Morse complexes are gradient-based topological descriptors with close connections to Morse theory. They are widely applicable in scientific visualization as they serve as important abstractions for gaining insights into the topology of scalar fields. Data uncertainty inherent to scalar fields due to randomness in their acquisition and processing, however, limits our understanding of Morse complexes as structural abstractions. We, therefore, explore uncertainty visualization of an ensemble of 2D Morse complexes that arises from scalar fields coupled with data uncertainty. We propose several statistical summary maps as new entities for quantifying structural variations and visualizing positional uncertainties of Morse complexes in ensembles. Specifically, we introduce three types of statistical summary maps – the probabilistic map , the significance map , and the survival map – to characterize the uncertain behaviors of gradient flows. We demonstrate the utility of our proposed approach using wind, flow, and ocean eddy simulation datasets.

For inverse problems one attempts to infer spatially variable functions from indirect measurements of a system. To practitioners of inverse problems, the concept of ``information'' is familiar when discussing key questions such as which parts of the function can be inferred accurately and which cannot. For example, it is generally understood that we can identify system parameters accurately only close to detectors, or along ray paths between sources and detectors, because we have ``the most information'' for these places.

Although referenced in many publications, the ``information'' that is invoked in such contexts is not a well understood and clearly defined quantity. Herein, we present a definition of information density that is based on the variance of coefficients as derived from a Bayesian reformulation of the inverse problem. We then discuss three areas in which this information density can be useful in practical algorithms for the solution of inverse problems, and illustrate the usefulness in one of these areas -- how to choose the discretization mesh for the function to be reconstructed -- using numerical experiments.

Time-varying vector fields produced by computational fluid dynamics simulations are often prohibitively large and pose challenges for accurate interactive analysis and exploration. To address these challenges, reduced Lagrangian representations have been increasingly researched as a means to improve scientific time-varying vector field exploration capabilities. This paper presents a novel deep neural network-based particle tracing method to explore time-varying vector fields represented by Lagrangian flow maps. In our workflow, in situ processing is first utilized to extract Lagrangian flow maps, and deep neural networks then use the extracted data to learn flow field behavior. Using a trained model to predict new particle trajectories offers a fixed small memory footprint and fast inference. To demonstrate and evaluate the proposed method, we perform an in-depth study of performance using a well-known analytical data set, the Double Gyre. Our study considers two flow map extraction strategies, the impact of the number of training samples and integration durations on efficacy, evaluates multiple sampling options for training and testing, and informs hyperparameter settings. Overall, we find our method requires a fixed memory footprint of 10.5 MB to encode a Lagrangian representation of a time-varying vector field while maintaining accuracy. For post hoc analysis, loading the trained model costs only two seconds, significantly reducing the burden of I/O when reading data for visualization. Moreover, our parallel implementation can infer one hundred locations for each of two thousand new pathlines in 1.3 seconds using one NVIDIA Titan RTX GPU.

Electrocardiographic imaging (ECGI) presents a clinical opportunity to noninvasively understand the sources of arrhythmias for individual patients. To help increase the effectiveness of ECGI, we provide new ways to visualise associated measurement and modelling errors. In this paper, we study source localisation uncertainty in two steps: First, we perform Monte Carlo simulations of a simple inverse ECGI source localisation model with error sampling to understand the variations in ECGI solutions. Second, we present multiple visualisation techniques, including confidence maps, level-sets, and topology-based visualisations, to better understand uncertainty in source localization. Our approach offers a new way to study uncertainty in the ECGI pipeline.

Performing exploratory analysis and visualization of large-scale time-varying computational science applications is challenging due to inaccuracies that arise from under-resolved data. In recent years, Lagrangian representations of the vector field computed using in situ processing are being increasingly researched and have emerged as a potential solution to enable exploration. However, prior works have offered limited estimates of the encumbrance on the simulation code as they consider “theoretical” in situ environments. Further, the effectiveness of this approach varies based on the nature of the vector field, benefitting from an in-depth investigation for each application area. With this study, an extended version of Sane et al. (2021), we contribute an evaluation of Lagrangian analysis viability and efficacy for simulation codes executing at scale on a supercomputer. We investigated previously unexplored cosmology and seismology applications as well as conducted a performance benchmarking study by using a hydrodynamics mini-application targeting exascale computing. To inform encumbrance, we integrated in situ infrastructure with simulation codes, and evaluated Lagrangian in situ reduction in representative homogeneous and heterogeneous HPC environments. To inform post hoc accuracy, we conducted a statistical analysis across a range of spatiotemporal configurations as well as a qualitative evaluation. Additionally, our study contributes cost estimates for distributed-memory post hoc reconstruction. In all, we demonstrate viability for each application — data reduction to less than 1% of the total data via Lagrangian representations, while maintaining accurate reconstruction and requiring under 10% of total execution time in over 90% of our experiments.

