Topological and geometric segmentation methods provide powerful concepts for detailed field analysis and visualization. However, when it comes to a quantitative analysis that requires highly accurate geometric segmentation, there is a large discrepancy between the promising theory and the available computational approaches. In this paper, we compare and evaluate various segmentation methods with the aim to identify and quantify the extent of these discrepancies. Thereby, we focus on an application from quantum chemistry: the analysis of electron density fields. It is a scalar quantity that can be experimentally measured or theoretically computed. In the evaluation we consider methods originating from the domain of quantum chemistry and computational topology. We apply the methods to the charge density of a set of crystals and molecules. Therefore, we segment the volumes into atomic regions and derive and compare quantitative measures such as total charge and dipole moments from these regions. As a result, we conclude that an accurate geometry determination can be crucial for correctly segmenting and analyzing a scalar field, here demonstrated on the electron density field.

This paper is concerned with the extraction of the surface topology of tensor fields on 2D triangulated manifoldsembedded in 3D. In scientific visualization topology is a meaningful instrument to get a hold on the structure of agiven dataset. Due to the discontinuity of tensor fields on a piecewise planar domain, standard topology extractionmethods result in an incomplete topological skeleton. In particular with regard to the high computational costs ofthe extraction this is not satisfactory. This paper provides a method for topology extraction of tensor fields thatleads to complete results. The core idea is to include the locations of discontinuity into the topological analysis.For this purpose the model of continuous transition bridges is introduced, which allows to capture the entiretopology on the discontinuous field. The proposed method is applied to piecewise linear three-dimensional tensorfields defined on the vertices of the triangulation and for piecewise constant two or three-dimensional tensor fieldsgiven per triangle, e.g. rate of strain tensors of piecewise linear flow fields.

We present a topology-based segmentation as means for visualizing 2D symmetric tensor fields. The segmentation uses directional as well as eigenvalue characteristics of the underlying field to delineate cells of similar (or dissimilar) behavior in the tensor field. A special feature of the resulting cells is that their shape expresses the tensor behavior inside the cells and thus also can be considered as a kind of glyph representation. This allows a qualitative comprehension of important structures of the field. The resulting higher-level abstraction of the field provides valuable analysis. The extraction of the integral topological skeleton using both major and minor eigenvector fields serves as a structural pre-segmentation and renders all directional structures in the field. The resulting curvilinear cells are bounded by tensorlines and already delineate regions of equivalent eigenvector behavior. This pre-segmentation is further adaptively refined to achieve a segmentation reflecting regions of similar eigenvalue and eigenvector characteristics. Cell refinement involves both subdivision and merging of cells achieving a predetermined resolution, accuracy and uniformity of the segmentation. The buildingblocks of the approach can be intuitively customized to meet the demands or different applications. Application to tensor fields from numerical stress simulations demonstrates the effectiveness of our method.

Blood flow simulations play an important role for the understanding of vascular diseases, such as aneurysms. However, analysis of the resulting flow patterns, especially comparisons across patient groups, are challenging. Typically, the hemodynamic analysis relies on trial and error inspection of the flow data based on pathline visualizations and surface renderings. Visualizing too many pathlines at once may obstruct interesting features, e.g., embedded vortices, whereas with too little pathlines, particularities such as flow characteristics in aneurysm blebs might be missed. While filtering and clustering techniques support this task, they require the pre-computation of pathlines densely sampled in the space-time domain. Not only does this become prohibitively expensive for large patient groups, but the results often suffer from undersampling artifacts. In this work, we propose the usage of evolutionary algorithms to reduce the overhead of computing pathlines that do not contribute to the analysis, while simultaneously reducing the undersampling artifacts. Integrated in an interactive framework, it efficiently supports the evaluation of hemodynamics for clinical research and treatment planning in case of cerebral aneurysms. The specification of general optimization criteria for entire patient groups allows the blood flow data to be batch-processed. We present clinical cases to demonstrate the benefits of our approach especially in presence of aneurysm blebs. Furthermore, we conducted an evaluation with four expert neuroradiologists. As a result, we report advantages of our method for treatment planning to underpin its clinical potential.  

Feature-based approaches have recently become very popular in computer vision and image analysis applications, and are becoming a promising direction in shape retrieval. SHREC’11 robust feature detection and description benchmark simulates the feature detection and description stages of feature-based shape retrieval algorithms. The benchmark tests the performance of shape feature detectors and descriptors under a wide variety of transformations. The benchmark allows evaluating how algorithms cope with certain classes of transformations and strength of the transformations that can be dealt with. The present paper is a report of the SHREC’11 robust feature detection and description benchmark results.

