The Contour Spectrum

We introduce the contour spectrum, a user interface component that improves qualitative user interaction and provides real-time exact quantification in the visualization of isocontours. The contour spectrum is a signature consisting of a variety of scalar data and contour attributes, computed over the range of scalar values w 2!.We explore the use of surface area, volume, and gradientintegral of the contour that are shown to be univariate B-spline functions of the scalar value w for multi-dimensional unstructured triangular grids. These quantitative properties are calculated in real-time and presented to the user as a collection of signature graphs (plots of functions of w) to assist in selecting relevant isovalues w 0 for informative visualization. For timevarying data, these quantitative properties can also be computed over time, and displayed using a 2D interface, giving the user an overview of the time-varying function, and allowing interaction in both isovalue and timestep. The effectiveness of the current system and potential extensions are discussed

Analysis of the Two-Level NO PLIF Model for Low-Temperature High-Speed Flow Applications

The current work compares experimentally obtained nitric oxide (NO) laser-induced fluorescence (LIF) spectra with the equivalent spectra obtained analytically. The experimental spectra are computed from captured images of fluorescence in a gas cell and from a laser sheet passing through the fuel-air mixing flowfield produced by a high-speed fuel injector. The fuel injector is a slender strut that is currently being studied as a part of the Enhanced Injection and Mixing Project (EIMP) at the NASA Langley Research Center. This injector is placed downstream of a Mach 6 facility nozzle, which simulates the high Mach number airflow at the entrance of a scramjet combustor, and injects helium, which is used as an inert substitute for hydrogen fuel. Experimental planar (P) LIF is obtained by using a UV laser to excite fluorescence from the NO molecules that are present in either a gas cell or the facility air used for the EIMP experiments. The experimental data are obtained for several segments of the NO fluorescence spectrum. The selected segments encompass LIF lines with rotational quantum numbers appropriate for low-to-moderate temperature flows similar to those corresponding to the nominal experimental flow conditions. The experimental LIF spectra are then evaluated from the data and compared with those obtained from the theoretical models. The theoretical spectra are obtained from LIFBASE and LINUS software, and from a simplified version of the two-level fluorescence model. The equivalent analytic PLIF images are also obtained by applying only the simplified model to the results of the Reynolds-averaged simulations (RAS) of the mixing flowfield. Good agreement between the experimental and theoretical results provides increased confidence in both the simplified LIF modeling and CFD simulations for further investigations of high-speed injector performance using this approach

VolRoverN: Enhancing Surface and Volumetric Reconstruction for Realistic Dynamical Simulation of Cellular and Subcellular Function

Establishing meaningful relationships between cellular structure and function requires accurate morphological reconstructions. In particular, there is an unmet need for high quality surface reconstructions to model subcellular and synaptic interactions among neurons and glia at nanometer resolution. We address this need with VolRoverN, a software package that produces accurate, efficient, and automated 3D surface reconstructions from stacked 2D contour tracings. While many techniques and tools have been developed in the past for 3D visualization of cellular structure, the reconstructions from VolRoverN meet specific quality criteria that are important for dynamical simulations. These criteria include manifoldness, water-tightness, lack of self- and object-object-intersections, and geometric accuracy. These enhanced surface reconstructions are readily extensible to any cell type and are used here on spiny dendrites with complex morphology and axons from mature rat hippocampal area CA1. Both spatially realistic surface reconstructions and reduced skeletonizations are produced and formatted by VolRoverN for easy input into analysis software packages for neurophysiological simulations at multiple spatial and temporal scales ranging from ion electro-diffusion to electrical cable models

A Fast and Scalable System to Visualize Contour Gradient from Spatio-temporal Data

Changes in geological processes that span over the years may often go unnoticed due to their inherent noise and variability. Natural phenomena such as riverbank erosion, and climate change in general, is invisible to humans unless appropriate measures are taken to analyze the underlying data. Visualization helps geological sciences to generate scientific insights into such long-term geological events. Commonly used approaches such as side-by-side contour plots and spaghetti plots do not provide a clear idea about the historical spatial trends. To overcome this challenge, we propose an image-gradient based approach called ContourDiff. ContourDiff overlays gradient vector over contour plots to analyze the trends of change across spatial regions and temporal domain. Our approach first aggregates for each location, its value differences from the neighboring points over the temporal domain, and then creates a vector field representing the prominent changes. Finally, it overlays the vectors (differential trends) along the contour paths, revealing the differential trends that the contour lines (isolines) experienced over time. We designed an interface, where users can interact with the generated visualization to reveal changes and trends in geospatial data. We evaluated our system using real-life datasets, consisting of millions of data points, where the visualizations were generated in less than a minute in a single-threaded execution. We show the potential of the system in detecting subtle changes from almost identical images, describe implementation challenges, speed-up techniques, and scope for improvements. Our experimental results reveal that ContourDiff can reliably visualize the differential trends, and provide a new way to explore the change pattern in spatiotemporal data. The expert evaluation of our system using real-life WRF (Weather Research and Forecasting) model output reveals the potential of our technique to generate useful insights on the spatio-temporal trends of geospatial variables

A Comparative Study of the Perceptual Sensitivity of Topological Visualizations to Feature Variations

Color maps are a commonly used visualization technique in which data are mapped to optical properties, e.g., color or opacity. Color maps, however, do not explicitly convey structures (e.g., positions and scale of features) within data. Topology-based visualizations reveal and explicitly communicate structures underlying data. Although we have a good understanding of what types of features are captured by topological visualizations, our understanding of people's perception of those features is not. This paper evaluates the sensitivity of topology-based isocontour, Reeb graph, and persistence diagram visualizations compared to a reference color map visualization for synthetically generated scalar fields on 2-manifold triangular meshes embedded in 3D. In particular, we built and ran a human-subject study that evaluated the perception of data features characterized by Gaussian signals and measured how effectively each visualization technique portrays variations of data features arising from the position and amplitude variation of a mixture of Gaussians. For positional feature variations, the results showed that only the Reeb graph visualization had high sensitivity. For amplitude feature variations, persistence diagrams and color maps demonstrated the highest sensitivity, whereas isocontours showed only weak sensitivity. These results take an important step toward understanding which topology-based tools are best for various data and task scenarios and their effectiveness in conveying topological variations as compared to conventional color mapping

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

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

Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators

The challenge of tensor field visualization is to provide simple and comprehensible representations of data which vary both directionally and spatially. We explore the use of differential operators to extract features from tensor fields. These features can be used to generate skeleton representations of the data that accurately characterize the global field structure. Previously, vector field operators such as gradient, divergence, and curl have previously been used to visualize of flow fields. In this paper, we use generalizations of these operators to locate and classify tensor field degenerate points and to partition the field into regions of homogeneous behavior. We describe the implementation of our feature extraction and demonstrate our new techniques on synthetic data sets of order 2, 3 and 4

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

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