High-Performance Computing (HPC) produces ever-growing amounts of data that is more complex, potentially multidimensional, and multimodal, takes up resources and a high level of technological experience often not available to domain experts. In this work, we present DaVE - a curated database of visualization examples, which aims to provide state-of-the-art and advanced visualization methods that arise in the context of HPC applications. Based on domain- or data-specific descriptors entered by the user, DaVE provides a list of appropriate visualization techniques, each accompanied by descriptions, examples, references, and resources. Sample code, adaptable container templates, and recipes for easy integration in HPC applications can be downloaded for easy access to high-fidelity visualizations. While the database is currently filled with a limited number of entries based on a broad evaluation of needs and challenges of current HPC users, DaVE is designed to be easily extended by experts from both the visualization and HPC communities.

This system paper documents the technical foundations for the extension of the Topology ToolKit (TTK) to distributed-memory parallelism with the Message Passing Interface (MPI). While several recent papers introduced topology-based approaches for distributed-memory environments, these were reporting experiments obtained with tailored, mono-algorithm implementations. In contrast, we describe in this paper a versatile approach (supporting both triangulated domains and regular grids) for the support of topological analysis pipelines, i.e., a sequence of topological algorithms interacting together, possibly on distinct numbers of processes. While developing this extension, we faced several algorithmic and software engineering challenges, which we document in this paper. Specifically, we describe an MPI extension of TTK's data structure for triangulation representation and traversal, a central component to the global performance and generality of TTK's topological implementations. We also introduce an intermediate interface between TTK and MPI, both at the global pipeline level, and at the fine-grain algorithmic level. We provide a taxonomy for the distributed-memory topological algorithms supported by TTK, depending on their communication needs and provide examples of hybrid MPI+thread parallelizations. Detailed performance analyses show that parallel efficiencies range from 20% to 80% (depending on the algorithms), and that the MPI-specific preconditioning introduced by our framework induces a negligible computation time overhead. We illustrate the new distributed-memory capabilities of TTK with an example of advanced analysis pipeline, combining multiple algorithms, run on the largest publicly available dataset we have found (120 billion vertices) on a standard cluster with 64 nodes (for a total of 1536 cores). Finally, we provide a roadmap for the completion of TTK's MPI extension, along with generic recommendations for each algorithm communication category.

Over the last decade merge trees have been proven to support a plethora of visualization and analysis tasks since they effectively abstract complex datasets. This paper describes the ExTreeM-Algorithm: A scalable algorithm for the computation of merge trees via extremum graphs. The core idea of ExTreeM is to first derive the extremum graph G of an input scalar field f defined on a cell complex K, and subsequently compute the unaugmented merge tree of f on G instead of K; which are equivalent. Any merge tree algorithm can be carried out significantly faster on G, since K in general contains substantially more cells than G. To further speed up computation, ExTreeM includes a tailored procedure to derive merge trees of extremum graphs. The computation of the fully augmented merge tree, i.e., a merge tree domain segmentation of K, can then be performed in an optional post-processing step. All steps of ExTreeM consist of procedures with high parallel efficiency, and we provide a formal proof of its correctness. Our experiments, performed on publicly available datasets, report a speedup of up to one order of magnitude over the state-of-the-art algorithms included in the TTK and VTK-m software libraries, while also requiring significantly less memory and exhibiting excellent scaling behavior.

This article presents a well-scaling parallel algorithm for the computation of Morse-Smale (MS) segmentations, including the region separators and region boundaries. The segmentation of the domain into ascending and descending manifolds, solely defined on the vertices, improves the computational time using path compression and fully segments the border region. Region boundaries and region separators are generated using a multi-label marching tetrahedra algorithm. This enables a fast and simple solution to find optimal parameter settings in preliminary exploration steps by generating an MS complex preview. It also poses a rapid option to generate a fast visual representation of the region geometries for immediate utilization. Two experiments demonstrate the performance of our approach with speedups of over an order of magnitude in comparison to two publicly available implementations. The example section shows the similarity to the MS complex, the useability of the approach, and the benefits of this method with respect to the presented datasets. We provide our implementation with the paper.

Comparative visualization of scalar fields is often facilitated using similarity measures such as edit distances. In this paper, we describe a novel approach for similarity analysis of scalar fields that combines two recently introduced techniques: Wasserstein geodesics/barycenters as well as path mappings, a branch decomposition-independent edit distance. Effectively, we are able to leverage the reduced susceptibility of path mappings to small perturbations in the data when compared with the original Wasserstein distance. Our approach therefore exhibits superior performance and quality in typical tasks such as ensemble summarization, ensemble clustering, and temporal reduction of time series, while retaining practically feasible runtimes. Beyond studying theoretical properties of our approach and discussing implementation aspects, we describe a number of case studies that provide empirical insights into its utility for comparative visualization, and demonstrate the advantages of our method in both synthetic and real-world scenarios. We supply a C++ implementation that can be used to reproduce our results.