The analysis of 2D flow data is often guided by the search for characteristic structures with semantic meaning. One way to approach this question is to identify structures of interest by a human observer, with the goal of finding similar structures in the same or other datasets. The major challenges related to this task are to specify the notion of similarity and define respective pattern descriptors. While the descriptors should be invariant to certain transformations, such as rotation and scaling, they should provide a similarity measure with respect to other transformations, such as deformations. In this paper, we propose to use moment invariants as pattern descriptors for flow fields. Moment invariants are one of the most popular techniques for the description of objects in the field of image recognition. They have recently also been applied to identify 2D vector patterns limited to the directional properties of flow fields. Moreover, we discuss which transformations should be considered for the application to flow analysis. In contrast to previous work, we follow the intuitive approach of moment normalization, which results in a complete and independent set of translation, rotation, and scaling invariant flow field descriptors. They also allow to distinguish flow features with different velocity profiles. We apply the moment invariants in a pattern recognition algorithm to a real world dataset and show that the theoretical results can be extended to discrete functions in a robust way.

The analysis of 2D flow data is often guided by the search for characteristic structures with semantic meaning. One way to approach this question is to identify structures of interest by a human observer, with the goal of finding similar structures in the same or other datasets. The major challenges related to this task are to specify the notion of similarity and define respective pattern descriptors. While the descriptors should be invariant to certain transformations, such as rotation and scaling, they should provide a similarity measure with respect to other transformations, such as deformations. In this paper, we propose to use moment invariants as pattern descriptors for flow fields. Moment invariants are one of the most popular techniques for the description of objects in the field of image recognition. They have recently also been applied to identify 2D vector patterns limited to the directional properties of flow fields. Moreover, we discuss which transformations should be considered for the application to flow analysis. In contrast to previous work, we follow the intuitive approach of moment normalization, which results in a complete and independent set of translation, rotation, and scaling invariant flow field descriptors. They also allow to distinguish flow features with different velocity profiles. We apply the moment invariants in a pattern recognition algorithm to a real world dataset and show that the theoretical results can be extended to discrete functions in a robust way.

We generalize the framework of moments and introduce a definition of invariants for three-dimensional vector fields. To do so, we use the method of moment normalization that has been shown to be useful in the two dimensions. Using invariant moments, we show how to search for patterns in these fields independent from their position, orientation and scale. From the first order vector moment tensor, we construct a complete and independent set of descriptors. We test the invariants in queries on synthetic and real world flow fields.

We present a state-of-the-art report on time-dependent flow topology. We survey representative papers in visualization and provide a taxonomy of existing approaches that generalize flow topology from time-independent to time-dependent settings. The approaches are classified based upon four categories: tracking of steady topology, reference frame adaption, pathline classification or clustering, and generalization of critical points. Our unique contributions include introducing a set of desirable mathematical properties to interpret physical meaningfulness for time-dependent flow visualization, inferring mathematical properties associated with selective research papers, and utilizing such properties for classification. The five most important properties identified in the existing literature include coincidence with the steady case, induction of a partition within the domain, Lagrangian invariance, objectivity, and Galilean invariance.

High-pressure chemistry is known to inspire the creation of unexpected new classes of compounds with exceptional properties. Here, we employ the laser-heated diamond anvil cell technique for synthesis of a Dirac material BeN4. A triclinic phase of beryllium tetranitride tr-BeN4 was synthesized from elements at similar to 85 GPa. Upon decompression to ambient conditions, it transforms into a compound with atomic-thick BeN4 layers interconnected via weak van der Waals bonds and consisting of polyacetylene-like nitrogen chains with conjugated pi systems and Be atoms in square-planar coordination. Theoretical calculations for a single BeN4 layer show that its electronic lattice is described by a slightly distorted honeycomb structure reminiscent of the graphene lattice and the presence of Dirac points in the electronic band structure at the Fermi level. The BeN4 layer, i.e., beryllonitrene, represents a qualitatively new class of 2D materials that can be built of a metal atom and polymeric nitrogen chains and host anisotropic Dirac fermions.

Ab initio simulations of a multi-component alloy using density functional theory (DFT) were combined with experiments on thin films of the same material using X-ray photoelectron spectroscopy (XPS) to study the connection between the electronic and atomic structures of multi-component alloys. The DFT simulations were performed on an equimolar HfNbTiVZr multi-component alloy. Structure and charge transfer were evaluated using relaxed, non-relaxed, as well as elemental reference structures. The use of a fixed sphere size model allowed quantification of charge transfer, and separation into different contributions. The charge transfer was generally found to follow electronegativity trends and results in a reduced size mismatch between the elements, and thus causes a considerable reduction of the lattice distortions compared to a traditional assumption based on tabulated atomic radii. A calculation of the average deviation from the average radius (i.e. the so-called delta-parameter) based on the atomic Voronoi volumes gave a reduction of delta from ca. 6% (using the volumes in elemental reference phases) to ca. 2% (using the volumes in the relaxed multi-component alloy phase). The reliability of the theoretical results was confirmed by XPS measurements of a Hf22Nb19Ti18V19Zr21 thin film deposited by sputter deposition. The experimentally observed core level binding energy shifts (CLS), as well as peak broadening due to a range of chemical surroundings, for each element showed good agreement with the calculated DFT values. The single solid solution phase of the sample was confirmed by X-ray diffraction (XRD) and transmission electron microscopy (TEM) including energy dispersive spectroscopy (EDS) with nm-resolution. These observations show that the HfNbTiVZr solid solution phase is non-ideal, and that chemical bonding plays an important part in the structure formation, and presumably also in the properties. Our conclusions should be transferable to other multi-component alloy systems, as well as some other multi-component material systems, and open up interesting possibilities for the design of material properties via the electronic structure and controlled charge transfer between selected metallic elements in the materials.

