The 2024 VGTC Visualization Lifetime Achievement Award goes to Hans-Christian Hege for his fundamental technical contributions to visualization and visualization software with a focus on applications in the natural sciences, medicine and engineering. The 2024 VGTC Visualization Lifetime Achievement Award goes to Min Chen for his contributions to the theoretical foundations of visualization as well as outstanding work on novel and impactful applications. Min Chen started his journey of research in 1984 at Swansea University where he developed his academic career. Since 2011, he has been professor of scientific visualization in the Department of Engineering Science and a fellow of Pembroke College, University of Oxford.

One of the fundamental problems in neurobiological research is to understand how neural circuits generate behaviors in response to sensory stimuli. Elucidating such neural circuits requires anatomical and functional information about the neurons that are active during the processing of the sensory information and generation of the respective response, as well as an identification of the connections between these neurons. With modern imaging techniques, both morphological properties of individual neurons as well as functional information related to sensory processing, information integration and behavior can be obtained. Given the resulting information, neurobiologists are faced with the task of identifying the anatomical structures down to individual neurons that are linked to the studied behavior and the processing of the respective sensory stimuli. Here, we present a novel interactive tool that assists neurobiologists in the aforementioned tasks by allowing them to extract hypothetical neural circuits constrained by anatomical and functional data. Our approach is based on two types of structural data: brain regions that are anatomically or functionally defined, and morphologies of individual neurons. Both types of structural data are interlinked and augmented with additional information. The presented tool allows the expert user to identify neurons using Boolean queries. The interactive formulation of these queries is supported by linked views, using, among other things, two novel 2D abstractions of neural circuits. The approach was validated in two case studies investigating the neural basis of vision-based behavioral responses in zebrafish larvae. Despite this particular application, we believe that the presented tool will be of general interest for exploring hypotheses about neural circuits in other species, genera and taxa.

Recent advances in connectomics research enable the acquisition of increasing amounts of data about the connectivity patterns of neurons. How can we use this wealth of data to efficiently derive and test hypotheses about the principles underlying these patterns? A common approach is to simulate neuronal networks using a hypothesized wiring rule in a generative model and to compare the resulting synthetic data with empirical data. However, most wiring rules have at least some free parameters, and identifying parameters that reproduce empirical data can be challenging as it often requires manual parameter tuning. Here, we propose to use simulation-based Bayesian inference (SBI) to address this challenge. Rather than optimizing a fixed wiring rule to fit the empirical data, SBI considers many parametrizations of a rule and performs Bayesian inference to identify the parameters that are compatible with the data. It uses simulated data from multiple candidate wiring rule parameters and relies on machine learning methods to estimate a probability distribution (the 'posterior distribution over parameters conditioned on the data') that characterizes all data-compatible parameters. We demonstrate how to apply SBI in computational connectomics by inferring the parameters of wiring rules in an in silico model of the rat barrel cortex, given in vivo connectivity measurements. SBI identifies a wide range of wiring rule parameters that reproduce the measurements. We show how access to the posterior distribution over all data-compatible parameters allows us to analyze their relationship, revealing biologically plausible parameter interactions and enabling experimentally testable predictions. We further show how SBI can be applied to wiring rules at different spatial scales to quantitatively rule out invalid wiring hypotheses. Our approach is applicable to a wide range of generative models used in connectomics, providing a quantitative and efficient way to constrain model parameters with empirical connectivity data.

Abstract Our ability to grasp and understand complex phenomena is essentially based on recognizing structures and relating these to each other. For example, any meteorological description of a weather condition and explanation of its evolution recurs to meteorological structures, such as convection and circulation structures, cloud fields and rain fronts. All of these are spatiotemporal structures, defined by time‐dependent patterns in the underlying fields. Typically, such a structure is defined by a verbal description that corresponds to the more or less uniform, often somewhat vague mental images of the experts. However, a precise, formal definition of the structures or, more generally, of the concepts is often desirable, e.g., to enable automated data analysis or the development of phenomenological models. Here, we present a systematic approach and an interactive tool to obtain formal definitions of spatiotemporal structures. The tool enables experts to evaluate and compare different structure definitions on the basis of data sets with time‐dependent fields that contain the respective structure. Since structure definitions are typically parameterized, an essential part is to identify parameter ranges that lead to desired structures in all time steps. In addition, it is important to allow a quantitative assessment of the resulting structures simultaneously. We demonstrate the use of the tool by applying it to two meteorological examples: finding structure definitions for vortex cores and center lines of temporarily evolving tropical cyclones. Ideally, structure definitions should be objective and applicable to as many data sets as possible. However, finding such definitions, e.g., for the common atmospheric structures in meteorology, can only be a long‐term goal. The proposed procedure, together with the presented tool, is just a first systematic approach aiming at facilitating this long and arduous way.

Abstract Thin, curved structures occur in many volumetric datasets. Their analysis using classical volume rendering is difficult because parts of such structures can bend away or hide behind occluding elements. This problem cannot be fully compensated by effective navigation alone, as structure‐adapted navigation in the volume is cumbersome and only parts of the structure are visible in each view. We solve this problem by rendering a spatially transformed view of the volume so that an unobstructed visualization of the entire curved structure is obtained. As a result, simple and intuitive navigation becomes possible. The domain of the spatial transform is defined by a triangle mesh that is topologically equivalent to an open disc and that approximates the structure of interest. The rendering is based on ray‐casting, in which the rays traverse the original volume. In order to carve out volumes of varying thicknesses, the lengths of the rays as well as the positions of the mesh vertices can be easily modified by interactive painting under view control. We describe a prototypical implementation and demonstrate the interactive visual inspection of complex structures from digital humanities, biology, medicine, and material sciences. The visual representation of the structure as a whole allows for easy inspection of interesting substructures in their original spatial context. Overall, we show that thin, curved structures in volumetric data can be excellently visualized using ray‐casting‐based volume rendering of transformed views defined by guiding surface meshes, supplemented by interactive, local modifications of ray lengths and vertex positions.