Abstract In this work, we propose a visual analytics system to analyze deep reinforcement learning (deepRL) models working on the track reconstruction of charged particles in the field of particle physics. The data of these charged particles are in the form of point clouds with high-dimensional features. We use one of the existing post hoc saliency methods of explainable artificial intelligence (XAI) and extend its adaptation to compute saliency attributions for the input data corresponding to the output of the model. Our proposed system helps users to explore these saliency attributions corresponding to the high-dimensional input data of the machine learning model and interpret the decision-making process of the model. In particular, we provide the users with multiple task-oriented components, different types of linked views and interactive tools to analyze the model. We explain how to use the system by outlining a typical user workflow and demonstrate the system’s usefulness using several case studies which address specific analysis tasks.

Abstract Machine learning algorithms are widely applied to create powerful prediction models. With increasingly complex models, humans' ability to understand the decision function (that maps from a high‐dimensional input space) is quickly exceeded. To explain a model's decisions, black‐box methods have been proposed that provide either non‐linear maps of the global topology of the decision boundary, or samples that allow approximating it locally. The former loses information about distances in input space, while the latter only provides statements about given samples, but lacks a focus on the underlying model for precise ‘What‐If'‐reasoning. In this paper, we integrate both approaches and propose an interactive exploration method using local linear maps of the decision space. We create the maps on high‐dimensional hyperplanes—2D‐slices of the high‐dimensional parameter space—based on statistical and personal feature mutability and guided by feature importance. We complement the proposed workflow with established model inspection techniques to provide orientation and guidance. We demonstrate our approach on real‐world datasets and illustrate that it allows identification of instance‐based decision boundary structures and can answer multi‐dimensional ‘What‐If'‐questions, thereby identifying counterfactual scenarios visually.

Abstract The computational work to perform particle advection‐based flow visualization techniques varies based on many factors, including number of particles, duration, and mesh type. In many cases, the total work is significant, and total execution time (“performance”) is a critical issue. This state‐of‐the‐art report considers existing optimizations for particle advection, using two high‐level categories: algorithmic optimizations and hardware efficiency. The sub‐categories for algorithmic optimizations include solvers, cell locators, I/O efficiency, and precomputation, while the sub‐categories for hardware efficiency all involve parallelism: shared‐memory, distributed‐memory, and hybrid. Finally, this STAR concludes by identifying current gaps in our understanding of particle advection performance and its optimizations.

Abstract Edit distances between merge trees of scalar fields have many applications in scientific visualization, such as ensemble analysis, feature tracking or symmetry detection. In this paper, we propose branch mappings, a novel approach to the construction of edit mappings for merge trees. Classic edit mappings match nodes or edges of two trees onto each other, and therefore have to either rely on branch decompositions of both trees or have to use auxiliary node properties to determine a matching. In contrast, branch mappings employ branch properties instead of node similarity information, and are independent of predetermined branch decompositions. Especially for topological features, which are typically based on branch properties, this allows a more intuitive distance measure which is also less susceptible to instabilities from small‐scale perturbations. For trees with 𝒪(n) nodes, we describe an 𝒪(n4) algorithm for computing optimal branch mappings, which is faster than the only other branch decomposition‐independent method in the literature by more than a linear factor. Furthermore, we compare the results of our method on synthetic and real‐world examples to demonstrate its practicality and utility.

We present Knowledge Rocks, an implementation strategy and guideline for augmenting visualization systems to knowledge-assisted visualization systems, as defined by the KAVA model. Visualization systems become more and more sophisticated. Hence, it is increasingly important to support users with an integrated knowledge base in making constructive choices and drawing the right conclusions. We support the effective reactivation of visualization software resources by augmenting them with knowledge-assistance. To provide a general and yet supportive implementation strategy, we propose an implementation process that bases on an application-agnostic architecture. This architecture is derived from existing knowledge-assisted visualization systems and the KAVA model. Its centerpiece is an ontology that is able to automatically analyze and classify input data, linked to a database to store classified instances. We discuss design decisions and advantages of the KR framework and illustrate its broad area of application in diverse integration possibilities of this architecture into an existing visualization system. In addition, we provide a detailed case study by augmenting an it-security system with knowledge-assistance facilities.

This paper describes a localized algorithm for the topological simplification of scalar data, an essential pre-processing step of topological data analysis (TDA). Given a scalar field f and a selection of extrema to preserve, the proposed localized topological simplification (LTS) derives a function g that is close to f and only exhibits the selected set of extrema. Specifically, sub- and superlevel set components associated with undesired extrema are first locally flattened and then correctly embedded into the global scalar field, such that these regions are guaranteed-from a combinatorial perspective-to no longer contain any undesired extrema. In contrast to previous global approaches, LTS only and independently processes regions of the domain that actually need to be simplified, which already results in a noticeable speedup. Moreover, due to the localized nature of the algorithm, LTS can utilize shared-memory parallelism to simplify regions simultaneously with a high parallel efficiency (70%). Hence, LTS significantly improves interactivity for the exploration of simplification parameters and their effect on subsequent topological analysis. For such exploration tasks, LTS brings the overall execution time of a plethora of TDA pipelines from minutes down to seconds, with an average observed speedup over state-of-the-art techniques of up to ×36. Furthermore, in the special case where preserved extrema are selected based on topological persistence, an adapted version of LTS partially computes the persistence diagram and simultaneously simplifies features below a predefined persistence threshold. The effectiveness of LTS, its parallel efficiency, and its resulting benefits for TDA are demonstrated on several simulated and acquired datasets from different application domains, including physics, chemistry, and biomedical imaging.