We study with a two-dimensional particle-in-cell simulation the stability of a discontinuity or piston, which separates an electron–positron cloud from a cooler electron–proton plasma. Such a piston might be present in the relativistic jets of accreting black holes separating the jet material from the surrounding ambient plasma and when pair clouds form during an x-ray flare and expand into the plasma of the accretion disk corona. We inject a pair plasma at a simulation boundary with a mildly relativistic temperature and mean speed. It flows across a spatially uniform electron–proton plasma, which is permeated by a background magnetic field. The magnetic field is aligned with one simulation direction and oriented orthogonally to the mean velocity vector of the pair cloud. The expanding pair cloud expels the magnetic field and piles it up at its front. It is amplified to a value large enough to trap ambient electrons. The current of the trapped electrons, which is carried with the expanding cloud front, drives an electric field that accelerates protons. A solitary wave grows and changes into a piston after it saturated. Our simulations show that this piston undergoes a collisionless instability similar to a Rayleigh–Taylor instability. The undular mode grows and we observe fingers in the proton density distribution. The effect of the instability is to deform the piston but it cannot destroy it.

We present the results from a particle-in-cell (PIC) simulation that models the interaction between a spatially localized electron-positron cloud and an electron-ion plasma. The latter is permeated by a magnetic field that is initially spatially uniform and aligned with the mean velocity vector of the pair cloud. The pair cloud expels the magnetic field and piles it up into an electromagnetic piston. Its electromagnetic field is strong enough to separate the pair cloud from the ambient plasma in the direction that is perpendicular to the cloud propagation direction. The piston propagates away from the spine of the injected pair cloud and it accelerates the protons to a high nonrelativistic speed. The accelerated protons form an outer cocoon that will eventually become separated from the unperturbed ambient plasma by a fast magnetosonic shock. No electromagnetic piston forms at the front of the cloud and a shock is mediated here by the filamentation instability. The final plasma distribution resembles that of a hydrodynamic jet. Collisionless plasma jets may form in the coronal plasma of accreting black holes and the interaction between the strong magnetic field of the piston and the hot pair cloud may contribute to radio emissions by such objects.

Aims. We study the effect a guiding magnetic field has on the formation and structure of a pair jet that propagates through a collisionless electron–proton plasma at rest.

Methods. We model with a particle-in-cell (PIC) simulation a pair cloud with a temperature of 400 keV and a mean speed of 0.9c (c - light speed). Pair particles are continuously injected at the boundary. The cloud propagates through a spatially uniform, magnetized, and cool ambient electron–proton plasma at rest. The mean velocity vector of the pair cloud is aligned with the uniform background magnetic field. The pair cloud has a lateral extent of a few ion skin depths.

Results. A jet forms in time. Its outer cocoon consists of jet-accelerated ambient plasma and is separated from the inner cocoon by an electromagnetic piston with a thickness that is comparable to the local thermal gyroradius of jet particles. The inner cocoon consists of pair plasma, which lost its directed flow energy while it swept out the background magnetic field and compressed it into the electromagnetic piston. A beam of electrons and positrons moves along the jet spine at its initial speed. Its electrons are slowed down and some positrons are accelerated as they cross the head of the jet. The latter escape upstream along the magnetic field, which yields an excess of megaelectronvolt positrons ahead of the jet. A filamentation instability between positrons and protons accelerates some of the protons, which were located behind the electromagnetic piston at the time it formed, to megaelectronvolt energies.

Conclusions. A microscopic pair jet in collisionless plasma has a structure that is similar to that predicted by a hydrodynamic model of relativistic astrophysical pair jets. It is a source of megaelectronvolt positrons. An electromagnetic piston acts as the contact discontinuity between the inner and outer cocoons. It would form on subsecond timescales in a plasma with a density that is comparable to that of the interstellar medium in the rest frame of the latter. A supercritical fast magnetosonic shock will form between the pristine ambient plasma and the jet-accelerated plasma on a timescale that exceeds our simulation time by an order of magnitude.

In this work we explore evolutionary algorithms for selected a visualization application. We demonstrate its potential using an example from flow visualization showing promising first results. Evolutionary algorithms, as guided search approach, find close-to-optimal solutions with respect to some fitness function in an iterative process using biologically motivated mechanisms like selection, mutation and recombination. As such, they provide a powerful alternative to filtering methods commonly used in visualization where the space of possible candidates is densely sampled in a pre-processing step from which the best candidates are selected and visualized. This approach however tends to be increasingly inefficient with growing data size or expensive candidate computations resulting in large pre-processing times. We present an evolutionary algorithm for the problem of streamline selection to highlight features of interest in flow data. Our approach directly optimizes the solution candidates with respect to a user selected fitness function requiring significantly less computations. At the same time the problem of possible under-sampling is solved since we are not tied to a preset resolution. We demonstrate our approach on the well-known flow around an obstacle as case with a two-dimensional search space. The blood flow in an aneurysm serves as an example with a three-dimensional search space. For both, the achieved results are comparable to line filtering approaches with much less line computations.

