Visualization

The visualization of variability in 3D shapes or surfaces, which is a type of ensemble uncertainty visualization for volume data, provides a means of understanding the underlying distribution for a collection or ensemble of surfaces. While ensemble visualization for surfaces is already described in the literature, we conduct an expert-based evaluation in a particular medical imaging application: the construction of atlases or templates from a population of images. In this work, we extend contour boxplots to 3D, allowing us to evaluate it against an enumeration-style visualization of the ensemble members and also other conventional visualizations used by atlas builders, namely examining the atlas image and the corresponding images/data provided as part of the construction process. We present feedback from domain experts on the efficacy of contour boxplots compared to other modalities when used as part of the atlas construction and analysis stages of their work.

Large-scale molecular dynamics (MD) simulations are commonly used for simulating the synthesis and ion diffusion of battery materials. A good battery anode material is determined by its capacity to store ion or other diffusers. However, modeling of ion diffusion dynamics and transport properties at large length and long time scales would be impossible with current MD codes. To analyze the fundamental properties of these materials, therefore, we turn to geometric and topological analysis of their structure. In this paper, we apply a novel technique inspired by discrete Morse theory to the Delaunay triangulation of the simulated geometry of a thermally annealed carbon nanosphere. We utilize our computed structures to drive further geometric analysis to extract the interstitial diffusion structure as a single mesh. Our results provide a new approach to analyze the geometry of the simulated carbon nanosphere, and new insights into the role of carbon defect size and distribution in determining the charge capacity and charge dynamics of these carbon based battery materials.

Modern science, technology, and politics are all permeated by data that comes from people, measurements, or computational processes. While this data is often incomplete, corrupt, or lacking in sufficient accuracy and precision, explicit consideration of uncertainty is rarely part of the computational and decision making pipeline. The CCC Workshop on Quantification, Communication, and Interpretation of Uncertainty in Simulation and Data Science explored this problem, identifying significant shortcomings in the ways we currently process, present, and interpret uncertain data. Specific recommendations on a research agenda for the future were made in four areas: uncertainty quantification in large-scale computational simulations, uncertainty quantification in data science, software support for uncertainty computation, and better integration of uncertainty quantification and communication to stakeholders.

Scientific visualization has many effective methods for examining and exploring scalar and vector fields, but rather fewer for multi-variate fields. We report the first general purpose approach for the interactive extraction of geometric separating surfaces in bivariate fields. This method is based on fiber surfaces: surfaces constructed from sets of fibers, the multivariate analogues of isolines. We show simple methods for fiber surface definition and extraction. In particular, we show a simple and efficient fiber surface extraction algorithm based on Marching Cubes. We also show how to construct fiber surfaces interactively with geometric primitives in the range of the function. We then extend this to build user interfaces that generate parameterized families of fiber surfaces with respect to arbitrary polylines and polygons. In the special case of isovalue-gradient plots, fiber surfaces capture features geometrically for quantitative analysis that have previously only been analysed visually and qualitatively using multi-dimensional transfer functions in volume rendering. We also demonstrate fiber surface extraction on a variety of bivariate data

We present a novel approach to rendering large particle data sets from molecular dynamics, astrophysics and other sources. We employ a new data structure adapted from the original balanced k-d tree, which allows for representation of data with trivial or no overhead. In the OSPRay visualization framework, we have developed an efficient CPU algorithm for traversing, classifying and ray tracing these data. Our approach is able to render up to billions of particles on a typical workstation, purely on the CPU, without any approximations or level-of-detail techniques, and optionally with attribute-based color mapping, dynamic range query, and advanced lighting models such as ambient occlusion and path tracing.

Ab initio molecular dynamics (AIMD) simulations are increasingly useful in modeling, optimizing and synthesizing materials in energy sciences. In solving Schrodinger's equation, they generate the electronic structure of the simulated atoms as a scalar field. However, methods for analyzing these volume data are not yet common in molecular visualization. The Morse-Smale complex is a proven, versatile tool for topological analysis of scalar fields. In this paper, we apply the discrete Morse-Smale complex to analysis of first-principles battery materials simulations. We consider a carbon nanosphere structure used in battery materials research, and employ Morse-Smale decomposition to determine the possible lithium ion diffusion paths within that structure. Our approach is novel in that it uses the wavefunction itself as opposed distance fields, and that we analyze the 1-skeleton of the Morse-Smale complex to reconstruct our diffusion paths. Furthermore, it is the first application where specific motifs in the graph structure of the complete 1-skeleton define features, namely carbon rings with specific valence. We compare our analysis of DFT data with that of a distance field approximation, and discuss implications on larger classical molecular dynamics simulations.