Contemporary scientific data sets require fast and scalable topological analysis to enable visualization, simplification and interaction. Within this field, parallel merge tree construction has seen abundant recent contributions, with a trend of decentralized, task-parallel or SMP-oriented algorithms dominating in terms of total runtime. However, none of these recent approaches computed complete merge trees on distributed systems, leaving this field to traditional divide & conquer approaches. This article introduces a scalable, parallel and distributed algorithm for merge tree construction outperforming the previously fastest distributed solution by a factor of around three. This is achieved by a task-parallel identification of individual merge tree arcs by growing regions around critical points in the data, without any need for ordered progression or global data structures, based on a novel insight introducing a sufficient local boundary for region growth.

Abstract We present a state‐of‐the‐art report on time‐dependent flow topology. We survey representative papers in visualization and provide a taxonomy of existing approaches that generalize flow topology from time‐independent to time‐dependent settings. The approaches are classified based upon four categories: tracking of steady topology, reference frame adaption, pathline classification or clustering, and generalization of critical points. Our unique contributions include introducing a set of desirable mathematical properties to interpret physical meaningfulness for time‐dependent flow visualization, inferring mathematical properties associated with selective research papers, and utilizing such properties for classification. The five most important properties identified in the existing literature include coincidence with the steady case, induction of a partition within the domain, Lagrangian invariance, objectivity, and Galilean invariance.

Abstract We describe a novel technique for the simultaneous visualization of multiple scalar fields, e.g. representing the members of an ensemble, based on their contour trees. Using tree alignments, a graph‐theoretic concept similar to edit distance mappings, we identify commonalities across multiple contour trees and leverage these to obtain a layout that can represent all trees simultaneously in an easy‐to‐interpret, minimally‐cluttered manner. We describe a heuristic algorithm to compute tree alignments for a given similarity metric, and give an algorithm to compute a joint layout of the resulting aligned contour trees. We apply our approach to the visualization of scalar field ensembles, discuss basic visualization and interaction possibilities, and demonstrate results on several analytic and real‐world examples.

Abstract Streamlines are an extensively utilized flow visualization technique for understanding, verifying, and exploring computational fluid dynamics simulations. One of the major challenges associated with the technique is selecting which streamlines to display. Using a large number of streamlines results in dense, cluttered visualizations, often containing redundant information and occluding important regions, whereas using a small number of streamlines could result in missing key features of the flow. Many solutions to select a representative set of streamlines have been proposed by researchers over the past two decades. In this state‐of‐the‐art report, we analyze and classify seed placement and streamline selection (SPSS) techniques used by the scientific flow visualization community. At a high‐level, we classify techniques into automatic and manual techniques, and further divide automatic techniques into three strategies: density‐based, feature‐based, and similarity‐based. Our analysis evaluates the identified strategy groups with respect to focus on regions of interest, minimization of redundancy, and overall computational performance. Finally, we consider the application contexts and tasks for which SPSS techniques are currently applied and have potential applications in the future.

Operation technology networks, i.e. hard- and software used for monitoring and controlling physical/industrial processes, have been considered immune to cyber attacks for a long time. A recent increase of attacks in these networks proves this assumption wrong. Several technical constraints lead to approaches to detect attacks on industrial processes using available sensor data. This setting differs fundamentally from anomaly detection in IT-network traffic and requires new visualization approaches adapted to the common periodical behavior in OT-network data. We present a tailored visualization system that utilizes inherent features of measurements from industrial processes to full capacity to provide insight into the data and support triage analysis by laymen and experts. The novel combination of spiral plots with results from anomaly detection was implemented in an interactive system. The capabilities of our system are demonstrated using sensor and actuator data from a real-world water treatment process with introduced attacks. Exemplary analysis strategies are presented. Finally, we evaluate effectiveness and usability of our system and perform an expert evaluation.

This work describes an approach for the interactive visual analysis of large-scale simulations, where numerous superlevel set components and their evolution are of primary interest. The approach first derives, at simulation runtime, a specialized Cinema database that consists of images of component groups, and topological abstractions. This database is processed by a novel graph operation-based nested tracking graph algorithm (GO-NTG) that dynamically computes NTGs for component groups based on size, overlap, persistence, and level thresholds. The resulting NTGs are in turn used in a feature-centered visual analytics framework to query specific database elements and update feature parameters, facilitating flexible post hoc analysis.

Abstract Data reduction is increasingly being applied to scientific data for numerical simulations, scientific visualizations and data analyses. It is most often used to lower I/O and storage costs, and sometimes to lower in‐memory data size as well. With this paper, we consider five categories of data reduction techniques based on their information loss: (1) truly lossless, (2) near lossless, (3) lossy, (4) mesh reduction and (5) derived representations. We then survey available techniques in each of these categories, summarize their properties from a practical point of view and discuss relative merits within a category. We believe, in total, this work will enable simulation scientists and visualization/data analysis scientists to decide which data reduction techniques will be most helpful for their needs.