Abstract We present visual analysis methods for the evaluation of tomographic fiber reconstruction algorithms by means of analysis, visual debugging and comparison of reconstructed fibers in materials science. The methods are integrated in a tool (FIAKER) that supports the entire workflow. It enables the analysis of various fiber reconstruction algorithms, of differently parameterized fiber reconstruction algorithms and of individual steps in iterative fiber reconstruction algorithms. Insight into the performance of fiber reconstruction algorithms is obtained by a list‐based ranking interface. A 3D view offers interactive visualization techniques to gain deeper insight, e.g., into the aggregated quality of the examined fiber reconstruction algorithms and parameterizations. The tool was designed in close collaboration with researchers who work with fiber‐reinforced polymers on a daily basis and develop algorithms for tomographic reconstruction and characterization of such materials. We evaluate the tool using synthetic datasets as well as tomograms of real materials. Five case studies certify the usefulness of the tool, showing that it significantly accelerates the analysis and provides valuable insights that make it possible to improve the fiber reconstruction algorithms. The main contribution of the paper is the well‐considered combination of methods and their seamless integration into a visual tool that supports the entire workflow. Further findings result from the analysis of (dis‐)similarity measures for fibers as well as from the discussion of design decisions. It is also shown that the generality of the analytical methods allows a wider range of applications, such as the application in pore space analysis.

Abstract Simulations and measurements of blood and airflow inside the human circulatory and respiratory system play an increasingly important role in personalized medicine for prevention, diagnosis and treatment of diseases. This survey focuses on three main application areas. (1) Computational fluid dynamics (CFD) simulations of blood flow in cerebral aneurysms assist in predicting the outcome of this pathologic process and of therapeutic interventions. (2) CFD simulations of nasal airflow allow for investigating the effects of obstructions and deformities and provide therapy decision support. (3) 4D phase‐contrast (4D PC) magnetic resonance imaging of aortic haemodynamics supports the diagnosis of various vascular and valve pathologies as well as their treatment. An investigation of the complex and often dynamic simulation and measurement data requires the coupling of sophisticated visualization, interaction and data analysis techniques. In this paper, we survey the large body of work that has been conducted within this realm. We extend previous surveys by incorporating nasal airflow, addressing the joint investigation of blood flow and vessel wall properties and providing a more fine‐granular taxonomy of the existing techniques. From the survey, we extract major research trends and identify open problems and future challenges. The survey is intended for researchers interested in medical flow but also more general, in the combined visualization of physiology and anatomy, the extraction of features from flow field data and feature‐based visualization, the visual comparison of different simulation results and the interactive visual analysis of the flow field and derived characteristics.

The analysis and visualization of nucleic acids (RNA and DNA) is playing an increasingly important role due to their fundamental importance for all forms of life and the growing number of known 3D structures of such molecules. The great complexity of these structures, in particular, those of RNA, demands interactive visualization to get deeper insights into the relationship between the 2D secondary structure motifs and their 3D tertiary structures. Over the last decades, a lot of research in molecular visualization has focused on the visual exploration of protein structures while nucleic acids have only been marginally addressed. In contrast to proteins, which are composed of amino acids, the ingredients of nucleic acids are nucleotides. They form structuring patterns that differ from those of proteins and, hence, also require different visualization and exploration techniques. In order to support interactive exploration of nucleic acids, the computation of secondary structure motifs as well as their visualization in 2D and 3D must be fast. Therefore, in this paper, we focus on the performance of both the computation and visualization of nucleic acid structure. We present a ray casting-based visualization of RNA and DNA secondary and tertiary structures, which enables for the first time real-time visualization of even large molecular dynamics trajectories. Furthermore, we provide a detailed description of all important aspects to visualize nucleic acid secondary and tertiary structures. With this, we close an important gap in molecular visualization.

We present a novel approach to turn smartphones/ tablets into tangible near-surface devices with augmented reality (AR) capability on virtually any passive surface, like desks, tables and wallboards. A low-cost optoelectronic add-on for the device back camera enables position tracking on an almost-invisible printable fiducial marker grid. This approach is promising in terms of adoption potential because it can be used anywhere with existing devices, requires no dedicated hardware installations and is applicable to a broad range of real-world applications.

Abstract Structural properties of molecules are of primary concern in many fields. This report provides a comprehensive overview on techniques that have been developed in the fields of molecular graphics and visualization with a focus on applications in structural biology. The field heavily relies on computerized geometric and visual representations of three‐dimensional, complex, large and time‐varying molecular structures. The report presents a taxonomy that demonstrates which areas of molecular visualization have already been extensively investigated and where the field is currently heading. It discusses visualizations for molecular structures, strategies for efficient display regarding image quality and frame rate, covers different aspects of level of detail and reviews visualizations illustrating the dynamic aspects of molecular simulation data. The survey concludes with an outlook on promising and important research topics to foster further success in the development of tools that help to reveal molecular secrets.

Abstract In this report we review and structure the branch of molecular visualization that is concerned with the visual analysis of cavities in macromolecular protein structures. First the necessary background, the domain terminology, and the goals of analytical reasoning are introduced. Based on a comprehensive collection of relevant research works, we present a novel classification for cavity detection approaches and structure them into four distinct classes: grid‐based, Voronoi‐based, surface‐based, and probe‐based methods. The subclasses are then formed by their combinations. We match these approaches with corresponding visualization technologies starting with direct 3D visualization, followed with non‐spatial visualization techniques that for example abstract the interactions between structures into a relational graph, straighten the cavity of interest to see its profile in one view, or aggregate the time sequence into a single contour plot. We also discuss the current state of methods for the visual analysis of cavities in dynamic data such as molecular dynamics simulations. Finally, we give an overview of the most common tools that are actively developed and used in the structural biology and biochemistry research. Our report is concluded by an outlook on future challenges in the field.

The most popular molecular surface in molecular visualization is the solvent excluded surface (SES). It provides information about the accessibility of a biomolecule for a solvent molecule that is geometrically approximated by a sphere. During a period of almost four decades, the SES has served for many purposes - including visualization, analysis of molecular interactions and the study of cavities in molecular structures. However, if one is interested in the surface that is accessible to a molecule whose shape differs significantly from a sphere, a different concept is necessary. To address this problem, we generalize the definition of the SES by replacing the probe sphere with the full geometry of the ligand defined by the arrangement of its van der Waals spheres. We call the new surface ligand excluded surface (LES) and present an efficient, grid-based algorithm for its computation. Furthermore, we show that this algorithm can also be used to compute molecular cavities that could host the ligand molecule. We provide a detailed description of its implementation on CPU and GPU. Furthermore, we present a performance and convergence analysis and compare the LES for several molecules, using as ligands either water or small organic molecules.