We present an interactive approach to analyse flow fields using a new type of particle system, which is composed of autonomous particles exploring the flow. While particles provide a very intuitive way to visualize flows, it is a challenge to capture the important features with such systems. Particles tend to cluster in regions of low velocity and regions of interest are often sparsely populated. To overcome these disadvantages, we propose an automatic adaption of the particle density with respect to local importance measures. These measures are user defined and the systems sensitivity to them can be adjusted interactively. Together with the particle history, these measures define a probability for particles to multiply or die, respectively. There is no communication between the particles and no neighbourhood information has to be maintained. Thus, the particles can be handled in parallel and support a real‐time investigation of flow fields. To enhance the visualization, the particles' properties and selected field measures are also used to specify the systems rendering parameters, such as colour and size. We demonstrate the effectiveness of our approach on different simulated vector fields from technical and medical applications.

In this paper, we propose a concept to design, track, and compare application-specific feature definitions expressed as sets of critical points. Our work has been inspired by the observation that in many applications a large variety of different feature definitions for the same concept are used. Often, these definitions compete with each other and it is unclear which definition should be used in which context. A prominent example is the definition of cyclones in climate research. Despite the differences, frequently these feature definitions can be related to topological concepts.

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Blood flow data from direct measurements (4D flow MRI) or numerical simulations opens new possibilities for the understanding of the development of cardiac diseases. However, before this new data can be used in clinical studies or for diagnosis, it is important to develop a notion of the characteristics of typical flow structures. To support this process we developed a novel blood flow clustering and exploration method. The method builds on the concept of coherent flow structures. Coherence maps for cross-sectional slices are defined to show the overall degree of coherence of the flow. In coherent regions the method summarizes the dominant blood flow using a small number of pathline representatives. In contrast to other clustering approaches the clustering is restricted to coherent regions and pathlines with low coherence values, which are not suitable for clustering and thus are not forced into clusters. The coherence map is based on the Finite-time Lyapunov Exponent (FTLE). It is created on selected planes in the inflow respective outflow area of a region of interest. The FTLE value measures the rate of separation of pathlines originating from this plane. Different to previous work using FTLE we do not focus on separating extremal lines but on local minima and regions of low FTLE intensities to extract coherent flow. The coherence map and the extracted clusters serve as basis for the flow exploration. The extracted clusters can be selected and inspected individually. Their flow rate and coherence provide a measure for their significance. Switching off clusters reduces the amount of occlusion and reveals the remaining part of the flow. The non-coherent regions can also be explored by interactive manual pathline seeding in the coherence map.

In this paper, we tackle the challenge of effective Transfer Function (TF) design for Direct Volume Rendering (DVR) of full-color datasets. We propose a novel TF design toolbox based on color similarity which is used to adjust opacity as well as replacing colors. We show that both CIE L*u*v* chromaticity and the chroma component of YCbCr are equally suited as underlying color space for the TF widgets. In order to maximize the area utilized in the TF editor, we renormalize the color space based on the histogram of the dataset. Thereby, colors representing a higher share of the dataset are depicted more prominently, thus providing a higher sensitivity for fine-tuning TF widgets. The applicability of our TF design toolbox is demonstrated by volume ray casting challenging full-color volume data including the visible male cryosection dataset and examples from 3D histology.

Frequency distributions (FD) are an important instrument when analyzing and investigating scientific data. In volumetric visualization, for example, frequency distributions visualized as histograms, often assist the user in the process of designing transferfunction (TF) primitives. Yet a single point in the distribution can correspond to multiple features in the data, particularly inlow-dimensional TFs that dominate time-critical domains such as health care. In this paper, we propose contributions to thearea of medical volume data exploration, in particular Computed Tomography (CT) data, based on the decomposition of localfrequency distributions (LFD). By considering the local neighborhood utilizing LFDs we can incorporate a measure for neighborhood similarity to differentiate features thereby enhancing the classification abilities of existing methods. This also allowsus to link the attribute space of the histogram with the spatial properties of the data to improve the user experience and simplifythe exploration step. We propose three approaches for data exploration which we illustrate with several visualization caseshighlighting distinct features that are not identifiable when considering only the global frequency distribution. We demonstratethe power of the method on selected datasets