Abstract Eulerian Method of Moment (MoM) solvers are gaining popularity for multi‐phase CFD simulation involving bubbles or droplets in process engineering. Because the actual positions of bubbles are uncertain, the spatial distribution of bubbles is described by scalar fields of moments, which can be interpreted as probability density functions. Visualizing these simulation results and comparing them to physical experiments is challenging, because neither the shape nor the distribution of bubbles described by the moments lend themselves to visual interpretation. In this work, we describe a visualization approach that provides explicit instances of the bubble distribution and produces bubble geometry based on local flow properties. To facilitate animation, the instancing of the bubble distribution provides coherence over time by advancing bubbles between time steps and updating the distribution. Our approach provides an intuitive visualization and enables direct visual comparison of simulation results to physical experiments.

Abstract Tracking graphs are a well established tool in topological analysis to visualize the evolution of components and their properties over time, i.e., when components appear, disappear, merge, and split. However, tracking graphs are limited to a single level threshold and the graphs may vary substantially even under small changes to the threshold. To examine the evolution of features for varying levels, users have to compare multiple tracking graphs without a direct visual link between them. We propose a novel, interactive, nested graph visualization based on the fact that the tracked superlevel set components for different levels are related to each other through their nesting hierarchy. This approach allows us to set multiple tracking graphs in context to each other and enables users to effectively follow the evolution of components for different levels simultaneously. We demonstrate the effectiveness of our approach on datasets from finite pointset methods, computational fluid dynamics, and cosmology simulations.

Abstract This paper presents the state of the art in the area of topology‐based visualization. It describes the process and results of an extensive annotation for generating a definition and terminology for the field. The terminology enabled a typology for topological models which is used to organize research results and the state of the art. Our report discusses relations among topological models and for each model describes research results for the computation, simplification, visualization, and application. The paper identifies themes common to subfields, current frontiers, and unexplored territory in this research area.

In car manufacturing, quality management and control are important parts of the series process. In series production, many parts are controlled in various ways in some or all stages of assembly. While tactile measurements are mostly restricted to the points on an inspection plan, this restriction does not apply to optical measurements. We propose a method based on the theory of Pareto sets (multivariate topological analysis) to cope with the large amount of data produced by optical measurements and to find points of interest on the measured surface in addition to the inspection plan. We describe a method which automatically detects areas of systematic errors on a component and visualizes them on the triangulated surface. The visualization can help experts to decide, whether a detected feature is severe enough to be added to the inspection plan.

The increasing amount of data generated by Location Based Social Networks (LBSN) such as Twitter, Flickr, or Foursquare, is currently drawing the attention of urban planners, as it is a new source of data that contains valuable information about the behavior of the inhabitants of a city. Making this data accessible to the urban planning domain can add value to the decision making processes. However, the analysis of the spatial and temporal characteristics of this data in the context of urban planning is an ongoing research problem. This paper describes ongoing work in the design and development of a visual exploration tool to facilitate this task. The proposed design provides an approach towards the integration of a visual exploration tool and the capabilities of a visual query system from a multilevel perspective (e.g., multiple spatial scales and temporal resolutions implicit in LBSN data). A preliminary discussion about the design and the potential insights that can be gained from the exploration and analysis of this data with the proposed tool is presented, along with the conclusions and future work for the continuation of this work.

Analysis of spatio-temporal event data is of central importance in many domains of science and policy making. Current visualization methods rely on animation, small multiples, and space-time cubes to enable spatio-temporal data exploration. These methods require the user to remember state spaces or deal with layout occlusions when exploring their data. To overcome such issues, we propose a novel visualization technique for such data that applies the topological notion of Reeb graphs to identify hotspots as areas of relatively high event density within kernel density estimates. We illustrate that the topological identification of hotspots proposed in this paper is able to elucidate lifetime, properties, and relationships of hotspots by visualizing their temporal evolution based on the spatio-temporal Reeb graph. To validate our approach, we demonstrate our method on an epidemiological and a crime dataset. The resulting visualizations assist users in quickly identifying and comprehending important dates, events, hotspot properties, and relationships between hotspots.

Topological and structural analysis of multivariate data is aimed at improving the understanding and usage of such data through identification of intrinsic features and structural relationships among multiple variables. We present two novel methods for simplifying so-called Pareto sets that describe such structural relationships. Such simplification is a precondition for meaningful visualization of structurally rich or noisy data. As a framework for simplification operations, we introduce a decomposition of the data domain into regions of equivalent structural behavior and the reachability graph that describes global connectivity of Pareto extrema. Simplification is then performed as a sequence of edge collapses in this graph; to determine a suitable sequence of such operations, we describe and utilize a comparison measure that reflects the changes to the data that each operation represents. We demonstrate and evaluate our methods on synthetic and real-world examples.

Abstract Analysis of chemical constituents from mass spectrometry of aerosols involves non‐negative matrix factorization, an approximation of high‐dimensional data in lower‐dimensional space. The associated optimization problem is non‐convex, resulting in crude approximation errors that are not accessible to scientists. To address this shortcoming, we introduce a new methodology for user‐guided error‐aware data factorization that entails an assessment of the amount of information contributed by each dimension of the approximation, an effective combination of visualization techniques to highlight, filter, and analyze error features, as well as a novel means to interactively refine factorizations. A case study and the domain‐expert feedback provided by the collaborating atmospheric scientists illustrate that our method effectively communicates errors of such numerical optimization results and facilitates the computation of high‐quality data factorizations in a simple and intuitive manner.