BACKGROUND: The internal cavities of proteins are dynamic structures and their dynamics may be associated with conformational changes which are required for the functioning of the protein. In order to study the dynamics of these internal protein cavities, appropriate tools are required that allow rapid identification of the cavities as well as assessment of their time-dependent structures. RESULTS: In this paper, we present such a tool and give results that illustrate the applicability for the analysis of molecular dynamics trajectories. Our algorithm consists of a pre-processing step where the structure of the cavity is computed from the Voronoi diagram of the van der Waals spheres based on coordinate sets from the molecular dynamics trajectory. The pre-processing step is followed by an interactive stage, where the user can compute, select and visualize the dynamic cavities. Importantly, the tool we discuss here allows the user to analyze the time-dependent changes of the components of the cavity structure. An overview of the cavity dynamics is derived by rendering the dynamic cavities in a single image that gives the cavity surface colored according to its time-dependent dynamics. CONCLUSION: The Voronoi-based approach used here enables the user to perform accurate computations of the geometry of the internal cavities in biomolecules. For the first time, it is possible to compute dynamic molecular paths that have a user-defined minimum constriction size. To illustrate the usefulness of the tool for understanding protein dynamics, we probe the dynamic structure of internal cavities in the bacteriorhodopsin proton pump.

Abstract An uncertain (scalar, vector, tensor) field is usually perceived as a discrete random field with a priori unknown probability distributions. To compute derived probabilities, e.g. for the occurrence of certain features, an appropriate probabilistic model has to be selected. The majority of previous approaches in uncertainty visualization were restricted to Gaussian fields. In this paper we extend these approaches to nonparametric models, which are much more flexible, as they can represent various types of distributions, including multimodal and skewed ones. We present three examples of nonparametric representations: (a) empirical distributions, (b) histograms and (c) kernel density estimates (KDE). While the first is a direct representation of the ensemble data, the latter two use reconstructed probability density functions of continuous random variables. For KDE we propose an approach to compute valid consistent marginal distributions and to efficiently capture correlations using a principal component transformation. Furthermore, we use automatic bandwidth selection, obtaining a model for probabilistic local feature extraction. The methods are demonstrated by computing probabilities of level crossings, critical points and vortex cores in simulated biofluid dynamics and climate data.

We propose a novel GPU-based approach to render virtual X-ray projections of deformable tetrahedral meshes. These meshes represent the shape and the internal density distribution of a particular anatomical structure and are derived from statistical shape and intensity models (SSIMs). We apply our method to improve the geometric reconstruction of 3D anatomy (e.g. pelvic bone) from 2D X-ray images. For that purpose, shape and density of a tetrahedral mesh are varied and virtual X-ray projections are generated within an optimization process until the similarity between the computed virtual X-ray and the respective anatomy depicted in a given clinical X-ray is maximized. The OpenGL implementation presented in this work deforms and projects tetrahedral meshes of high resolution (200.000+ tetrahedra) at interactive rates. It generates virtual X-rays that accurately depict the density distribution of an anatomy of interest. Compared to existing methods that accumulate X-ray attenuation in deformable meshes, our novel approach significantly boosts the deformation/projection performance. The proposed projection algorithm scales better with respect to mesh resolution and complexity of the density distribution, and the combined deformation and projection on the GPU scales better with respect to the number of deformation parameters. The gain in performance allows for a larger number of cycles in the optimization process. Consequently, it reduces the risk of being stuck in a local optimum. We believe that our approach will improve treatments in orthopedics, where 3D anatomical information is essential.

Abstract Most visual analysis tasks require interactive adjustment of parameter values. In general, a linear variation of a parameter, using for instance a GUI slider, changes the visual result in a perceptually non‐linear way. This hampers interactive adjustment of parameters, especially in regions where rapid perceptual changes occur. Selecting a good parameter value therefore remains a time‐consuming and often difficult task. We propose a novel technique to build a non‐linear function that maps a new parameter to the original parameter. By prefixing this function to the original parameter and using the new parameter as input, a linear relationship between input and visual feedback is obtained. To construct the non‐linear function, we measure the variation of the visual result using image metrics. Given a suitable perceptual image metric, perceptually linear image variations are achieved. We demonstrate the practical utility of our approach by implementing two common image metrics, a perceptual and a non‐perceptual one, and by applying the method to a few visual analysis tasks.

Abstract The properties of both inorganic and organic materials and the function of biological structures can often only be understood by analyzing them simultaneously on atomic and nanoscopic, if not mesoscopic, scale. Here, the problem arises to render millions to billions of atoms. We propose a method by which it is possible to interactively visualize atomic data, bridging five orders of magnitude in length scale. For this, we propose a simple yet efficient GPU rendering method that enables interactive visualization of biological structures consisting of up to several billions of atoms. To be able to load all atomic data onto the GPU, we exploit the fact that biological structures often consist of recurring molecular substructures. We also exploit that these objects typically are rendered opaquely, so that only a fraction of the atoms is visible. The method is demonstrated on both biological structures as well as atom probe tomography data of an inorganic specimen. We conclude with a discussion about when ‐during ascension from atomic to mesoscopic scale – level‐of‐detail representations become necessary.

Abstract In this paper methods for extraction of local features in crisp vector fields are extended to uncertain fields. While in a crisp field local features are either present or absent at some location, in an uncertain field they are present with some probability. We model sampled uncertain vector fields by discrete Gaussian random fields with empirically estimated spatial correlations. The variability of the random fields in a spatial neighborhood is characterized by marginal distributions. Probabilities for the presence of local features are formulated in terms of low‐dimensional integrals over such marginal distributions. Specifically, we define probabilistic equivalents for critical points and vortex cores. The probabilities are computed by Monte Carlo integration. For identification of critical points and cores of swirling motion we employ the Poincaré index and the criterion by Sujudi and Haimes. In contrast to previous global methods we take a local perspective and directly extract features in divergence‐free fields as well. The method is able to detect saddle points in a straight forward way and works on various grid types. It is demonstrated by applying it to simulated unsteady flows of biofluid and climate dynamics.

