research

Scientific Visualization

Scientific visualization, sometimes referred to as visual data analysis, uses the graphical representation of data as a means of gaining understanding and insight into the data. Scientific visualization research at SCI has focused on applications spanning computational fluid dynamics, medical imaging and analysis, and fire simulations. Research involves novel algorithm development to building tools and systems that assist in the comprehension of massive amounts of scientific data. In helping researchers to comprehend spatial and temporal relationships between data, interactive techniques provide better cues than noninteractive techniques; therefore, much of scientific visualization research focuses on better methods for visualization and rendering at interactive rates.

Visualization Project Sites:

Visualization



The Nested Blocks and Guidelines Model
M.D. Meyer, M. Sedlmair, P.S. Quinan, T. Munzner. In Journal of Information Visualization, Special Issue on Evaluation (BELIV), 2014.

We propose the nested blocks and guidelines model (NBGM) for the design and validation of visualization systems. The NBGM extends the previously proposed four-level nested model by adding finer grained structure within each level, providing explicit mechanisms to capture and discuss design decision rationale. Blocks are the outcomes of the design process at a specific level, and guidelines discuss relationships between these blocks. Blocks at the algorithm and technique levels describe design choices, as do data blocks at the abstraction level, whereas task abstraction blocks and domain situation blocks are identified as the outcome of the designer's understanding of the requirements. In the NBGM, there are two types of guidelines: within-level guidelines provide comparisons for blocks within the same level, while between-level guidelines provide mappings between adjacent levels of design. We analyze several recent papers using the NBGM to provide concrete examples of how a researcher can use blocks and guidelines to describe and evaluate visualization research. We also discuss the NBGM with respect to other design models to clarify its role in visualization design. Using the NBGM, we pinpoint two implications for visualization evaluation. First, comparison of blocks at the domain level must occur implicitly downstream at the abstraction level; and second, comparison between blocks must take into account both upstream assumptions and downstream requirements. Finally, we use the model to analyze two open problems: the need for mid-level task taxonomies to fill in the task blocks at the abstraction level, as well as the need for more guidelines mapping between the algorithm and technique levels.




Reflections on How Designers Design With Data
A. Bigelow, S. Drucker, D. Fisher, M.D. Meyer. In Proceedings of the ACM International Conference on Advanced Visual Interfaces (AVI), Note: Awarded Best Paper!, 2014.

In recent years many popular data visualizations have emerged that are created largely by designers whose main area of expertise is not computer science. Designers generate these visualizations using a handful of design tools and environments. To better inform the development of tools intended for designers working with data, we set out to understand designers' challenges and perspectives. We interviewed professional designers, conducted observations of designers working with data in the lab, and observed designers working with data in team settings in the wild. A set of patterns emerged from these observations from which we extract a number of themes that provide a new perspective on design considerations for visualization tool creators, as well as on known engineering problems.




Information Visualization for Science and Policy: Engaging Users and Avoiding Bias
G. McInerny, M. Chen, R. Freeman, D. Gavaghan, M.D. Meyer, F. Rowland, D. Spiegelhalter, M. Steganer, G. Tessarolo, J. Hortal. In Trends in Ecology & Evolution, Vol. 29, No. 3, pp. 148--157. 2014.
DOI: 10.1016/j.tree.2014.01.003

Visualisations and graphics are fundamental to studying complex subject matter. However, beyond acknowledging this value, scientists and science-policy programmes rarely consider how visualisations can enable discovery, create engaging and robust reporting, or support online resources. Producing accessible and unbiased visualisations from complicated, uncertain data requires expertise and knowledge from science, policy, computing, and design. However, visualisation is rarely found in our scientific training, organisations, or collaborations. As new policy programmes develop [e.g., the Intergovernmental Platform on Biodiversity and Ecosystem Services (IPBES)], we need information visualisation to permeate increasingly both the work of scientists and science policy. The alternative is increased potential for missed discoveries, miscommunications, and, at worst, creating a bias towards the research that is easiest to display.




Design Activity Framework for Visualization Design
S. McKenna, D. Mazur, J. Agutter, M.D. Meyer. In IEEE Transactions on Visualization and Computer Graphics (TVCG), 2014.