Abstract How can the notion of topological structures for single scalar fields be extended to multifields? In this paper we propose a definition for such structures using the concepts of Pareto optimality and Pareto dominance. Given a set of piecewise‐linear, scalar functions over a common simplical complex of any dimension, our method finds regions of “consensus” among single fields’ critical points and their connectivity relations. We show that our concepts are useful to data analysis on real‐world examples originating from fluid‐flow simulations; in two cases where the consensus of multiple scalar vortex predictors is of interest and in another case where one predictor is studied under different simulation parameters. We also compare the properties of our approach with current alternatives.

Sets of simulation runs based on parameter and model variation, so-called ensembles, are increasingly used to model physical behaviors whose parameter space is too large or complex to be explored automatically. Visualization plays a key role in conveying important properties in ensembles, such as the degree to which members of the ensemble agree or disagree in their behavior. For ensembles of time-varying vector fields, there are numerous challenges for providing an expressive comparative visualization, among which is the requirement to relate the effect of individual flow divergence to joint transport characteristics of the ensemble. Yet, techniques developed for scalar ensembles are of little use in this context, as the notion of transport induced by a vector field cannot be modeled using such tools. We develop a Lagrangian framework for the comparison of flow fields in an ensemble. Our techniques evaluate individual and joint transport variance and introduce a classification space that facilitates incorporation of these properties into a common ensemble visualization. Variances of Lagrangian neighborhoods are computed using pathline integration and Principal Components Analysis. This allows for an inclusion of uncertainty measurements into the visualization and analysis approach. Our results demonstrate the usefulness and expressiveness of the presented method on several practical examples.

Multifluid simulations often create volume fraction data, representing fluid volumes per region or cell of a fluid data set. Accurate and visually realistic extraction of fluid boundaries is a challenging and essential task for efficient analysis of multifluid data. In this work, we present a new material interface reconstruction method for such volume fraction data. Within each cell of the data set, our method utilizes a gradient field approximation based on trilinearly blended Coons-patches to generate a volume fraction function, representing the change in volume fractions over the cells. A continuously varying isovalue field is applied to this function to produce a smooth interface that preserves the given volume fractions well. Further, the method allows user-controlled balance between volume accuracy and physical plausibility of the interface. The method works on two- and three-dimensional Cartesian grids, and handles multiple materials. Calculations are performed locally and utilize only the one-ring of cells surrounding a given cell, allowing visualizations of the material interfaces to be easily generated on a GPU or in a large-scale distributed parallel environment. Our results demonstrate the robustness, accuracy, and flexibility of the developed algorithms.

Characterizing the interplay between the vortices and forces acting on a wind turbine's blades in a qualitative and quantitative way holds the potential for significantly improving large wind turbine design. This paper introduces an integrated pipeline for highly effective wind and force field analysis and visualization. We extract vortices induced by a turbine's rotation in a wind field, and characterize vortices in conjunction with numerically simulated forces on the blade surfaces as these vortices strike another turbine's blades downstream. The scientifically relevant issue to be studied is the relationship between the extracted, approximate locations on the blades where vortices strike the blades and the forces that exist in those locations. This integrated approach is used to detect and analyze turbulent flow that causes local impact on the wind turbine blade structure. The results that we present are based on analyzing the wind and force field data sets generated by numerical simulations, and allow domain scientists to relate vortex-blade interactions with power output loss in turbines and turbine life expectancy. Our methods have the potential to improve turbine design to save costs related to turbine operation and maintenance.

Peak finding provides more accurate classification for direct volume rendering by sampling directly at local maxima in a transfer function, allowing for better reproduction of high-frequency features. However, the 1D peak finding technique does not extend to higherdimensional classification. In this work, we develop a new method for peak finding with multidimensional transfer functions, which looks for peaks along the image of the ray. We use piecewise approximations to dynamically sample in transfer function space between world-space samples. As with unidimensional peak finding, this approach is useful for specifying transfer functions with greater precision, and for accurately rendering noisy volume data at lower sampling rates. Multidimensional peak finding produces comparable image quality with order-of-magnitude better performance, and can reproduce features omitted entirely by standard classification. With no precomputation or storage requirements, it is an attractive alternative to preintegration for multidimensional transfer functions.

In this paper, we present a novel technique that allows for the coupled computation and visualization of salient flow structures at interactive frame rates. Our approach is built upon a hierarchical representation of the Finite-time Lyapunov Exponent (FTLE) field, which is adaptively sampled and rendered to meet the need of the current visual setting. The performance of our method allows the user to explore large and complex data sets across scales and to inspect their features at arbitrary resolution. The paper discusses an efficient implementation of this strategy on graphics hardware and provides results for an analytical flow and several CFD simulation data sets.

The study of aerosol composition for air quality research involves the analysis of high-dimensional single particle mass spectrometry data. We describe, apply, and evaluate a novel interactive visual framework for dimensionality reduction of such data. Our framework is based on non-negative matrix factorization with specifically defined regularization terms that aid in resolving mass spectrum ambiguity. Thereby, visualization assumes a key role in providing insight into and allowing to actively control a heretofore elusive data processing step, and thus enabling rapid analysis meaningful to domain scientists. In extending existing black box schemes, we explore design choices for visualizing, interacting with, and steering the factorization process to produce physically meaningful results. A domain-expert evaluation of our system performed by the air quality research experts involved in this effort has shown that our method and prototype admits the finding of unambiguous and physically correct lower-dimensional basis transformations of mass spectrometry data at significantly increased speed and a higher degree of ease.