Abstract We present the first general scheme to describe all four types of characteristic curves of flow fields – stream, path, streak, and time lines – as tangent curves of a derived vector field. Thus, all these lines can be obtained by a simple integration of an autonomous ODE system. Our approach draws on the principal ideas of the recently introduced tangent curve description of streak lines. We provide the first description of time lines as tangent curves of a derived vector field, which could previously only be constructed in a geometric manner. Furthermore, our scheme gives rise to new types of curves. In particular, we introduce advected stream lines as a parameter‐free variant of the time line metaphor. With our novel mathematical description of characteristic curves, a large number of feature extraction and analysis tools becomes available for all types of characteristic curves, which were previously only available for stream and path lines. We will highlight some of these possible applications including the computation of time line curvature fields and the extraction of cores of swirling advected stream lines.

We present a Visual Analytics approach that addresses the detection of interesting patterns in numerical time series, specifically from environmental sciences. Crucial for the detection of interesting temporal patterns are the time scale and the starting points one is looking at. Our approach makes no assumption about time scale and starting position of temporal patterns and consists of three main steps: an algorithm to compute statistical values for all possible time scales and starting positions of intervals, visual identification of potentially interesting patterns in a matrix visualization, and interactive exploration of detected patterns. We demonstrate the utility of this approach in two scientific scenarios and explain how it allowed scientists to gain new insight into the dynamics of environmental systems.

Scientists, engineers and physicians are used to analyze 3D data with slice-based visualizations. Radiologists for example are trained to read slices of medical imaging data. Despite the numerous examples of sophisticated 3D rendering techniques, domain experts, who still prefer slice-based visualization do not consider these to be very useful. Since 3D renderings have the advantage of providing an overview at a glance, while 2D depictions better serve detailed analyses, it is of general interest to better combine these methods. Recently there have been attempts to bridge this gap between 2D and 3D renderings. These attempts include specialized techniques for volume picking in medical imaging data that result in repositioning slices. In this paper, we present a new volume picking technique called WYSIWYP ("what you see is what you pick") that, in contrast to previous work, does not require pre-segmented data or metadata and thus is more generally applicable. The positions picked by our method are solely based on the data itself, the transfer function, and the way the volumetric rendering is perceived by the user. To demonstrate the utility of the proposed method, we apply it to automated positioning of slices in volumetric scalar fields from various application areas. Finally, we present results of a user study in which 3D locations selected by users are compared to those resulting from WYSIWYP. The user study confirms our claim that the resulting positions correlate well with those perceived by the user.

Abstract In this paper we revisit the computation and visualization of equivalents to isocontours in uncertain scalar fields. We model uncertainty by discrete random fields and, in contrast to previous methods, also take arbitrary spatial correlations into account. Starting with joint distributions of the random variables associated to the sample locations, we compute level crossing probabilities for cells of the sample grid. This corresponds to computing the probabilities that the well‐known symmetry‐reduced marching cubes cases occur in random field realizations. For Gaussian random fields, only marginal density functions that correspond to the vertices of the considered cell need to be integrated. We compute the integrals for each cell in the sample grid using a Monte Carlo method. The probabilistic ansatz does not suffer from degenerate cases that usually require case distinctions and solutions of ill‐conditioned problems. Applications in 2D and 3D, both to synthetic and real data from ensemble simulations in climate research, illustrate the influence of spatial correlations on the spatial distribution of uncertain isocontours.

Acceleration is a fundamental quantity of flow fields that captures Galilean invariant properties of particle motion. Considering the magnitude of this field, minima represent characteristic structures of the flow that can be classified as saddle- or vortex-like. We made the interesting observation that vortex-like minima are enclosed by particularly pronounced ridges. This makes it possible to define boundaries of vortex regions in a parameter-free way. Utilizing scalar field topology, a robust algorithm can be designed to extract such boundaries. They can be arbitrarily shaped. An efficient tracking algorithm allows us to display the temporal evolution of vortices. Various vortex models are used to evaluate the method. We apply our method to two-dimensional model systems from computational fluid dynamics and compare the results to those arising from existing definitions.

Visual analysis is widely used to study the behavior of molecules. Of particular interest are the analysis of molecular interactions and the investigation of binding sites. For large molecules, however, it is difficult to detect possible binding sites and paths leading to these sites by pure visual inspection. In this paper, we present new methods for the computation and visualization of potential molecular paths. Using a novel filtering method, we extract the significant paths from the Voronoi diagram of spheres. For the interactive visualization of molecules and their paths, we present several methods using deferred shading and other state-of-the-art techniques. To allow for a fast overview of reachable regions of the molecule, we illuminate the molecular surface using a large number of light sources placed on the extracted paths. We also provide a method to compute the extension surface of selected paths and visualize it using the skin surface. Furthermore, we use the extension surface to clip the molecule to allow easy visual tracking of even deeply buried paths. The methods are applied to several proteins to demonstrate their usefulness.

Uncertainty is ubiquitous in science, engineering and medicine. Drawing conclusions from uncertain data is the normal case, not an exception. While the field of statistical graphics is well established, only a few 2D and 3D visualization and feature extraction methods have been devised that consider uncertainty. We present mathematical formulations for uncertain equivalents of isocontours based on standard probability theory and statistics and employ them in interactive visualization methods. As input data, we consider discretized uncertain scalar fields and model these as random fields. To create a continuous representation suitable for visualization we introduce interpolated probability density functions. Furthermore, we introduce numerical condition as a general means in feature-based visualization. The condition number-which potentially diverges in the isocontour problem-describes how errors in the input data are amplified in feature computation. We show how the average numerical condition of isocontours aids the selection of thresholds that correspond to robust isocontours. Additionally, we introduce the isocontour density and the level crossing probability field; these two measures for the spatial distribution of uncertain isocontours are directly based on the probabilistic model of the input data. Finally, we adapt interactive visualization methods to evaluate and display these measures and apply them to 2D and 3D data sets.