We present a practical approach to generate stochastic anisotropic samples with Poisson-disk characteristic over a two-dimensional domain. In contrast to isotropic samples, we understand anisotropic samples as non-overlapping ellipses whose size and density match a given anisotropic metric. Anisotropic noise samples are useful for many visualization and graphics applications. The spot samples can be used as input for texture generation, e.g., line integral convolution (LIC), but can also be used directly for visualization. The definition of the spot samples using a metric tensor makes them especially suitable for the visualization of tensor fields that can be translated into a metric. Our work combines ideas from sampling theory and mesh generation. To generate these samples with the desired properties we construct a first set of non-overlapping ellipses whose distribution closely matches the underlying metric. This set of samples is used as input for a generalized anisotropic Lloyd relaxation to distribute noise samples more evenly. Instead of computing the Voronoi tessellation explicitly, we introduce a discrete approach which combines the Voronoi cell and centroid computation in one step. Our method supports automatic packing of the elliptical samples, resulting in textures similar to those generated by anisotropic reaction-diffusion methods. We use Fourier analysis tools for quality measurement of uniformly distributed samples. The resulting samples have nice sampling properties, for example, they satisfy a blue noise property where low frequencies in the power spectrum are reduced to a minimum.

We present a simple and efficient approach to generate a dense set of anisotropic, spatially varying glyphs over a two-dimensional domain. Such glyph samples are useful for many visualization and graphics applications. The glyphs are embedded in a set of nonoverlapping ellipses whose size and density match a given anisotropic metric. An additional parameter controls the arrangement of the ellipses on lines, which can be favorable for some applications, for example, vector fields and distracting for others. To generate samples with the desired properties, we combine ideas from sampling theory and mesh generation. We start with constructing a first set of nonoverlapping ellipses whose distribution closely matches the underlying metric. This set of samples is used as input for a generalized anisotropic Lloyd relaxation to distribute samples more evenly.

Oceanic eddies, which are highly mass-coherent vortices traveling through the earth's waters, are of special interest for their mixing properties. Therefore, large-scale ensemble simulations are performed to approximate their possible evolution. Analyzing their development and transport behavior requires a stable extraction of both their shape and properties of water masses within. We present a framework for extracting the time series of full 3D eddy geometries based on an winding angle criterion. Our analysis tools enables users to explore the results in-depth by linking extracted volumes to extensive statistics collected across several ensemble members. The methods are showcased on an ensemble simulation of the Red Sea. We show that our extraction produces stable and coherent geometries even for highly irregular eddies in the Red Sea. These capabilities are utilized to evaluate the stability of our method with respect to variations of user-defined parameters. Feedback gathered from domain experts was very positive and indicates that our methods will be considered for newly simulated, even larger data sets.

We present a concept for interactive rendering of multiple data sets of varying type, including geometry and volumetric data, in one scene with correct transparency. Typical visualization applications involve multiple data fields from various sources. A thorough understanding of such data often requires combined rendering of theses fields. The choice of the visualization concepts, and thus the rendering techniques, depends on the context and type of the individual fields. Efficiently combining different techniques in one scene, however, is not always a straightforward task. We tackle this problem by using an A-buffer based approach to gather color and transparency information from different sources, combine them and generate the final output image. Thereby we put special emphasis on efficiency and low memory consumption to allow a smooth exploration of the data. Therefore, we compare different A-buffer implementations with respect to memory consumption and memory access pattern. Additionally we introduce an early-fragment-discarding heuristic using inter-frame information to speed up the rendering..

We propose an efficient algorithm that computes the Morse–Smale complex for 3D gray-scale images. This complex allows for an efficient computation of persistent homology since it is, in general, much smaller than the input data but still contains all necessary information. Our method improves a recently proposed algorithm to extract the Morse–Smale complex in terms of memory consumption and running time. It also allows for a parallel computation of the complex. The computational complexity of the Morse–Smale complex extraction solely depends on the topological complexity of the input data. The persistence is then computed using the Morse–Smale complex by applying an existing algorithm with a good practical running time. We demonstrate that our method allows for the computation of persistent homology for large data on commodity hardware.

We propose a memory-efficient method that computes persistent homology for 3D gray-scale images. The basic idea is to compute the persistence of the induced Morse-Smale complex. Since in practice this complex is much smaller than the input data, significantly less memory is required for the subsequent computations. We propose a novel algorithm that efficiently extracts the Morse-Smale complex based on algorithms from discrete Morse theory. The proposed algorithm is thereby optimal with a computational complexity of O(n2). The persistence is then computed using the Morse-Smale complex by applying an existing algorithm with a good practical running time. We demonstrate that our method allows for the computation of persistent homology for large data on commodity hardware.

Publisher Summary Variational modeling techniques are powerful tools for free-form modeling in CAD/CAM applications. Some of the basic principles are carrying over to scientific visualization. Others have to be modified and some totally new methods have been developed over the past couple of years. This chapter gives an extended survey of this area. Surfaces and solids designed in a computer graphics environment have many applications in modeling, animation, and visualization. The chapter concentrates on the visualization part. The chapter starts with the basics from differential geometry, which are essential for any variational method. Then, it surveys on variational surface modeling. The last step is the visualization part of geometric modeling. In this context, surface curves like geodesies and curvature lines play an important role. The corresponding differential equations are nonlinear, and in most cases numerical algorithms must be used. To be sure to visualize features at a high quality, algorithms with an inherent quality control are needed. The chapter presents the geometric algorithms, which satisfy this demand.