Many flow visualization techniques, especially integration-based methods, are problematic when the measured data exhibit noise and discretization issues. Particularly, this is the case for flow-sensitive phase-contrast magnetic resonance imaging (PC-MRI) data sets which not only record anatomic information, but also time-varying flow information. We propose a novel approach for the visualization of such data sets using integration-based methods. Our ideas are based upon finite-time Lyapunov exponents (FTLE) and enable identification of vessel boundaries in the data as high regions of separation. This allows us to correctly restrict integration-based visualization to blood vessels. We validate our technique by comparing our approach to existing anatomy-based methods as well as addressing the benefits and limitations of using FTLE to restrict flow. We also discuss the importance of parameters, i.e., advection length and data resolution, in establishing a well-defined vessel boundary. We extract appropriate flow lines and surfaces that enable the visualization of blood flow within the vessels. We further enhance the visualization by analyzing flow behavior in the seeded region and generating simplified depictions.

Streamline computation in a very large vector field data set represents a significant challenge due to the nonlocal and data-dependent nature of streamline integration. In this paper, we conduct a study of the performance characteristics of hybrid parallel programming and execution as applied to streamline integration on a large, multicore platform. With multicore processors now prevalent in clusters and supercomputers, there is a need to understand the impact of these hybrid systems in order to make the best implementation choice. We use two MPI-based distribution approaches based on established parallelization paradigms, parallelize over seeds and parallelize over blocks, and present a novel MPI-hybrid algorithm for each approach to compute streamlines. Our findings indicate that the work sharing between cores in the proposed MPI-hybrid parallel implementation results in much improved performance and consumes less communication and I/O bandwidth than a traditional, nonhybrid distributed implementation.

Driven by the ability to generate ever-larger, increasingly complex data, there is an urgent need in the scientific community for scalable analysis methods that can rapidly identify salient trends in scientific data. Query-Driven Visualization (QDV) strategies are among the small subset of techniques that can address both large and highly complex data sets. This paper extends the utility of QDV strategies with a statistics-based framework that integrates nonparametric distribution estimation techniques with a new segmentation strategy to visually identify statistically significant trends and features within the solution space of a query. In this framework, query distribution estimates help users to interactively explore their query's solution and visually identify the regions where the combined behavior of constrained variables is most important, statistically, to their inquiry. Our new segmentation strategy extends the distribution estimation analysis by visually conveying the individual importance of each variable to these regions of high statistical significance. We demonstrate the analysis benefits these two strategies provide and show how they maybe used to facilitate the refinement of constraints over variables expressed in a user's query. We apply our method to data sets from two different scientific domains to demonstrate its broad applicability.

Area-preserving maps are found across a wide range of scientific and engineering problems. Their study is made challenging by the significant computational effort typically required for their inspection but more fundamentally by the fractal complexity of salient structures. The visual inspection of these maps reveals a remarkable topological picture consisting of fixed (or periodic) points embedded in so-called island chains, invariant manifolds, and regions of ergodic behavior. This paper is concerned with the effective visualization and precise topological analysis of area-preserving maps with two degrees of freedom from numerical or analytical data. Specifically, a method is presented for the automatic extraction and characterization of fixed points and the computation of their invariant manifolds, also known as separatrices, to yield a complete picture of the structures present within the scale and complexity bounds selected by the user. This general approach offers a significant improvement over the visual representations that are so far available for area-preserving maps. The technique is demonstrated on a numerical simulation of magnetic confinement in a fusion reactor.

A new material interface reconstruction method for volume fraction data is presented. Our method is comprised of two components: first, we generate initial interface topology; then, using a combination of smoothing and volumetric forces within an active interface model, we iteratively transform the initial material interfaces into high-quality surfaces that accurately approximate the problem's volume fractions. Unlike all previous work, our new method produces material interfaces that are smooth, continuous across cell boundaries, and segment cells into regions with proper volume. These properties are critical during visualization and analysis. Generating high-quality mesh representations of material interfaces is required for accurate calculations of interface statistics, and dramatically increases the utility of material boundary visualizations.

Applying certain visualization techniques to datasets described on unstructured grids requires the interpolation of variables of interest at arbitrary locations within the dataset's domain of definition. Typical solutions to the problem of finding the grid element enclosing a given interpolation point make use of a variety of spatial subdivision schemes. However, existing solutions are memory- intensive, do not scale well to large grids, or do not work reliably on grids describing complex geometries. In this paper, we propose a data structure and associated construction algorithm for fast cell location in unstructured grids, and apply it to the interpolation problem. Based on the concept of bounding interval hierarchies, the proposed approach is memory-efficient, fast and numerically robust. We examine the performance characteristics of the proposed approach and compare it to existing approaches using a number of benchmark problems related to vector field visualization. Furthermore, we demonstrate that our approach can successfully accommodate large datasets, and discuss application to visualization on both CPUs and GPUs.