An important aspect in visualization design is the connection between what a designer does and the decisions the designer makes. Existing design process models, however, do not explicitly link back to models for visualization design decisions. We bridge this gap by introducing the design activity framework, a process model that explicitly connects to the nested model, a well-known visualization design decision model. The framework includes four overlapping activities that characterize the design process, with each activity explicating outcomes related to the nested model. Additionally, we describe and characterize a list of exemplar methods and how they overlap among these activities. The design activity framework is the result of reflective discussions from a collaboration on a visualization redesign project, the details of which we describe to ground the framework in a real-world design process. Lastly, from this redesign project we provide several research outcomes in the domain of cybersecurity, including an extended data abstraction and rich opportunities for future visualization research.



 
Surface boxplots
M.G. Genton, C.R. Johnson, K. Potter, G. Stenchikov, Y. Sun. In Stat Journal, Vol. 3, No. 1, pp. 1--11. 2014.

In this paper, we introduce a surface boxplot as a tool for visualization and exploratory analysis of samples of images. First, we use the notion of volume depth to order the images viewed as surfaces. In particular, we define the median image. We use an exact and fast algorithm for the ranking of the images. This allows us to detect potential outlying images that often contain interesting features not present in most of the images. Second, we build a graphical tool to visualize the surface boxplot and its various characteristics. A graph and histogram of the volume depth values allow us to identify images of interest. The code is available in the supporting information of this paper. We apply our surface boxplot to a sample of brain images and to a sample of climate model outputs.



 
Freeprocessing: Transparent in situ visualization via data interception
T. Fogal, F. Proch, A. Schiewe, O. Hasemann, A. Kempf, J. Krueger. In Proceedings of the 14th Eurographics Conference on Parallel Graphics and Visualization, EGPGV, Eurographics Association, 2014.

In situ visualization has become a popular method for avoiding the slowest component of many visualization pipelines: reading data from disk. Most previous in situ work has focused on achieving visualization scalability on par with simulation codes, or on the data movement concerns that become prevalent at extreme scales. In this work, we consider in situ analysis with respect to ease of use and programmability. We describe an abstraction that opens up new applications for in situ visualization, and demonstrate that this abstraction and an expanded set of use cases can be realized without a performance cost.



 
Visualizing Simulated Electrical Fields from Electroencephalography and Transcranial Electric Brain Stimulation: A Comparative Evaluation
S. Eichelbaum, M. Dannhauer, M. Hlawitschka, D. Brooks, T.R. Knosche, G. Scheuermanna. In Neuroimage, 2014.
DOI: 10.1016/j.neuroimage.2014.04.085

Electrical activity of neuronal populations is a crucial aspect of brain activity. This activity is not measured directly but recorded as electrical potential changes using head surface electrodes (electroencephalogram - EEG). Head surface electrodes can also be deployed to inject electrical currents in order to modulate brain activity (transcranial electric stimulation techniques) for therapeutic and neuroscientific purposes. In electroencephalography and noninvasive electric brain stimulation, electrical fields mediate between electrical signal sources and regions of interest (ROI). These fields can be very complicated in structure, and are influenced in a complex way by the conductivity profile of the human head. Visualization techniques play a central role to grasp the nature of those fields because such techniques allow for an effective conveyance of complex data and enable quick qualitative and quantitative assessments. The examination of volume conduction effects of particular head model parameterizations (e.g., skull thickness and layering), of brain anomalies (e.g., holes in the skull, tumors), location and extent of active brain areas (e.g., high concentrations of current densities) and around current injecting electrodes can be investigated using visualization. Here, we evaluate a number of widely used visualization techniques, based on either the potential distribution or on the current-flow. In particular, we focus on the extractability of quantitative and qualitative information from the obtained images, their effective integration of anatomical context information, and their interaction. We present illustrative examples from clinically and neuroscientifically relevant cases and discuss the pros and cons of the various visualization techniques.




Ovis: A Framework for Visual Analysis of Ocean Forecast Ensembles
T. Hollt, A. Magdy, P. Zhan, G. Chen, G. Gopalakrishnan, I. Hoteit, C.D. Hansen, M. Hadwiger. In IEEE Transactions on Visualization and Computer Graphics (TVCG), Vol. PP, No. 99, pp. 1. 2014.
DOI: 10.1109/TVCG.2014.2307892