Importance. Medical images are essential for modern medicine and an important research subject in visualization. However, medical experts are often not aware of the many advanced three-dimensional (3D) medical image visualization techniques that could increase their capabilities in data analysis and assist the decision-making process for specific medical problems. Our paper provides a review of 3D visualization techniques for medical images, intending to bridge the gap between medical experts and visualization researchers. Highlights. Fundamental visualization techniques are revisited for various medical imaging modalities, from computational tomography to diffusion tensor imaging, featuring techniques that enhance spatial perception, which is critical for medical practices. The state-of-the-art of medical visualization is reviewed based on a procedure-oriented classification of medical problems for studies of individuals and populations. This paper summarizes free software tools for different modalities of medical images designed for various purposes, including visualization, analysis, and segmentation, and it provides respective Internet links. Conclusions. Visualization techniques are a useful tool for medical experts to tackle specific medical problems in their daily work. Our review provides a quick reference to such techniques given the medical problem and modalities of associated medical images. We summarize fundamental techniques and readily available visualization tools to help medical experts to better understand and utilize medical imaging data. This paper could contribute to the joint effort of the medical and visualization communities to advance precision medicine.

We present a nonparametric statistical framework for the quantification, analysis, and propagation of data uncertainty in direct volume rendering (DVR). The state-of-the-art statistical DVR framework allows for preserving the transfer function (TF) of the ground truth function when visualizing uncertain data; however, the existing framework is restricted to parametric models of uncertainty. In this paper, we address the limitations of the existing DVR framework by extending the DVR framework for nonparametric distributions. We exploit the quantile interpolation technique to derive probability distributions representing uncertainty in viewing-ray sample intensities in closed form, which allows for accurate and efficient computation. We evaluate our proposed nonparametric statistical models through qualitative and quantitative comparisons with the mean-field and parametric statistical models, such as uniform and Gaussian, as well as Gaussian mixtures. In addition, we present an extension of the state-of-the-art rendering parametric framework to 2D TFs for improved DVR classifications. We show the applicability of our uncertainty quantification framework to ensemble, downsampled, and bivariate versions of scalar field datasets.

In situ computation of Lagrangian flow maps to enable post hoc time-varying vector field analysis has recently become an active area of research. However, the current literature is largely limited to theoretical settings and lacks a solution to address scalability of the technique in distributed memory. To improve scalability, we propose and evaluate the benefits and limitations of a simple, yet novel, performance optimization. Our proposed optimization is a communication-free model resulting in local Lagrangian flow maps, requiring no message passing or synchronization between processes, intrinsically improving scalability, and thereby reducing overall execution time and alleviating the encumbrance placed on simulation codes from communication overheads. To evaluate our approach, we computed Lagrangian flow maps for four time-varying simulation vector fields and investigated how execution time and reconstruction accuracy are impacted by the number of GPUs per compute node, the total number of compute nodes, particles per rank, and storage intervals. Our study consisted of experiments computing Lagrangian flow maps with up to 67M particle trajectories over 500 cycles and used as many as 2048 GPUs across 512 compute nodes. In all, our study contributes an evaluation of a communication-free model as well as a scalability study of computing distributed Lagrangian flow maps at scale using in situ infrastructure on a modern supercomputer.

We propose a data-driven space-filling curve method for 2D and 3D visualization. Our flexible curve traverses the data elements in the spatial domain in a way that the resulting linearization better preserves features in space compared to existing methods. We achieve such data coherency by calculating a Hamiltonian path that approximately minimizes an objective function that describes the similarity of data values and location coherency in a neighborhood. Our extended variant even supports multiscale data via quadtrees and octrees. Our method is useful in many areas of visualization, including multivariate or comparative visualization,ensemble visualization of 2D and 3D data on regular grids, or multiscale visual analysis of particle simulations. The effectiveness of our method is evaluated with numerical comparisons to existing techniques and through examples of ensemble and multivariate datasets.