Integral surfaces are ideal tools to illustrate vector fields and fluid flow structures. However, these surfaces can be visually complex and exhibit difficult geometric properties, owing to strong stretching, shearing and folding of the flow from which they are derived. Many techniques for non-photorealistic rendering have been presented previously. It is, however, unclear how these techniques can be applied to integral surfaces. In this paper, we examine how transparency and texturing techniques can be used with integral surfaces to convey both shape and directional information. We present a rendering pipeline that combines these techniques aimed at faithfully and accurately representing integral surfaces while improving visualization insight. The presented pipeline is implemented directly on the GPU, providing real-time interaction for all rendering modes, and does not require expensive preprocessing of integral surfaces after computation.

Understanding vector fields resulting from large scientific simulations is an important and often difficult task. Streamlines, curves that are tangential to a vector field at each point, are a powerful visualization method in this context. Application of streamline-based visualization to very large vector field data represents a significant challenge due to the non-local and data-dependent nature of streamline computation, and requires careful balancing of computational demands placed on I/O, memory, communication, and processors. In this paper we review two parallelization approaches based on established parallelization paradigms (static decomposition and on-demand loading) and present a novel hybrid algorithm for computing streamlines. Our algorithm is aimed at good scalability and performance across the widely varying computational characteristics of streamline-based problems. We perform performance and scalability studies of all three algorithms on a number of prototypical application problems and demonstrate that our hybrid scheme is able to perform well in different settings.

Time and streak surfaces are ideal tools to illustrate time-varying vector fields since they directly appeal to the intuition about coherently moving particles. However, efficient generation of high-quality time and streak surfaces for complex, large and time-varying vector field data has been elusive due to the computational effort involved. In this work, we propose a novel algorithm for computing such surfaces. Our approach is based on a decoupling of surface advection and surface adaptation and yields improved efficiency over other surface tracking methods, and allows us to leverage inherent parallelization opportunities in the surface advection, resulting in more rapid parallel computation. Moreover, we obtain as a result of our algorithm the entire evolution of a time or streak surface in a compact representation, allowing for interactive, high-quality rendering, visualization and exploration of the evolving surface. Finally, we discuss a number of ways to improve surface depiction through advanced rendering and texturing, while preserving interactivity, and provide a number of examples for real-world datasets and analyze the behavior of our algorithm on them.

Abstract Material interface reconstruction (MIR) is the task of constructing boundary interfaces between regions of homogeneous material, while satisfying volume constraints, over a structured or unstructured spatial domain. In this paper, we present a discrete approach to MIR based upon optimizing the labeling of fractional volume elements within a discretization of the problem's original domain. We detail how to construct and initially label a discretization, and introduce a volume conservative swap move for optimization. Furthermore, we discuss methods for extracting and visualizing material interfaces from the discretization. Our technique has significant advantages over previous methods: we produce interfaces between multiple materials that are continuous across cell boundaries for time‐varying and static data in arbitrary dimension with bounded error.

Abstract 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.

We present a novel approach for the direct computation of integral surfaces in time-dependent vector fields. As opposed to previous work, which we analyze in detail, our approach is based on a separation of integral surface computation into two stages: surface approximation and generation of a graphical representation. This allows us to overcome several limitations of existing techniques. We first describe an algorithm for surface integration that approximates a series of time lines using iterative refinement and computes a skeleton of the integral surface. In a second step, we generate a well-conditioned triangulation. Our approach allows a highly accurate treatment of very large time-varying vector fields in an efficient, streaming fashion. We examine the properties of the presented methods on several example datasets and perform a numerical study of its correctness and accuracy. Finally, we investigate some visualization aspects of integral surfaces.

The recently introduced notion of Finite-Time Lyapunov Exponent to characterize Coherent Lagrangian Structures provides a powerful framework for the visualization and analysis of complex technical flows. Its definition is simple and intuitive, and it has a deep theoretical foundation. While the application of this approach seems straightforward in theory, the associated computational cost is essentially prohibitive. Due to the Lagrangian nature of this technique, a huge number of particle paths must be computed to fill the space-time flow domain. In this paper, we propose a novel scheme for the adaptive computation of FTLE fields in two and three dimensions that significantly reduces the number of required particle paths. Furthermore, for three-dimensional flows, we show on several examples that meaningful results can be obtained by restricting the analysis to a well-chosen plane intersecting the flow domain. Finally, we examine some of the visualization aspects of FTLE-based methods and introduce several new variations that help in the analysis of specific aspects of a flow.

Acoustic quality in room acoustics is measured by well defined quantities, like definition, which can be derived from simulated impulse response filters or measured values. These take into account the intensity and phase shift of multiple reflections due to a wave front emanating from a sound source. Definition (D50) and clarity (C50) for example correspond to the fraction of the energy received in total to the energy received in the first 50 ms at a certain listener position. Unfortunately, the impulse response measured at a single point does not provide any information about the direction of reflections, and about the reflection surfaces which contribute to this measure. For the visualization of room acoustics, however, this information is very useful since it allows to discover regions with high contribution and provides insight into the influence of all reflecting surfaces to the quality measure. We use the phonon tracing method to calculate the contribution of the reflection surfaces to the impulse response for different listener positions. This data is used to compute importance values for the geometry taking a certain acoustic metric into account. To get a visual insight into the directional aspect, we map the importance to the reflecting surfaces of the geometry. This visualization indicates which parts of the surfaces need to be changed to enhance the chosen acoustic quality measure. We apply our method to the acoustic improvement of a lecture hall by means of enhancing the overall speech comprehensibility (clarity) and evaluate the results using glyphs to visualize the clarity (C50) values at listener positions throughout the room.