We present a novel integrated visualization system that enables interactive visual analysis of ensemble simulations of the sea surface height that is used in ocean forecasting. The position of eddies can be derived directly from the sea surface height and our visualization approach enables their interactive exploration and analysis. The behavior of eddies is important in different application settings of which we present two in this paper. First, we show an application for interactive planning of placement as well as operation of off-shore structures using real-world ensemble simulation data of the Gulf of Mexico. Off-shore structures, such as those used for oil exploration, are vulnerable to hazards caused by eddies, and the oil and gas industry relies on ocean forecasts for efficient operations. We enable analysis of the spatial domain, as well as the temporal evolution, for planning the placement and operation of structures. Eddies are also important for marine life. They transport water over large distances and with it also heat and other physical properties as well as biological organisms. In the second application we present the usefulness of our tool, which could be used for planning the paths of autonomous underwater vehicles, so called gliders, for marine scientists to study simulation data of the largely unexplored Red Sea.




DTIPrep: Quality Control of Diffusion-Weighted Images
I. Oguz, M. Farzinfar, J. Matsui, F. Budin, Z. Liu, G. Gerig, H.J. Johnson, M.A. Styner. In Frontiers in Neuroinformatics, Vol. 8, No. 4, 2014.
DOI: 10.3389/fninf.2014.00004

In the last decade, diffusion MRI (dMRI) studies of the human and animal brain have been used to investigate a multitude of pathologies and drug-related effects in neuroscience research. Study after study identifies white matter (WM) degeneration as a crucial biomarker for all these diseases. The tool of choice for studying WM is dMRI. However, dMRI has inherently low signal-to-noise ratio and its acquisition requires a relatively long scan time; in fact, the high loads required occasionally stress scanner hardware past the point of physical failure. As a result, many types of artifacts implicate the quality of diffusion imagery. Using these complex scans containing artifacts without quality control (QC) can result in considerable error and bias in the subsequent analysis, negatively affecting the results of research studies using them. However, dMRI QC remains an under-recognized issue in the dMRI community as there are no user-friendly tools commonly available to comprehensively address the issue of dMRI QC. As a result, current dMRI studies often perform a poor job at dMRI QC.

Thorough QC of diffusion MRI will reduce measurement noise and improve reproducibility, and sensitivity in neuroimaging studies; this will allow researchers to more fully exploit the power of the dMRI technique and will ultimately advance neuroscience. Therefore, in this manuscript, we present our open-source software, DTIPrep, as a unified, user friendly platform for thorough quality control of dMRI data. These include artifacts caused by eddy-currents, head motion, bed vibration and pulsation, venetian blind artifacts, as well as slice-wise and gradient-wise intensity inconsistencies. This paper summarizes a basic set of features of DTIPrep described earlier and focuses on newly added capabilities related to directional artifacts and bias analysis.




Visualization Collaborations: What Works and Why
R.M. Kirby, M.D. Meyer. In IEEE Computer Graphics and Applications: Visualization Viewpoints, Vol. 33, No. 6, pp. 82--88. 2013.

In 1987, Bruce McCormick and his colleagues outlined the current state and future vision of visualization in scientific computing.1 That same year, Donna Cox pioneered her concept of the "Renaissance team"-a multidisciplinary team of experts focused on solving visualization problems.2 Even if a member of the visualization community has never read McCormick and his colleagues' report or heard Donna Cox speak, he or she has probably been affected by some of their ideas.

Of particular interest to us is their vision for collaboration. McCormick and his colleagues envisioned an interdisciplinary team that through close interaction would develop visualization tools that not only were effective in the context of their immediate collaborative environment but also could be reused by scientists and engineers in other fields. McCormick and his colleagues categorized the types of researchers they imagined constituting these teams, one type being the "visualization scientist/engineer." They even commented on the skills these individuals might have. However, they provided little guidance on how to make such teams successful.

In the more than 25 years since the report, researchers have refined the concepts of interaction versus collaboration,3 interdisciplinary versus multidisciplinary teams,4,5 and independence versus interdependence.6 Here, we use observations from our collective 18 years of collaborative visualization research to help shed light on not just the composition of current and future visualization collaborative teams but also pitfalls and recommendations for successful collaboration. Although our statements might reflect what seasoned visualization researchers are already doing, we believe that reexpressing and possibly reaffirming basic collaboration principles provide benefits.




Scalable Visualization and Interactive Analysis Using Massive Data Streams
V. Pascucci, P.-T. Bremer, A. Gyulassy, G. Scorzelli, C. Christensen, B. Summa, S. Kumar. In Cloud Computing and Big Data, Advances in Parallel Computing, Vol. 23, IOS Press, pp. 212--230. 2013.