The articles in this special section focus on scientific visualization and information technology. Visual communication can provide a method to make information known or understandable to the general public. Visual communication in public spaces, such as museums, science centers, and mainstream media, is gaining momentum driven by the success of interactive visualization in exploration of scientific data. We are now seeing different installations and specific tools to convey knowledge through interactive and exploratory visual communication in a wide variety of settings. For this Special Issue, we solicited papers describing work based on visualization in public spaces from both a technology and methodology perspective.

Although turbulence suggests randomness and disorder, organized motions that cause spatiotemporal 'coherent structures' are of particular interest. Revealing such structures in numerically given turbulent or semi-turbulent flows is of interest both for practically working engineers and theoretically oriented physicists. However, as long as there is no common agreement about the mathematical definition of coherent structures, extracting such structures is a vaguely defined task. Instead of searching for a general definition, the data visualization community takes a pragmatic approach and provides various tool chains implemented in flexible software frameworks that allow the user to extract distinct flow field structures. Thus physicists or engineers can select those flow structures which might advance their insight best. We present different approaches to distill important features from turbulent flows and discuss the necessary steps to be taken on the example of Lagrangian coherent structures.

Tensors are used to describe complex physical processes in many applications. Examples include the distribution of stresses in technical materials, acting forces during seismic events, or remodeling of biological tissues. While tensors encode such complex information mathematically precisely, the semantic interpretation of a tensor is challenging. Visualization can be beneficial here and is frequently used by domain experts. Typical strategies include the use of glyphs, color plots, lines, and isosurfaces. However, data complexity is nowadays accompanied by the sheer amount of data produced by large-scale simulations and adds another level of obstruction between user and data. Given the limitations of traditional methods, and the extra cognitive effort of simple methods, more advanced tensor field visualization approaches have been the focus of this work. This survey aims to provide an overview of recent research results with a strong application-oriented focus, targeting applications based on continuum mechanics, namely the fields of structural, bio-, and geomechanics. As such, the survey is complementing and extending previously published surveys. Its utility is twofold: (i) It serves as basis for the visualization community to get an overview of recent visualization techniques. (ii) It emphasizes and explains the necessity for further research for visualizations in this context.

The annual meeting 2017 of the Swedish Computer Graphics Association (SIGRAD) took place at Linköping University, Campus Norrköping in Norrköping, Sweden in August 2017. SIGRAD is an event where researchers and industry professionals meet to discuss novel visions and developments in the field of computer graphics and related areas, such as visualization and human-computer interaction (HCI). Since SIGRAD was started in 1976, it has developed into the major annual appointment for the Nordic community of graphics and visual computing experts with a broad range of backgrounds. It thereby addresses the increasing need for visual computing solutions in both commercial and academic areas. SIGRAD 2017 offered a strong scientific program consisting of international keynote speakers from research and industry, presentations of recent scientific achievements in the field within Sweden, and novel technological results from international contributors. The topics covered present a nice cross-section across the diverse research efforts in the domains.

Five original papers have been accepted for presentation after being peer-reviewed by an International Program Committee consisting of 22 highly qualified scientists. Each paper was reviewed, on average, by three reviewers from the committee. The accepted papers range from general computer graphics practices to practical applications and services that may benefit from the use of visualizations and computer graphics technologies. The extended participation of students at all levels of academia in research has been encouraged this year and 2 papers were selected which are first-authored by students studying at Master's Degree level.

This year, we continued the “Swedish Research Overview Session” introduced at last year’s conference. In this session, Swedish research groups are given the opportunity to present their academically outstanding, previously published work at the annual conference. All papers in this session have been published in an academically outstanding journals or conferences not more than two years prior to the SIGRAD conference.

We especially wish to thank our invited keynote speakers: Christoph Garth, University of Kaiserslautern, Germany, Ivan Viola, Vienna University of Technology, Austria, Claes Lundström, CMIV, Linköping University, and Samuel Ranta Eskola, Microsoft. Finally, we want to express our thanks to Gun-Britt Löfgren for helping us in organizing this event.

The SIGRAD 2017 organizers

Martin Falk, Daniel Jönsson, Ingrid Hotz

This chapter introduces a visualization method specifically tailored to the class of tensor fields with properties similar to stress and strain tensors. Such tensor fields play an important role in many application areas such as structure mechanics or solid state physics. The presented technique is a global method that represents the physical meaning of these tensor fields with their central features: regions of compression or expansion. The method consists of two steps: first, the tensor field is interpreted as a distortion of a flat metric with the same topological structure; second, the resulting metric is visualized using a texture-based approach. The method supports an intuitive distinction between positive and negative eigenvalues.