Morse complexes are gradient-based topological descriptors with close connections to Morse theory. They are widely applicable in scientific visualization as they serve as important abstractions for gaining insights into the topology of scalar fields. Noise inherent to scalar field data due to acquisitions and processing, however, limits our understanding of the Morse complexes as structural abstractions. We, therefore, explore uncertainty visualization of an ensemble of 2D Morse complexes that arise from scalar fields coupled with data uncertainty. We propose statistical summary maps as new entities for capturing structural variations and visualizing positional uncertainties of Morse complexes in ensembles. Specifically, we introduce two types of statistical summary maps -- the Probabilistic Map and the Survival Map -- to characterize the uncertain behaviors of local extrema and local gradient flows, respectively. We demonstrate the utility of our proposed approach using synthetic and real-world datasets.

We present dw2, a flexible and easy-to-use software infrastructure for interactive rendering of large tiled display walls. Our library represents the tiled display wall as a single virtual screen through a display "service", which renderers connect to and send image tiles to be displayed, either from an on-site or remote cluster. The display service can be easily configured to support a range of typical network and display hardware configurations; the client library provides a straightforward interface for easy integration into existing renderers. We evaluate the performance of our display wall service in different configurations using a CPU and GPU ray tracer, in both on-site and remote rendering scenarios using multiple display walls.

Adaptive mesh refinement (AMR) techniques allow for representing a simulation’s computation domain in an adaptive fashion. Although these techniques have found widespread adoption in high-performance computing simulations, visualizing their data output interactively and without cracks or artifacts remains challenging. In this paper, we present an efficient solution for direct volume rendering and hybrid implicit isosurface ray tracing of tree-based AMR (TB-AMR) data. We propose a novel reconstruction strategy, Generalized Trilinear Interpolation (GTI), to interpolate across AMR level boundaries without cracks or discontinuities in the surface normal. We employ a general sparse octree structure supporting a wide range of AMR data, and use it to accelerate volume rendering, hybrid implicit isosurface rendering and value queries. We demonstrate that our approach achieves artifact-free isosurface and volume rendering and provides higher quality output images compared to existing methods at interactive rendering rates.

We propose a photographic method to show scalar values of high dynamic range (HDR) by color mapping for 2D visualization. We combine (1) tone-mapping operators that transform the data to the display range of the monitor while preserving perceptually important features based on a systematic evaluation and (2) simulated glares that highlight high-value regions. Simulated glares are effective for highlighting small areas (of a few pixels) that may not be visible with conventional visualizations; through a controlled perception study, we confirm that glare is preattentive. The usefulness of our overall photographic HDR visualization is validated through the feedback of expert users.

We present a framework for the analysis of uncertainty in isocontour extraction. The marching squares (MS) algorithm for isocontour reconstruction generates a linear topology that is consistent with hyperbolic curves of a piecewise bilinear interpolation. The saddle points of the bilinear interpolant cause topological ambiguity in isocontour extraction. The midpoint decider and the asymptotic decider are well-known mathematical techniques for resolving topological ambiguities. The latter technique investigates the data values at the cell saddle points for ambiguity resolution. The uncertainty in data, however, leads to uncertainty in underlying bilinear interpolation functions for the MS algorithm, and hence, their saddle points. In our work, we study the behavior of the asymptotic decider when data at grid vertices is uncertain. First, we derive closed-form distributions characterizing variations in the saddle point values for uncertain bilinear interpolants. The derivation assumes uniform and nonparametric noise models, and it exploits the concept of ratio distribution for analytic formulations. Next, the probabilistic asymptotic decider is devised for ambiguity resolution in uncertain data using distributions of the saddle point values derived in the first step. Finally, the confidence in probabilistic topological decisions is visualized using a colormapping technique. We demonstrate the higher accuracy and stability of the probabilistic asymptotic decider in uncertain data with regard to existing decision frameworks, such as deciders in the mean field and the probabilistic midpoint decider, through the isocontour visualization of synthetic and real datasets.