We present a novel approach for analyzing two-dimensional (2D) flow field data based on the idea of invariant moments. Moment invariants have traditionally been used in computer vision applications, and we have adapted them for the purpose of interactive exploration of flow field data. The new class of moment invariants we have developed allows us to extract and visualize 2D flow patterns, invariant under translation, scaling, and rotation. With our approach one can study arbitrary flow patterns by searching a given 2D flow data set for any type of pattern as specified by a user. Further, our approach supports the computation of moments at multiple scales, facilitating fast pattern extraction and recognition. This can be done for critical point classification, but also for patterns with greater complexity. This multi-scale moment representation is also valuable for the comparative visualization of flow field data. The specific novel contributions of the work presented are the mathematical derivation of the new class of moment invariants, their analysis regarding critical point features, the efficient computation of a novel feature space representation, and based upon this the development of a fast pattern recognition algorithm for complex flow structures.

We present, extend, and apply a method to extract the contribution of a subregion of a data set to the global flow. To isolate this contribution, we decompose the flow in the subregion into a potential flow that is induced by the original flow on the boundary and a localized flow. The localized flow is obtained by subtracting the potential flow from the original flow. Since the potential flow is free of both divergence and rotation, the localized flow retains the original features and captures the region-specific flow that contains the local contribution of the considered subdomain to the global flow. In the remainder of the paper, we describe an implementation on unstructured grids in both two and three dimensions for steady and unsteady flow fields. We discuss the application of some widely used feature extraction methods on the localized flow and describe applications like reverse-flow detection using the potential flow. Finally, we show that our algorithm is robust and scalable by applying it to various flow data sets and giving performance figures.

Stream surfaces are a classic flow visualization technique used to portray the characteristics of vector fields, and texture advection research has made rapid advances in recent years. We present a novel hybrid visualization of texture advection on stream surfaces. This approach conveys properties of the vector field that stream surfaces alone cannot. We apply the visualization technique to various patterns of flow from CFD data important to automotive engine simulation including two patterns of in-cylinder flow (swirl and tumble motion) as well as flow through a cooling jacket. In addition, we explore multiple vector fields defined at the stream surface such as velocity, vorticity, and pressure gradient. The results of our investigation highlight both the strengths and limitations of the hybrid stream surface-texture advection visualization technique and offer new insight to engineers exploring and analyzing their simulations.

In this paper we present an approach to the analysis of the contribution of a small subregion in a dataset to the global flow. To this purpose, we subtract the potential flow that is induced by the boundary of the sub-domain from the original flow. Since the potential flow is free of both divergence and rotation, the localized flow field retains the original features. In contrast to similar approaches, by making explicit use of the boundary flow of the subregion, we manage to isolate the region-specific flow that contains exactly the local contribution of the considered subdomain to the global flow. In the remainder of the paper, we describe an implementation on unstructured grids in both two and three dimensions. We discuss the application of several widely used feature extraction methods on the localized flow, with an emphasis on topological schemes.

We present a visual analysis and exploration of fluid flow through a cooling jacket. Engineers invest a large amount of time and serious effort to optimize the flow through this engine component because of its important role in transferring heat away from the engine block. In this study we examine the design goals that engineers apply in order to construct an ideal-as-possible cooling jacket geometry and use a broad range of visualization tools in order to analyze, explore, and present the results. We systematically employ direct, geometric, and texture-based flow visualization techniques as well as automatic feature extraction and interactive feature-based methodology. And we discuss the relative advantages and disadvantages of these approaches as well as the challenges, both technical and perceptual with this application. The result is a feature-rich state-of-the-art flow visualization analysis applied to an important and complex data set from real-world computational fluid dynamics simulations.

We present an approach for monitoring the positions of vector field singularities and related structural changes in time-dependent datasets. The concept of singularity index is discussed and extended from the well-understood planar case to the more intricate three-dimensional setting. Assuming a tetrahedral grid with linear interpolation in space and time, vector field singularities obey rules imposed by fundamental invariants (Poincare index), which we use as a basis for an efficient tracking algorithm. We apply the presented algorithm to CFD datasets to illustrate its purpose. We examine structures that exhibit topological variations with time and describe some of the insight gained with our method. Examples are given that show a correlation in the evolution of physical quantities that play a role in vortex breakdown.

Vortex breakdowns and flow recirculation are essential phenomena in aeronautics where they appear as a limiting factor in the design of modern aircrafts. Because of the inherent intricacy of these features, standard flow visualization techniques typically yield cluttered depictions. The paper addresses the challenges raised by the visual exploration and validation of two CFD simulations involving vortex breakdown. To permit accurate and insightful visualization we propose a new approach that unfolds the geometry of the breakdown region by letting a plane travel through the structure along a curve. We track the continuous evolution of the associated projected vector field using the theoretical framework of parametric topology. To improve the understanding of the spatial relationship between the resulting curves and lines we use direct volume rendering and multidimensional transfer functions for the display of flow-derived scalar quantities. This enriches the visualization and provides an intuitive context for the extracted topological information. Our results offer clear, synthetic depictions that permit new insight into the structural properties of vortex breakdowns.