The physical interpretation of mathematical features of tensor fields is highly application-specific. Existing visualization methods for tensor fields only cover a fraction of the broad application areas. We present a visualization method tailored specifically to the class of tensor field exhibiting properties similar to stress and strain tensors, which are commonly encountered in geomechanics. Our technique is a global method that represents the physical meaning of these tensor fields with their central features: regions of compression or expansion. The method is based on two steps: first, we define a positive definite metric, with the same topological structure as the tensor field; second, we visualize the resulting metric. The eigenvector fields are represented using a texture-based approach resembling line integral convolution (LIC) methods. The eigenvalues of the metric are encoded in free parameters of the texture definition. Our method supports an intuitive distinction between positive and negative eigenvalues. We have applied our method to synthetic and some standard data sets, and "real" data from earth science and mechanical engineering application.

We present a visualization method that for three-dimensional tensor fields based on the idea of a stretched or compressed piece of fabric used as a “texture” for a two-dimensional surfaces. The texture parameters as the fabric density reflect the physical properties of the tensor field. This method is especially appropriate for the visualization of stress and strain tensor fields that play an important role in many application areas including mechanics and solid state physics. To allow an investigation of a three-dimensional field we use a scalar field that defines a one-parameter family of iso-surfaces controlled by their iso-value. This scalar-field can be a “connected” scalar field, for example, pressure or an additional scalar field representing some symmetry or inherent structure of the dataset. Texture generation consists basically of three steps. The first is the transformation of the tensor field into a positive definite metric. The second step is the generation of an input for the final texture generation using line integral convolution (LIC). This input image consists of “bubbles” whose shape and density are controlled by the eigenvalues of the tensor field. This spot image incorporates the entire information content defined by the three eigenvalue fields. Convolving this input texture in direction of the eigenvector fields provides a continuous representation. This method supports an intuitive distinction between positive and negative eigenvalues and supports the additional visualization of a connected scalar field.

This book is a result of a workshop, the 8th of the successful TopoInVis workshop series, held in 2019 in Nyköping, Sweden. The workshop regularly gathers some of the world’s leading experts in this field. Thereby, it provides a forum for discussions on the latest advances in the field with a focus on finding practical solutions to open problems in topological data analysis for visualization. The contributions provide introductory and novel research articles including new concepts for the analysis of multivariate and time-dependent data, robust computational approaches for the extraction and approximations of topological structures with theoretical guarantees, and applications of topological scalar and vector field analysis for visualization. The applications span a wide range of scientific areas comprising climate science, material sciences, fluid dynamics, and astronomy. In addition, community efforts with respect to joint software development are reported and discussed.  

A challenge, visualization is often faced with, is the complex structure of scientific data. Complexity can arise in various ways, from high dimensionalities of domains and ranges, time series of measurements, ensemble simulations, to heterogeneous collections of data, such as combinations of measured and simulated data. Many of these complexities can be subsumed under a concept of multifields, and in fact, multifield visualization has been identified as one of the major current challenges in scientific visualization. In this chapter, we propose a multifield definition, which will allow us a systematic approach to discussing related research.

• Transfer result from one application to another between which there is otherwise not much exchange
• Bringing together ideas from applications and theory: Applications can stimulate new basic research, as basic results can be of great use in the applications
• Summarizing the state of the art and major open questions in the field
• Presenting new and innovative work with the capabilities of advancing the field

Interpolation is an essential step in the visualization process. While most data from simulations or experiments are discrete many visualization methods are based on smooth, continuous data approximation or interpolation methods. We introduce a new interpolation method for symmetrical tensor fields given on a triangulated domain. Differently from standard tensor field interpolation, which is based on the tensor components, we use tensor invariants, eigenvectors and eigenvalues, for the interpolation. This interpolation minimizes the number of eigenvectors and eigenvalues computations by restricting it to mesh vertices and makes an exact integration of the tensor lines possible. The tensor field topology is qualitatively the same as for the component wise-interpolation. Since the interpolation decouples the “shape” and “direction” interpolation it is shape-preserving, what is especially important for tracing fibers in diffusion MRI data.

Iso-surfaces or level-sets provide an effective and frequently used means for feature visualization. However, they are restricted to simple features for uni-variate data. The approach does not scale when moving to multi-variate data or when considering more complex feature definitions. In this paper, we introduce the concept of traits and feature level-sets, which can be understood as a generalization of level-sets as it includes iso-surfaces, and fiber surfaces as special cases. The concept is applicable to a large class of traits defined as subsets in attribute space, which can be arbitrary combinations of points, lines, surfaces and volumes.  It is implemented into a system that provides an interface to define traits in an interactive way and multiple rendering options. We demonstrate the effectiveness of the approach using multi-variate data sets of different nature, including vector and tensor data, from different application domains.

In this work, we propose trait-based merge trees a generalization of merge trees to feature level sets, targeting the analysis of tensor field or general multi-variate data. For this, we employ the notion of traits defined in attribute space as introduced in the feature level sets framework. The resulting distance field in attribute space induces a scalar field in the spatial domain that serves as input for topological data analysis. The leaves in the merge tree represent those areas in the input data that are closest to the defined trait and thus most closely resemble the defined feature. Hence, the merge tree yields a hierarchy of features that allows for querying the most relevant and persistent features. The presented method includes different query methods for the tree which enable the highlighting of different aspects. We demonstrate the cross-application capabilities of this approach with three case studies from different domains.