Deep brain stimulation (DBS) is an established therapy for treating patients with movement disorders such as Parkinson’s disease. Patient-specific computational modelling and visualisation have been shown to play a key role in surgical and therapeutic decisions for DBS. The computational models use brain imaging, such as magnetic resonance (MR) and computed tomography (CT), to determine the DBS electrode positions within the patient’s head. The finite resolution of brain imaging, however, introduces uncertainty in electrode positions. The DBS stimulation settings for optimal patient response are sensitive to the relative positioning of DBS electrodes to a specific neural substrate (white/grey matter). In our contribution, we study positional uncertainty in the DBS electrodes for imaging with finite resolution. In a three-step approach, we first derive a closed-form mathematical model characterising the geometry of the DBS electrodes. Second, we devise a statistical framework for quantifying the uncertainty in the positional attributes of the DBS electrodes, namely the direction of longitudinal axis and the contact-centre positions at subvoxel levels. The statistical framework leverages the analytical model derived in step one and a Bayesian probabilistic model for uncertainty quantification. Finally, the uncertainty in contact-centre positions is interactively visualised through volume rendering and isosurfacing techniques. We demonstrate the efficacy of our contribution through experiments on synthetic and real datasets. We show that the spatial variations in true electrode positions are significant for finite resolution imaging, and interactive visualisation can be instrumental in exploring probabilistic positional variations in the DBS lead.

We present a general high-performance technique for ray tracing generalized tube primitives. Our technique efficiently supports tube primitives with fixed and varying radii, general acyclic graph structures with bifurcations, and correct transparency with interior surface removal. Such tube primitives are widely used in scientific visualization to represent diffusion tensor imaging tractographies, neuron morphologies, and scalar or vector fields of 3D flow. We implement our approach within the OSPRay ray tracing framework, and evaluate it on a range of interactive visualization use cases of fixed- and varying-radius streamlines, pathlines, complex neuron morphologies, and brain tractographies. Our proposed approach provides interactive, high-quality rendering, with low memory overhead.

Recent advances in large-scale simulations have resulted in volume data of increasing size that stress the capabilities of off-the-shelf visualization tools. Users suffer from long data loading times, because large data must be read from disk into memory prior to rendering the first frame. In this work, we present a volume renderer that enables high-fidelity interactive visualization of large volumes on multi-core CPU architectures. Compared to existing CPU-based visualization frameworks, which take minutes or hours for data loading, our renderer allows users to get a data overview in seconds. Using a hierarchical representation of raw volumes and ray-guided streaming, we reduce the data loading time dramatically and improve the user's interactivity experience. We also examine system design choices with respect to performance and scalability. Specifically, we evaluate the hierarchy generation time, which has been ignored in most prior work, but which can become a significant bottleneck as data scales. Finally, we create a module on top of the OSPRay ray tracing framework that is ready to be integrated into general-purpose visualization frameworks such as Paraview.

To conduct computational forward and inverse EEG studies of brain electrical activity, researchers must construct realistic head and brain computer models, which is both challenging and time consuming. The availability of realistic head models and corresponding imaging data is limited in terms of imaging modalities and patient diversity. In this paper, we describe a detailed head modeling pipeline and provide a high-resolution, multimodal, open-source, female head and brain model. The modeling pipeline specifically outlines image acquisition, preprocessing, registration, and segmentation; three-dimensional tetrahedral mesh generation; finite element EEG simulations; and visualization of the model and simulation results. The dataset includes both functional and structural images and EEG recordings from two high-resolution electrode configurations. The intermediate results and software components are also included in the dataset to facilitate modifications to the pipeline. This project will contribute to neuroscience research by providing a high-quality dataset that can be used for a variety of applications and a computational pipeline that may help researchers construct new head models more efficiently.

We propose an image-space contrast enhancement method for color-encoded visualization. The contrast of an image is enhanced through a perceptually guided approach that interfaces with the user with a single and intuitive parameter of the virtual viewing distance. To this end, we analyze a multiscale contrast model of the input image and test the visibility of bandpass images of all scales at a virtual viewing distance. By adapting weights of bandpass images with a threshold model of spatial vision, this image-based method enhances contrast to compensate for contrast loss caused by viewing the image at a certain distance. Relevant features in the color image can be further emphasized by the user using overcompensation. The weights can be assigned with a simple band-based approach, or with an efficient pixel-based approach that reduces ringing artifacts. The method is efficient and can be integrated into any visualization tool as it is a generic image-based post-processing technique. Using highly diverse datasets, we show the usefulness of perception compensation across a wide range of typical visualizations.

In this paper, we propose a perceptually-guided visualization sharpening technique.We analyze the spectral behavior of an established comprehensive perceptual model to arrive at our approximated model based on an adapted weighting of the bandpass images from a Gaussian pyramid. The main benefit of this approximated model is its controllability and predictability for sharpening color-mapped visualizations. Our method can be integrated into any visualization tool as it adopts generic image-based post-processing, and it is intuitive and easy to use as viewing distance is the only parameter. Using highly diverse datasets, we show the usefulness of our method across a wide range of typical visualizations.