In this paper we address the difficult problem of parameter-finding in image segmentation. We replace a tedious manual process that is often based on guess-work and luck by a principled approach that systematically explores the parameter space. Our core idea is the following two-stage technique: We start with a sparse sampling of the parameter space and apply a statistical model to estimate the response of the segmentation algorithm. The statistical model incorporates a model of uncertainty of the estimation which we use in conjunction with the actual estimate in (visually) guiding the user towards areas that need refinement by placing additional sample points. In the second stage the user navigates through the parameter space in order to determine areas where the response value (goodness of segmentation) is high. In our exploration we rely on existing ground-truth images in order to evaluate the "goodness" of an image segmentation technique. We evaluate its usefulness by demonstrating this technique on two image segmentation algorithms: a three parameter model to detect microtubules in electron tomograms and an eight parameter model to identify functional regions in dynamic Positron Emission Tomography scans.

Abstract Molecular surfaces play an important role in studying the interactions between molecules. Visualizing the dynamic behavior of molecules is particularly interesting to gain insights into a molecular system. Only recently it has become possible to interactively visualize dynamic molecular surfaces using ray casting techniques. In this paper, we show how to further accelerate the construction and the rendering of the solvent excluded surface (SES) and the molecular skin surface (MSS). We propose several improvements to reduce the update times for displaying these molecular surfaces. First, we adopt a parallel approximate Voronoi diagram algorithm to compute the MSS. This accelerates the MSS computation by more than one order of magnitude on a single core. Second, we demonstrate that the contour‐buildup algorithm is ideally suited for computing the SES due to its inherently parallel structure. For both parallel algorithms, we observe good scalability up to 8 cores and, thus, obtain interactive frame rates for molecular dynamics trajectories of up to twenty thousand atoms for the SES and up to a few thousand atoms for the MSS. Third, we reduce the rendering time for the SES using tight‐fitting bounding quadrangles as rasterization primitives. These primitives also accelerate the rendering of the MSS. With these improvements, the interactive visualization of the MSS of dynamic trajectories of a few thousand atoms becomes for the first time possible. Nevertheless, the SES remains a few times faster than the MSS.

Abstract We introduce an approach to visualize stationary 2D vector fields with global uncertainty obtained by considering the transport of local uncertainty in the flow. For this, we extend the concept of vector field topology to uncertain vector fields by considering the vector field as a density distribution function. By generalizing the concepts of stream lines and critical points we obtain a number of density fields representing an uncertain topological segmentation. Their visualization as height surfaces gives insight into both the flow behavior and its uncertainty. We present a Monte Carlo approach where we integrate probabilistic particle paths, which lead to the segmentation of topological features. Moreover, we extend our algorithms to detect saddle points and present efficient implementations. Finally, we apply our technique to a number of real and synthetic test data sets.

The six papers in this special issue are extended versions of papers presented at the IEEE/EG International Symposium om Volume Graphics, held in September 2007 in Prague, and the joint event of the IEEE/EG International Symposia on Volume Graphics (VG '08) and Point-Based Graphics (PBG '08), held in August 2008 in Los Angeles.

This work introduces a novel streamline seeding technique based on dual streamlines that are orthogonal to the vector field, instead of tangential. The greedy algorithm presented here produces a net of orthogonal streamlines that is iteratively refined resulting in good domain coverage and a high degree of continuity and uniformity. The algorithm is easy to implement and efficient, and it naturally extends to curved surfaces.

Abstract We propose a new criterion to characterize hierarchical two‐dimensional vortex regions induced by swirling motion. Central to the definition are closed loops that intersect the flow field at a constant angle. The union of loops belonging to the same area of swirling motion defines a vortex region. These regions are disjunct but may be nested, thus introducing a spatial hierarchy of vortex regions. We present a parameter free algorithm for the identification of these regions. Since they are not restricted to star‐ or convex‐shaped geometries, we are able to identify also intricate regions, e.g., of elongated vortices. Computing an integrated value for each loop and mapping these values to a vortex region, introduces new ways for visualizing or filtering the vortex regions. Exemplary, an application based on the Rankine vortex model is presented. We apply our method to several CFD datasets and compare our results to existing approaches.

Rhinologists are often faced with the challenge of assessing nasal breathing from a functional point of view to derive effective therapeutic interventions. While the complex nasal anatomy can be revealed by visual inspection and medical imaging, only vague information is available regarding the nasal airflow itself: Rhinomanometry delivers rather unspecific integral information on the pressure gradient as well as on total flow and nasal flow resistance. In this article we demonstrate how the understanding of physiological nasal breathing can be improved by simulating and visually analyzing nasal airflow, based on an anatomically correct model of the upper human respiratory tract. In particular we demonstrate how various Information Visualization (InfoVis) techniques, such as a highly scalable implementation of parallel coordinates, time series visualizations, as well as unstructured grid multi-volume rendering, all integrated within a multiple linked views framework, can be utilized to gain a deeper understanding of nasal breathing. Evaluation is accomplished by visual exploration of spatio-temporal airflow characteristics that include not only information on flow features but also on accompanying quantities such as temperature and humidity. To our knowledge, this is the first in-depth visual exploration of the physiological function of the nose over several simulated breathing cycles under consideration of a complete model of the nasal airways, realistic boundary conditions, and all physically relevant time-varying quantities.

Modern experimental and computational fluid mechanics are increasingly concerned with the structure nature of fluid motion. Recent research has highlighted the analysis of one transport structure which is called Lagrangian coherent structure. However, the quantity nature of the flow transport is still unclear. In this paper, we focus on the transport characteristics of physical quantities and propose an approach to visualize the finite-time transport structure of quantity advection. This is similar to an integral convolution over a scalar field along path-lines of a flow field. Applied to a well-chosen set of physical quantity fields this yields structures giving insights into the dynamical processes of the underlying flow. We demonstrate our approach on a number of test data sets.

We present an approach to analyze mixing in flow fields by extracting vortex and strain features as extremal structures of derived scalar quantities that satisfy a duality property: they indicate vortical as well as high-strain (saddletype) regions. Specifically, we consider the Okubo-Weiss criterion and the recently introduced MZ-criterion. While the first is derived from a purely Eulerian framework, the latter is based on Lagrangian considerations. In both cases high values indicate vortex activity whereas low values indicate regions of high strain. By considering the extremal features of those quantities, we define the notions of a vortex and a strain skeleton in a hierarchical manner: the collection of maximal 0D, 1D and 2D structures assemble the vortex skeleton; the minimal structures identify the strain skeleton. We extract those features using scalar field topology and apply our method to a number of steady and unsteady 3D flow fields.