While volume rendering for scalar fields has been advanced into a powerful visualisation method, similar volumetric representations for tensor fields are still rare. The complexity of the data challenges not only the rendering but also the design of the transfer function. In this paper we propose an interface using glyph widgets to design a transfer function for the rendering of tensor data sets. Thereby the transfer function (TF) controls a volume rendering which represents sought after tensor-features and a texture that conveys directional information. The basis of the design interface is a two-dimensional projection of the attribute space. Characteristic representatives in the form of glyphs support an intuitive navigation through the attribute space. We provide three different options to select the representatives: automatic selection based on attribute space clustering, uniform sampling of the attribute space, or manually selected representatives. In contrast to glyphs placed into the 3D volume, we use glyphs with complex geometry as widgets to control the shape and extent of the representatives. In the final rendering the glyphs with their assigned colors play a similar role as a legend in an atlas like representation. The method provides an overview of the tensor field in the 3D volume at the same time as it allows the user to explore the tensor field in an attribute space. We demonstrate the flexibility of our approach on tensor fields for selected data sets with very different characteristics.

In this work, we propose a controlled simplification strategy for degenerated points in symmetric 2D tensor fields that is based on the topological notion of robustness. Robustness measures the structural stability of the degenerate points with respect to variation in the underlying field. We consider an entire pipeline for generating a hierarchical set of degenerate points based on their robustness values. Such a pipeline includes the following steps: the stable extraction and classification of degenerate points using an edge labeling algorithm, the computation and assignment of robustness values to the degenerate points, and the construction of a simplification hierarchy. We also discuss the challenges that arise from the discretization and interpolation of real world data.

The cause of irritable bowel syndrome (IBS), a chronic disorder characterized by abdominal pain and disturbed bowel habits, is largely unknown. It is believed to be related to physical properties in the gut, central mechanisms in the brain, psychological factors, or a combination of these. To understand the relationships within the gut-brain axis with respect to IBS, large numbers of measurements ranging from stool samples to functional magnetic resonance imaging are collected from patients with IBS and healthy controls. As such, IBS is a typical example in medical research where research turns into a big data analysis challenge. In this chapter we demonstrate the power of interactive visual data analysis and exploration to generate an environment for scientific reasoning and hypothesis formulation for data from multiple sources with different character. Three case studies are presented to show the utility of the presented work.

We present an application, and its development process, for interactive visual analysis of brain imaging data and clinical measurements. The application targets neuroscientists interested in understanding the correlations between active brain regions and physiological or psychological factors. The application has been developed in a participatory design process and has subsequently been released as the free software VisualNeuro. From initial observations of the neuroscientists workflow, we concluded that while existing tools provide powerful analysis options, they lack effective interactive exploration requiring the use of many tools side by side. Consequently, our application has been designed to simplify the workflow combining statistical analysis with interactive visual exploration. The resulting environment comprises parallel coordinates for effective overview and selection, Welchs t-test to filter out brain regions with statistically significant differences and multiple visualizations for comparison between brain regions and clinical parameters. These exploration concepts enable neuroscientists to interactively explore the complex bidirectional interplay between clinical and brain measurements and easily compare different patient groups. A qualitative user study has been performed with three neuroscientists from different domains. The study shows that the developed environment supports simultaneous analysis of more parameters, provides rapid pathways to insights and is an effective tool for hypothesis formation.

We present an interactive visual environment for linked analysis of brain imaging and clinical measurements. The environment is developed in an iterative participatory design process involving neuroscientists investigating the causes of brain-related complex diseases. The hypotheses formation process about correlations between active brain regions and physiological or psychological factors in studies with hundreds of subjects is a central part of the investigation. Observing the reasoning patterns during hypotheses formation, we concluded that while existing tools provide powerful analysis options, they lack effective interactive exploration, thus limiting the scientific scope and preventing extraction of knowledge from available data.Based on these observations, we designed methods that support neuroscientists by integrating their existing statistical analysis of multivariate subject data with interactive visual explorationto enable them to better understand differences between patient groups and the complex bidirectional interplay between clinical measurement and the brain. These exploration concepts enable neuroscientists, for the first time during their investigations, to interactively move between and reason about questions such as ‘which clinical measurements are correlated with a specific brain region?’ or ‘are there differences in brain activity between depressed young and old subjects?’. The environment uses parallel coordinates for effective overview and selection of subject groups, Welch's t-test to filter out brain regions with statistically significant differences, and multiple visualizations of Pearson correlations between brain regions and clinical parameters to facilitate correlation analysis. A qualitative user study was performed with three neuroscientists from different domains. The study shows that the developed environment supports simultaneous analysis of more parameters, provides rapid pathways to insights, and is an effective support tool for hypothesis formation.