One of the biggest challenges in high-energy physics is to analyze a complex mix of experimental and simulation data to gain new insights into the underlying physics. Currently, this analysis relies primarily on the intuition of trained experts often using nothing more sophisticated than default scatter plots. Many advanced analysis techniques are not easily accessible to scientists and not flexible enough to explore the potentially interesting hypotheses in an intuitive manner. Furthermore, results from individual techniques are often difficult to integrate, leading to a confusing patchwork of analysis snippets too cumbersome for data exploration. This paper presents a case study on how a combination of techniques from statistics, machine learning, topology, and visualization can have a significant impact in the field of inertial confinement fusion. We present the ND2AV: N-Dimensional Data Analysis and Visualization framework, a user-friendly tool aimed at exploiting the intuition and current work flow of the target users. The system integrates traditional analysis approaches such as dimension reduction and clustering with state-of-the-art techniques such as neighborhood graphs and topological analysis, and custom capabilities such as defining combined metrics on the fly. All components are linked into an interactive environment that enables an intuitive exploration of a wide variety of hypotheses while relating the results to concepts familiar to the users, such as scatter plots. ND2AV uses a modular design providing easy extensibility and customization for different applications. ND2AV is being actively used in the National Ignition Campaign and has already led to a number of unexpected discoveries.

The relation between two Morse functions defined on a smooth, compact, and orientable 2-manifold can be studied in terms of their Jacobi set. The Jacobi set contains points in the domain where the gradients of the two functions are aligned. Both the Jacobi set itself as well as the segmentation of the domain it induces, have shown to be useful in various applications. In practice, unfortunately, functions often contain noise and discretization artifacts, causing their Jacobi set to become unmanageably large and complex. Although there exist techniques to simplify Jacobi sets, they are unsuitable for most applications as they lack fine-grained control over the process, and heavily restrict the type of simplifications possible.

This paper introduces the theoretical foundations of a new simplification framework for Jacobi sets. We present a new interpretation of Jacobi set simplification based on the perspective of domain segmentation. Generalizing the cancellation of critical points from scalar functions to Jacobi sets, we focus on simplifications that can be realized by smooth approximations of the corresponding functions, and show how these cancellations imply simultaneous simplification of contiguous subsets of the Jacobi set. Using these extended cancellations as atomic operations, we introduce an algorithm to successively cancel subsets of the Jacobi set with minimal modifications to some userdefined metric. We show that for simply connected domains, our algorithm reduces a given Jacobi set to its minimal configuration, that is, one with no birth-death points (a birth-death point is a specific type of singularity within the Jacobi set where the level sets of the two functions and the Jacobi set have a common normal direction).

We introduce a novel interactive framework for visualizing and exploring high-dimensional datasets based on subspace analysis and dynamic projections. We assume the high-dimensional dataset can be represented by a mixture of low-dimensional linear subspaces with mixed dimensions, and provide a method to reliably estimate the intrinsic dimension and linear basis of each subspace extracted from the subspace clustering. Subsequently, we use these bases to define unique 2D linear projections as viewpoints from which to visualize the data. To understand the relationships among the different projections and to discover hidden patterns, we connect these projections through dynamic projections that create smooth animated transitions between pairs of projections. We introduce the view transition graph, which provides flexible navigation among these projections to facilitate an intuitive exploration. Finally, we provide detailed comparisons with related systems, and use real-world examples to demonstrate the novelty and usability of our proposed framework.

Massive simulations and arrays of sensing devices, in combination with increasing computing resources, have generated large, complex, high-dimensional datasets used to study phenomena across numerous fields of study. Visualization plays an important role in exploring such datasets. We provide a comprehensive survey of advances in high-dimensional data visualization over the past 15 years. We aim at providing actionable guidance for data practitioners to navigate through a modular view of the recent advances, allowing the creation of new visualizations along the enriched information visualization pipeline and identifying future opportunities for visualization research.