In nature and in flow experiments particles form patterns of swirling motion in certain locations. Existing approaches identify these structures by considering the behavior of stream lines. However, in unsteady flows particle motion is described by path lines which generally gives different swirling patterns than stream lines. We introduce a novel mathematical characterization of swirling motion cores in unsteady flows by generalizing the approach of Sujudi/Haimes to path lines. The cores of swirling particle motion are lines sweeping over time, i.e., surfaces in the space-time domain. They occur at locations where three derived 4D vectors become coplanar. To extract them, we show how to re-formulate the problem using the Parallel Vectors operator. We apply our method to a number of unsteady flow fields.

We describe a terrain rendering algorithm for spherical terrains based on clipmaps. It leverages the high geometry throughput of current GPU to render large static triangle sets. The vertices are displaced by a height map texture. Our main contribution is mapping of texture coordinates to calculate the height map sample position based on the static vertex offset and the variable view position.

This paper presents an approach to extracting a path line oriented topological segmentation for periodic 2D timedependent vector fields. Topological methods aiming in capturing the asymptotic behavior of path lines rarely exist because path lines are usually only defined over a fixed time-interval, making statements about their asymptotic behavior impossible. For the data class of periodic vector fields, this restriction does not apply any more. Our approach detects critical path lines as well as basins from which the path lines converge to the critical ones. We demonstrate our approach on a number of test data sets.

Abstract In this paper we extract and visualize the topological skeleton of two‐parameter‐dependent vector fields. This kind of vector data depends on two parameter dimensions, for instance physical time and a scale parameter. We show that two important classes of local bifurcations – fold and Hopf bifurcations – build line structures for which we present an approach to extract them. Furthermore we show that new kinds of structurally stable local bifurcations exist for this data, namely fold‐fold and Hopf‐fold bifurcations. We present a complete classification of them. We apply our topological extraction method to analyze a number of two‐parameter‐dependent vector fields with different physical interpretations of the two additional dimensions. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Line and Curve Generation I.3.3 [Computer Graphics]: Picture/Image Generation

While vortex region quantities are Galilean invariant, most methods for extracting vortex cores depend on the frame of reference. We present an approach to extracting vortex core lines independently of the frame of reference by extracting ridge and valley lines of Galilean invariant vortex region quantities. We discuss a generalization of this concept leading to higher dimensional features. For the visualization of extracted line features we use an iconic representation indicating their scale and extent. We apply our approach to datasets from numerical simulations and experimental measurements.

Analysis of phenomena that simultaneously occur on different spatial and temporal scales requires adaptive, hierarchical schemes to reduce computational and storage demands. Adaptive mesh refinement (AMR) schemes support both refinement in space that results in a time-dependent grid topology, as well as refinement in time that results in updates at higher rates for refined levels. Visualization of AMR data requires generating data for absent refinement levels at specific time steps. We describe a solution starting from a given set of "key frames" with potentially different grid topologies. The presented work was developed in a project involving several research institutes that collaborate in the field of cosmology and numerical relativity. AMR data results from simulations that are run on dedicated compute machines and is thus stored centrally, whereas the analysis of the data is performed on the local computers of the scientists. We built a distributed solution using remote procedure calls (RPC). To keep the application responsive, we split the bulk data transfer from the RPC response and deliver it asynchronously as a binary stream. The number of network round-trips is minimized by using high level operations. In summary, we provide an application for exploratory visualization of remotely stored AMR data.

We introduce an approach to tracking vortex core lines in time-dependent 3D flow fields which are defined by the parallel vectors approach. They build surface structures in the 4D space-time domain. To extract them, we introduce two 4D vector fields which act as feature flow fields, i.e., their integration gives the vortex core structures. As part of this approach, we extract and classify local bifurcations of vortex core lines in space-time. Based on a 4D stream surface integration, we provide an algorithm to extract the complete vortex core structure. We apply our technique to a number of test data sets.

This paper presents an approach to extracting and classifying higher order critical points of 3D vector fields. To do so, we place a closed convex surface s around the area of interest. Then we show that the complete 3D classification of a critical point into areas of different flow behavior is equivalent to extracting the topological skeleton of an appropriate 2D vector field on s, if each critical point is equipped with an additional bit of information. Out of this skeleton, we create an icon which replaces the complete topological structure inside s for the visualization. We apply our method to find a simplified visual representation of clusters of critical points, leading to expressive visualizations of topologically complex 3D vector fields.

This paper describes approaches to topologically segmenting 2D time-dependent vector fields. For this class of vector fields, two important classes of lines exist: stream lines and path lines. Because of this, two segmentations are possible: either concerning the behavior of stream lines or of path lines. While topological features based on stream lines are well established, we introduce path line oriented topology as a new visualization approach in this paper. As a contribution to stream line oriented topology, we introduce new methods to detect global bifurcations like saddle connections and cyclic fold bifurcations as well as a method of tracking all isolated closed stream lines. To get the path line oriented topology, we segment the vector field into areas of attracting, repelling, and saddle-like behavior of the path lines. We compare both kinds of topologies and apply them to a number of test data sets.

Datasets of tens of gigabytes are becoming common in computational and experimental science. This development is driven by advances in imaging technology, producing detectors with growing resolutions, as well as availability of cheap processing power and memory capacity in commodity-based computing clusters. We describe the design of a visualization system that allows scientists to interactively explore large remote data sets in an efficient and flexible way. The system is broadly applicable and currently used by medical scientists conducting an osteoporosis research project. Human vertebral bodies are scanned using a high resolution microCT scanner producing scans of roughly 8 GB size each. All participating research groups require access to the centrally stored data. Due to the rich internal bone structure, scientists need to interactively explore the full dataset at coarse levels, as well as visualize subvolumes of interest at the highest resolution. Our solution is based on HDF5 and GridFTP. When accessing data remotely, the HDF5 data processing pipeline is modified to support efficient retrieval of subvolumes. We reduce the overall latency and optimize throughput by executing high-level operations on the remote side. The GridFTP protocol is used to pass the HDF5 requests to a customized server. The approach takes full advantage of local graphics hardware for rendering. Interactive visualization is accomplished using a background thread to access the datasets stored in a multiresolution format. A hierarchical volume tenderer provides seamless integration of high resolution details with low resolution overviews.