Historically, data creation and storage has always outpaced the infrastructure for its movement and utilization. This trend is increasing now more than ever, with the ever growing size of scientific simulations, increased resolution of sensors, and large mosaic images. Effective exploration of massive scientific models demands the combination of data management, analysis, and visualization techniques, working together in an interactive setting. The ViSUS application framework has been designed as an environment that allows the interactive exploration and analysis of massive scientific models in a cache-oblivious, hardware-agnostic manner, enabling processing and visualization of possibly geographically distributed data using many kinds of devices and platforms.

For general purpose feature segmentation and exploration we discuss a new paradigm based on topological analysis. This approach enables the extraction of summaries of features present in the data through abstract models that are orders of magnitude smaller than the raw data, providing enough information to support general queries and perform a wide range of analyses without access to the original data.




Uncertainty Visualization in HARDI based on Ensembles of ODFs
F. Jiao, J.M. Phillips, Y. Gur, C.R. Johnson. In Proceedings of 2013 IEEE Pacific Visualization Symposium, pp. 193--200. 2013.
PubMed ID: 24466504

In this paper, we propose a new and accurate technique for uncertainty analysis and uncertainty visualization based on fiber orientation distribution function (ODF) glyphs, associated with high angular resolution diffusion imaging (HARDI). Our visualization applies volume rendering techniques to an ensemble of 3D ODF glyphs, which we call SIP functions of diffusion shapes, to capture their variability due to underlying uncertainty. This rendering elucidates the complex heteroscedastic structural variation in these shapes. Furthermore, we quantify the extent of this variation by measuring the fraction of the volume of these shapes, which is consistent across all noise levels, the certain volume ratio. Our uncertainty analysis and visualization framework is then applied to synthetic data, as well as to HARDI human-brain data, to study the impact of various image acquisition parameters and background noise levels on the diffusion shapes.




Comprehensible Presentation of Topological Information
G.H. Weber, K. Beketayev, P.-T. Bremer, B. Hamann, M. Haranczyk, M. Hlawitschka, V. Pascucci. No. LBNL-5693E, Lawrence Berkeley National Laboratory, 2013.

Topological information has proven very valuable in the analysis of scientific data. An important challenge that remains is presenting this highly abstract information in a way that it is comprehensible even if one does not have an in-depth background in topology. Furthermore, it is often desirable to combine the structural insight gained by topological analysis with complementary information, such as geometric information. We present an overview over methods that use metaphors to make topological information more accessible to non-expert users, and we demonstrate their applicability to a range of scientific data sets. With the increasingly complex output of exascale simulations, the importance of having effective means of providing a comprehensible, abstract overview over data will grow. The techniques that we present will serve as an important foundation for this purpose.




The CommonGround visual paradigm for biosurveillance
Y. Livnat, E. Jurrus, A.V. Gundlapalli, P. Gestland. In Proceedings of the 2013 IEEE International Conference on Intelligence and Security Informatics (ISI), pp. 352--357. 2013.
ISBN: 978-1-4673-6214-6
DOI: 10.1109/ISI.2013.6578857

Biosurveillance is a critical area in the intelligence community for real-time detection of disease outbreaks. Identifying epidemics enables analysts to detect and monitor disease outbreak that might be spread from natural causes or from possible biological warfare attacks. Containing these events and disseminating alerts requires the ability to rapidly find, classify and track harmful biological signatures. In this paper, we describe a novel visual paradigm to conduct biosurveillance using an Infectious Disease Weather Map. Our system provides a visual common ground in which users can view, explore and discover emerging concepts and correlations such as symptoms, syndromes, pathogens and geographic locations.




Uncertainty Visualization in Forward and Inverse Cardiac Models
B. Burton, B. Erem, K. Potter, P. Rosen, C.R. Johnson, D. Brooks, R.S. Macleod. In Computing in Cardiology CinC, pp. 57--60. 2013.
ISSN: 2325-8861

Quantification and visualization of uncertainty in cardiac forward and inverse problems with complex geometries is subject to various challenges. Specific to visualization is the observation that occlusion and clutter obscure important regions of interest, making visual assessment difficult. In order to overcome these limitations in uncertainty visualization, we have developed and implemented a collection of novel approaches. To highlight the utility of these techniques, we evaluated the uncertainty associated with two examples of modeling myocardial activity. In one case we studied cardiac potentials during the repolarization phase as a function of variability in tissue conductivities of the ischemic heart (forward case). In a second case, we evaluated uncertainty in reconstructed activation times on the epicardium resulting from variation in the control parameter of Tikhonov regularization (inverse case). To overcome difficulties associated with uncertainty visualization, we implemented linked-view windows and interactive animation to the two respective cases. Through dimensionality reduction and superimposed mean and standard deviation measures over time, we were able to display key features in large ensembles of data and highlight regions of interest where larger uncertainties exist.