We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate with a Gaussian kernel. This allows one to consider kernel density estimates, which are robust to spatial noise, subsampling, and approximate computation in comparison to raw point sets. This is achieved by examining the sublevel sets of the kernel distance, which isomorphically map to superlevel sets of the kernel density estimate. We prove new properties about the kernel distance, demonstrating stability results and allowing it to inherit reconstruction results from recent advances in distance-based topological reconstruction. Moreover, we provide an algorithm to estimate its topology using weighted Vietoris-Rips complexes.

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. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness which 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. This leads to a hierarchical simplification scheme that encodes flow magnitude in its perturbation metric. Our novel simplification algorithm is based on degree theory and has minimal boundary restrictions. Finally, we provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets. We show local and complete hierarchical simplifications for steady as well as unsteady vector fields.

Modern supercomputers have very powerful multi-core CPUs. The programming model on these supercomputer is switching from pure MPI to MPI for inter-node communication, and shared memory and threads for intra-node communication. Consequently the bottleneck in most systems is no longer computation but communication between nodes. In this paper, we present a new compositing algorithm for hybrid MPI parallelism that focuses on communication avoidance and overlapping communication with computation at the expense of evenly balancing the workload. The algorithm has three stages: a direct send stage where nodes are arranged in groups and exchange regions of an image, followed by a tree compositing stage and a gather stage. We compare our algorithm with radix-k and binary-swap from the IceT library in a hybrid OpenMP/MPI setting, show strong scaling results and explain how we generally achieve better performance than these two algorithms.

The degree of correlation between variables is used in many data analysis applications as a key measure of interdependence. The most common techniques for exploratory analysis of pairwise correlation in multivariate datasets, like scatterplot matrices and clustered heatmaps, however, do not scale well to large datasets, either computationally or visually. We present a new visualization that is capable of encoding pairwise correlation between hundreds of thousands variables, called the s-CorrPlot. The s-CorrPlot encodes correlation spatially between variables as points on scatterplot using the geometric structure underlying Pearson's correlation. Furthermore, we extend the s-CorrPlot with interactive techniques that enable animation of the scatterplot to new projections of the correlation space, as illustrated in the companion video in Supplemental Materials. We provide the s-CorrPlot as an open-source R-package and validate its effectiveness through a variety of methods including a case study with a biology collaborator.

Isosurface extraction is a fundamental technique used for both surface reconstruction and mesh generation. One method to extract well-formed isosurfaces is a particle system; unfortunately, particle systems can be slow. In this paper, we introduce an enhanced parallel particle system that uses the closest point embedding as the surface representation to speedup the particle system for isosurface extraction. The closest point embedding is used in the Closest Point Method (CPM), a technique that uses a standard three dimensional numerical PDE solver on two dimensional embedded surfaces. To fully take advantage of the closest point embedding, it is coupled with a Barnes-Hut tree code on the GPU. This new technique produces well-formed, conformal unstructured triangular and tetrahedral meshes from labeled multi-material volume datasets. Further, this new parallel implementation of the particle system is faster than any known methods for conformal multi-material mesh extraction. The resulting speed-ups gained in this implementation can reduce the time from labeled data to mesh from hours to minutes and benefits users, such as bioengineers, who employ triangular and tetrahedral meshes.

Keywords: scalar field methods, GPGPU, curvature based, scientific visualization

In this paper, we introduce a novel flow visualization technique for arbitrary surfaces. This new technique utilizes the closest point embedding to represent the surface, which allows for accurate particle advection on the surface as well as supports the unsteady flow line integral convolution (UFLIC) technique on the surface. This global approach is faster than previous parameterization techniques and prevents the visual artifacts associated with image-based approaches.

Keywords: vector field, flow visualization

This book contains papers presented at the Workshop on the Analysis of Large-scale,
High-Dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp,
France, June 2013. It features the work of some of the most prominent and recognized
leaders in the field who examine challenges as well as detail solutions to the analysis of
extreme scale data.
The book presents new methods that leverage the mutual strengths of both topological
and statistical techniques to support the management, analysis, and visualization
of complex data. It covers both theory and application and provides readers with an
overview of important key concepts and the latest research trends.
Coverage in the book includes multi-variate and/or high-dimensional analysis techniques,
feature-based statistical methods, combinatorial algorithms, scalable statistics algorithms,
scalar and vector field topology, and multi-scale representations. In addition, the book
details algorithms that are broadly applicable and can be used by application scientists to
glean insight from a wide range of complex data sets.