Topological methods aim at the segmentation of a vector field into areas of different flow behavior. For 2D time-dependent vector fields, two such segmentations are possible: either concerning the behavior of stream lines, or of path lines. While stream line oriented topology is well established, we introduce path line oriented topology as a new visualization approach in this paper. As a contribution to stream line oriented topology we introduce new methods to detect global bifurcations like saddle connections and cyclic fold bifurcations. To get the path line oriented topology we segment the vector field into areas of attracting, repelling and saddle-like behavior of the path lines. We compare both kinds of topologies and apply them to a number of data sets.

Abstract We present the first algorithm for constructing 3D vector fields based on their topological skeleton. The skeleton itself is modeled by interactively moving a number of control polygons. Then a piecewise linear vector field is automatically constructed which has the same topological skeleton as modeled before. This approach is based on a complete segmentation of the areas around critical points into sectors of different flow behavior. Based on this, we present the first approach to visualizing higher order critical points of 3D vector fields. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Line and Curve Generation I.3.7 [Computer Graphics]: Three‐Dimensional Graphics and Realism

WELCOME to the special section on Mathematics and Visualization. Mathematics is becoming an increasingly important tool in visualization, aiding the development and analysis of efficient algorithms and data structures. As visualization is beginning to evolve into a mature science and the underlying technology is becoming increasingly complex, the need for a rigorous framework is becoming obvious. Formal mathematical language provides a solid ground which allows us to embed visualization problems within an abstract setting and thereby to make well-established analytical tools applicable. For example, convergence issues and the numerical stability of visualization algorithms are essential for effective and reliable results in visualization. The editors of this special section have actively supported the convergence of mathematics and visualization as organizers of the international conference series Visualization and Mathematics since 1995, the film festival VideoMath at the International Congress of Mathematicians ICM 1998, as well as at various international workshops and summer schools. These activities helped to establish a small but worldwide community of researchers who perform work in this border area; they also gave rise to the new book series Mathematics + Visualization and the videoseries VideoMATH published by Springer Verlag. In particular, the international conference series Visualization and Mathematics in Berlin intensified the interaction of mathematicians and scientists from computer graphics and visualization. The current special section is comprised of a set of five carefully selected articles which are elaborated publications of the latest conference in 2002. In order to emphasize the interdisciplinary character of the young scientific field of mathematical visualization, the articles in this special section were selected to cover a broad range of topics from theory to praxis. The papers include topics from discrete and differential geometry, combinatorial and differential topology, graph theory, vector field analysis, geometry compression, image processing, signal processing, feature detection, image segmentation, numerical methods, and partial differential equations. The articles were selected by the editors of this special section and each carefully reviewed by at least three referees. In the following, we summarize the articles. “Applications of Forman’s Discrete Morse Theory to Topology Visualization and Mesh Compression” by Thomas Lewiner, Heio Lopes and Geovan Tavares: Many advances in science arise from the combination of different fields. Lewiner et al. relate Forman’s discrete geometry, a purely mathematical construction, with popular mesh compression schemes, such as Edgebreaker. This link unveils a new topological view on compression algorithms. The introduction of Forman’s discrete Morse theory and vector fields provides a new tool for topology visualization and the understanding of visualization algorithms. “Visualizing a Sphere Eversion” by George Francis and John M. Sullivan: Finding a process to turn a sphere inside out has been an active research area for geometers and topologists for more than 50 years. Mathematical visualization—using computer graphics tools, numerical algorithms, and geometric invention—provides an adequate collection of techniques to calculate and visualize the complex deformations of the eversion process. Here, mathematical visualization provides insight into abstract constructions and explains mathematics to a broader audience. The paper by Francis and Sullivan provides a glimpse of the exciting history of the sphere eversion problem and presents the underlying techniques of the author’s awarded computer graphics animation “Optiverse.” “Robust Feature Detection and Local Classification for Surfaces Based on Moment Analysis” by Ulrich Clarenz, Martin Rumpf, and Alex Telea: Geometry analysis and processing has become a major topic in computer graphics, as well as feature detection in visualization. The authors present a surface classification method for triangulated surfaces, with applications in surface fairing, mesh decimation, surface segmentation, and surface matching. The method uses local zero and first order moments as an alternative to curvature and utilizes structure tensor-like concepts. The method is well-founded, explained in detail, and shows convincing performance under various conditions. It provides an indicator for the smoothness of a given discrete surface and comes together with a built-in multiscale. Interesting aspects are the difference between the computation of moments in the smooth and nonsmooth surface as well as the analysis of how the moments scale with the scale parameter for smooth and nonsmooth areas. “Fast Evolution of Image Manifolds and Application to Filtering and Segmentation in 3D Medical Images” by Thomas Deschamps, Ravi Malladi, and Igor Ravve: Image analysis techniques are interesting in visualization as they represent “feature detection” methods for one major data type, namely, images. Additionally, many of IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. 10, NO. 5, SEPTEMBER/OCTOBER 2004 497

One of the reasons that topological methods have a limited popularity for the visualization of complex 3D flow fields is the fact that such topological structures contain a number of separating stream surfaces. Since these stream surfaces tend to hide each other as well as other topological features, for complex 3D topologies the visualizations become cluttered and hardly interpretable. This paper proposes to use particular stream lines called saddle connectors instead of separating stream surfaces and to depict single surfaces only on user demand. We discuss properties and computational issues of saddle connectors and apply these methods to complex flow data. We show that the use of saddle connectors makes topological skeletons available as a valuable visualization tool even for topologically complex 3D flow data.

In this paper, we present an algorithm that accelerates 3D texture-based volume rendering of large, sparse data sets, i.e., data sets where only a traction of the voxels contain relevant information. In texture-based approaches, the rendering performance is affected by the fill-rate, the size of texture memory, and the texture I/O bandwidth. For sparse data, these limitations can be circumvented by restricting most of the rendering work to the relevant parts of the volume. In order to efficiently enclose the corresponding regions with axis-aligned boxes, we employ a hierarchical data structure, known as an AMR (adaptive mesh refinement) tree. The hierarchy is generated utilizing a clustering algorithm. A good balance is thereby achieved between the size of the enclosed volume, i.e., the amount to render in graphics hardware and the number of axis-aligned regions, i.e., the number of texture coordinates to compute in software. The waste of texture memory by the power-of-two restriction is minimized by a 3D packing algorithm which arranges texture bricks economically in memory. Compared to an octree approach, the rendering performance is significantly increased and less parameter tuning is necessary.