Evaluation of Interactive Visualization on Mobile Computing Platforms for Selection of Deep Brain Stimulation Parameters
C. Butson, G. Tamm, S. Jain, T. Fogal, Jens Krueger. In IEEE Transactions on Visualization and Computer Graphics, Vol. 19, No. 1, January, 2013.

In recent years there has been significant growth in the use of patient-specific models to predict the effects of neuromodulation therapies such as deep brain stimulation (DBS). However, translating these models from a research environment to the everyday clinical workflow has been a challenge, primarily due to the complexity of the models and the expertise required in specialized visualization software. In this paper, we deploy the interactive visualization system ImageVis3D Mobile , which has been designed for mobile computing devices such as the iPhone or iPad, in an evaluation environment to visualize models of Parkinson’s disease patients who received DBS therapy. Selection of DBS settings is a significant clinical challenge that requires repeated revisions to achieve optimal therapeutic response, and is often performed without any visual representation of the stimulation system in the patient. We used ImageVis3D Mobile to provide models to movement disorders clinicians and asked them to use the software to determine: 1) which of the four DBS electrode contacts they would select for therapy; and 2) what stimulation settings they would choose. We compared the stimulation protocol chosen from the software versus the stimulation protocol that was chosen via clinical practice (independently of the study). Lastly, we compared the amount of time required to reach these settings using the software versus the time required through standard practice. We found that the stimulation settings chosen using ImageVis3D Mobile were similar to those used in standard of care, but were selected in drastically less time. We show how our visualization system, available directly at the point of care on a device familiar to the clinician, can be used to guide clinical decision making for selection of DBS settings. In our view, the positive impact of the system could also translate to areas other than DBS.




Contour Boxplots: A Method for Characterizing Uncertainty in Feature Sets from Simulation Ensembles
R.T. Whitaker, M. Mirzargar, R.M. Kirby. In IEEE Transactions on Visualization and Computer Graphics, Vol. 19, No. 12, pp. 2713--2722. December, 2013.
DOI: 10.1109/TVCG.2013.143
PubMed ID: 24051838

Ensembles of numerical simulations are used in a variety of applications, such as meteorology or computational solid mechanics, in order to quantify the uncertainty or possible error in a model or simulation. Deriving robust statistics and visualizing the variability of an ensemble is a challenging task and is usually accomplished through direct visualization of ensemble members or by providing aggregate representations such as an average or pointwise probabilities. In many cases, the interesting quantities in a simulation are not dense fields, but are sets of features that are often represented as thresholds on physical or derived quantities. In this paper, we introduce a generalization of boxplots, called contour boxplots, for visualization and exploration of ensembles of contours or level sets of functions. Conventional boxplots have been widely used as an exploratory or communicative tool for data analysis, and they typically show the median, mean, confidence intervals, and outliers of a population. The proposed contour boxplots are a generalization of functional boxplots, which build on the notion of data depth. Data depth approximates the extent to which a particular sample is centrally located within its density function. This produces a center-outward ordering that gives rise to the statistical quantities that are essential to boxplots. Here we present a generalization of functional data depth to contours and demonstrate methods for displaying the resulting boxplots for two-dimensional simulation data in weather forecasting and computational fluid dynamics.




ManyVis: Multiple Applications in an Integrated Visualization Environment
A. Rungta, B. Summa, D. Demir, P.-T. Bremer, V. Pascucci. In IEEE Transactions on Visualization and Computer Graphics (TVCG), pp. (to appear). 2013.