For quantitative examination of phenomena that simultaneously occur on very different spatial and temporal scales, adaptive hierarchical schemes are required. A special numerical multilevel technique, associated with a particular hierarchical data structure, is so-called adaptive mesh refinement (AMR). It allows one to bridge a wide range of spatial and temporal resolutions and therefore gains increasing popularity. We describe the interplay of several visualization and VR software packages for rendering time dependent AMR simulations of the evolution of the first star in the universe. The work was done in the framework of a television production for Discovery Channel television, "The Unfolding Universe.". Parts of the data were taken from one of the most complex AMR simulation ever carried out: It contained up to 27 levels of resolution, requiring modifications to the texture based AMR volume rendering algorithm that was used to depict the density distribution of the gaseous interstellar matter. A voice and gesture controlled CAVE application was utilized to define camera paths following the interesting features deep inside the computational domains. Background images created from cosmological computational data were combined with the final renderings.

We present a robust, noise-resistant criterion characterizing plane-like skeletons in binary voxel objects. It is based on a distance map and the geodesic distance along the object's boundary. A parameter allows us to control the noise sensitivity. If needed, homotopy with the original object might be reconstructed in a second step, using an improved distance ordered thinning algorithm. The skeleton is analyzed to create a geometric representation for rendering. Plane-like parts are transformed into an triangulated surface not enclosing a volume by a suitable triangulation scheme. The resulting surfaces have lower triangle count than those created with standard methods and tend to maintain the original geometry, even after simplification with a high decimation rate. Our algorithm allows us to interactively render expressive images of complex 3D structures, emphasizing independently plane-like and rod-like structures. The methods are applied for visualization of the microstructure of bone biopsies.

The bioactivity of a molecule strongly depends on its metastable conformational shapes and the transitions between these. Therefore, conformation analysis and visualization is a basic prerequisite for the understanding of biochemical processes. We present techniques for visual analysis of metastable molecular conformations. Core of these are flexibly applicable methods for alignment of molecular geometries, as well as methods for depicting shape and 'fuzziness' of metastable conformations. All analysis tools are provided in an integrated working environment. The described techniques are demonstrated with pharmaceutically active biomolecules.

Cactus is an open source problem solving environment designed for scientists and engineers. Its modular structure facilitates parallel computation across different architectures and collaborative code development between different groups. The Cactus Code originated in the academic research community, where it has been developed and used over many years by a large international collaboration of physicists and computational scientists. We discuss how the intensive computing requirements of physics applications now using the Cactus Code encourage the use of distributed and metacomputing, describe the development and experiments which have already been performed with Cactus, and detail how its design makes it an ideal application test-bed for Grid computing.

A new technique for interactive vector field visualization using large numbers of properly illuminated field lines is presented. Taking into account ambient, diffuse and specular reflection terms, as well as transparency and depth cueing, we employ a realistic shading model which significantly increases the quality and realism of the resulting images. While many graphics workstations offer hardware support for illuminating surface primitives, usually no means for an accurate shading of line primitives are provided. However, we show that proper illumination of lines can be implemented by exploiting the texture mapping capabilities of modern graphics hardware. In this way, high rendering performance with interactive frame rates can be achieved. We apply the technique to render large numbers of integral curves of a vector field. The impression of the resulting images can be further improved by a number of visual enhancements, like color coding or particle animation. We also describe methods for controlling the distribution of field lines in space. These methods enable us to use illuminated field lines for interactive exploration of vector fields.

A new technique for interactive vector field visualization using large numbers of properly illuminated stream lines is presented. Taking into account ambient, diffuse, and specular reflection terms as well as transparency, we employ a realistic shading model which significantly increases quality and realism of the resulting images. While many graphics workstations offer hardware support for illuminating surface primitives, usually no means for an accurate shading of line primitives are provided. However, we show that proper illumination of lines can be implemented by exploiting the texture mapping capabilities of modern graphics hardware. In this way high rendering performance with interactive frame rates can be achieved. We apply the technique to render large numbers of integral curves in a vector field. The impression of the resulting images can be further improved by making the curves partially transparent. We also describe methods for controlling the distribution of stream lines in space. These methods enable us to use illuminated stream lines within an interactive visualization environment.

Line Integral Convolution (LIC) is a powerful technique for generating striking images and animations from vector data. Introduced in 1993, the method has rapidly found many application areas, ranging from computer arts to scientific visualization. Based upon locally filtering an input texture along a curved stream line segment in a vector field, it is able to depict directional information at high spatial resolutions. We present a new method for computing LIC images. It employs simple box filter kernels only and minimizes the total number of stream lines to be computed. Thereby it reduces computational costs by an order of magnitude compared to the original algorithm. Our method utilizes fast, error-controlled numerical integrators. Decoupling the characteristic lengths in vector field grid, input texture and output image, it allows computation of filtered images at arbitrary resolution. This feature is of significance in computer animation as well as in scientific visualization, where it can be used to explore vector data by smoothly enlarging structure of details. We also present methods for improved texture animation, again employing box filter kernels only. To obtain an optimal motion effect, spatial decay of correlation between intensities

Efficient implementations of irregular problems on vector and parallel architectures generally are hard to realize. An important class of irregular problems are Gau-Seidel iteration schemes applied to irregular data sets. The unstructured data dependences arising there prevent restructuring compilers from generating efficient code for vector or parallel machines. It is shown, how to structure the data dependences by decomposing the data set using graph coloring techniques and by specifying a particular execution order already on the algorithm level. Methods to master the irregularities originating from different types of tasks are proposed. An example of application is given and possible future developments are mentioned. Contents 1 Introduction 1 2 Preliminaries 2 2.1 Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Data Dependences . . . . . . . . . . . . . . . . . . . . . . . . 3 3 Iteration Schemes 4 4 Gau-Seidel Iterations for Regular Problems 6 5 Ga...