As the visualization field matures, an increasing number of general toolkits are developed to cover a broad range of applications. However, no general tool can incorporate the latest capabilities for all possible applications, nor can the user interfaces and workflows be easily adjusted to accommodate all user communities. As a result, users will often chose either substandard solutions presented in familiar, customized tools or assemble a patchwork of individual applications glued through ad-hoc scripts and extensive, manual intervention. Instead, we need the ability to easily and rapidly assemble the best-in-task tools into custom interfaces and workflows to optimally serve any given application community. Unfortunately, creating such meta-applications at the API or SDK level is difficult, time consuming, and often infeasible due to the sheer variety of data models, design philosophies, limits in functionality, and the use of closed commercial systems. In this paper, we present the ManyVis framework which enables custom solutions to be built both rapidly and simply by allowing coordination and communication across existing unrelated applications. ManyVis allows users to combine software tools with complementary characteristics into one virtual application driven by a single, custom-designed interface.




Multiscale Modeling of Accidental Explosions and Detonations
J. Beckvermit, J. Peterson, T. Harman, S. Bardenhagen, C. Wight, Q. Meng, M. Berzins. In Computing in Science and Engineering, Vol. 15, No. 4, pp. 76--86. 2013.
DOI: 10.1109/MCSE.2013.89

Accidental explosions are exceptionally dangerous and costly, both in lives and money. Regarding world-wide conflict with small arms and light weapons, the Small Arms Survey has recorded over 297 accidental explosions in munitions depots across the world that have resulted in thousands of deaths and billions of dollars in damage in the past decade alone [45]. As the recent fertilizer plant explosion that killed 15 people in West, Texas demonstrates, accidental explosions are not limited to military operations. Transportation accidents also pose risks, as illustrated by the occasional train derailment/explosion in the nightly news, or the semi-truck explosion detailed in the following section. Unlike other industrial accident scenarios, explosions can easily affect the general public, a dramatic example being the PEPCON disaster in 1988, where windows were shattered, doors blown off their hinges, and flying glass and debris caused injuries up to 10 miles away.

While the relative rarity of accidental explosions speaks well of our understanding to date, their violence rightly gives us pause. A better understanding of these materials is clearly still needed, but a significant barrier is the complexity of these materials and the various length scales involved. In typical military applications, explosives are known to be ignited by the coalescence of hot spots which occur on micrometer scales. Whether this reaction remains a deflagration (burning) or builds to a detonation depends both on the stimulus and the boundary conditions or level of confinement. Boundary conditions are typically on the scale of engineered parts, approximately meters. Additional dangers are present at the scale of trucks and factories. The interaction of various entities, such as barrels of fertilizer or crates of detonators, admits the possibility of a sympathetic detonation, i.e. the unintended detonation of one entity by the explosion of another, generally caused by an explosive shock wave or blast fragments.

While experimental work has been and will continue to be critical to developing our fundamental understanding of explosive initiation, de agration and detonation, there is no practical way to comprehensively assess safety on the scale of trucks and factories experimentally. The scenarios are too diverse and the costs too great. Numerical simulation provides a complementary tool that, with the steadily increasing computational power of the past decades, makes simulations at this scale begin to look plausible. Simulations at both the micrometer scale, the "mesoscale", and at the scale of engineered parts, the "macro-scale", have been contributing increasingly to our understanding of these materials. Still, simulations on this scale require both massively parallel computational infrastructure and selective sampling of mesoscale response, i.e. advanced computational tools and modeling. The computational framework Uintah [1] has been developed for exactly this purpose.




2D Vector Field Simplification Based on Robustness
P. Skraba, Bei Wang, G. Chen, P. Rosen. SCI Technical Report, No. UUSCI-2013-004, SCI Institute, University of Utah, 2013.

Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification techniques based on the topological skeleton successively remove pairs of critical points connected by separatrices using distance or area-based relevance measures. These methods rely on the stable extraction of the topological skeleton, which can be difficult due to instability in numerical integration, especially when processing highly rotational flows. Further, the distance and area-based metrics are used to determine the cancellation ordering of features from a geometric point of view. Specifically, these metrics do not consider the flow magnitude, which is an important physical property of the flow. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness, which provides a complementary flow structure hierarchy to the traditional topological skeleton-based approach. Robustness enables the pruning of sets of critical points according to a quantitative measure of their stability, that is, the minimum amount of vector field perturbation required to remove them within a local neighborhood. This leads to a natural hierarchical simplification scheme with more physical consideration than purely topological-skeleton-based methods. Such a simplification does not depend on the topological skeleton of the vector field and therefore can handle more general situations (e.g. centers and pairs not connected by separatrices). We also provide a novel simplification algorithm based on degree theory with fewer restrictions and so can handle more general boundary conditions. We provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets.