Visualization of Discontinuous Vector Field Topology.

This paper extends the concept and the visualization of vector field topology to vector fields with discontinuities. We address the non-uniqueness of flow in such fields by introduction of a time-reversible concept of equivalence. This concept generalizes streamlines to streamsets and thus vector field topology to discontinuous vector fields in terms of invariant streamsets. We identify respective novel critical structures as well as their manifolds, investigate their interplay with traditional vector field topology, and detail the application and interpretation of our approach using specifically designed synthetic cases and a simulated case from physics.

True-to-scale DNA-density maps correlate with major accessibility differences between active and inactive chromatin.

Chromatin compaction differences may have a strong impact on accessibility of individual macromolecules and macromolecular assemblies to their DNA target sites. Estimates based on fluorescence microscopy with conventional resolution, however, suggest only modest compaction differences (∼2-10×) between the active nuclear compartment (ANC) and inactive nuclear compartment (INC). Here, we present maps of nuclear landscapes with true-to-scale DNA densities, ranging from <5 to >300 Mbp/µm3. Maps are generated from individual human and mouse cell nuclei with single-molecule localization microscopy at ∼20 nm lateral and ∼100 nm axial optical resolution and are supplemented by electron spectroscopic imaging. Microinjection of fluorescent nanobeads with sizes corresponding to macromolecular assemblies for transcription into nuclei of living cells demonstrates their localization and movements within the ANC and exclusion from the INC.

Tackling Tumour Cell Heterogeneity at the Super-Resolution Level in Human Colorectal Cancer Tissue.

Tumour cell heterogeneity, and its early individual diagnosis, is one of the most fundamental problems in cancer diagnosis and therapy. Single molecule localisation microscopy (SMLM) resolves subcellular features but has been limited to cultured cell lines only. Since nuclear chromatin architecture and microRNAs are critical in metastasis, we introduce a first-in-field approach for quantitative SMLM-analysis of chromatin nanostructure in individual cells in resected, routine-pathology colorectal carcinoma (CRC) patient tissue sections. Chromatin density profiles proved to differ for cells in normal and carcinoma colorectal tissues. In tumour sections, nuclear size and chromatin compaction percentages were significantly different in carcinoma versus normal epithelial and other cells of colorectal tissue. SMLM analysis in nuclei from normal colorectal tissue revealed abrupt changes in chromatin density profiles at the nanoscale, features not detected by conventional widefield microscopy. SMLM for microRNAs relevant for metastasis was achieved in colorectal cancer tissue at the nuclear level. Super-resolution microscopy with quantitative image evaluation algorithms provide powerful tools to analyse chromatin nanostructure and microRNAs of individual cells from normal and tumour tissue at the nanoscale. Our new perspectives improve the differential diagnosis of normal and (metastatically relevant) tumour cells at the single-cell level within the heterogeneity of primary tumours of patients.

Uncertainty in Continuous Scatterplots, Continuous Parallel Coordinates, and Fibers.

In this paper, we introduce uncertainty to continuous scatterplots and continuous parallel coordinates. We derive respective models, validate them with sampling-based brute-force schemes, and present acceleration strategies for their computation. At the same time, we show that our approach lends itself as well for introducing uncertainty into the definition of fibers in bivariate data. Finally, we demonstrate the properties and the utility of our approach using specifically designed synthetic cases and simulated data.

Gaia Sky: Navigating the Gaia Catalog.

In this paper, we present Gaia Sky, a free and open-source multiplatform 3D Universe system, developed since 2014 in the Data Processing and Analysis Consortium framework of ESA's Gaia mission. Gaia's data release 2 represents the largest catalog of the stars of our Galaxy, comprising 1.3 billion star positions, with parallaxes, proper motions, magnitudes, and colors. In this mission, Gaia Sky is the central tool for off-the-shelf visualization of these data, and for aiding production of outreach material. With its capabilities to effectively handle these data, to enable seamless navigation along the high dynamic range of distances, and at the same time to provide advanced visualization techniques including relativistic aberration and gravitational wave effects, currently no actively maintained cross-platform, modern, and open alternative exists.

Robust Detection and Visualization of Jet-Stream Core Lines in Atmospheric Flow.

Jet-streams, their core lines and their role in atmospheric dynamics have been subject to considerable meteorological research since the first half of the twentieth century. Yet, until today no consistent automated feature detection approach has been proposed to identify jet-stream core lines from 3D wind fields. Such 3D core lines can facilitate meteorological analyses previously not possible. Although jet-stream cores can be manually analyzed by meteorologists in 2D as height ridges in the wind speed field, to the best of our knowledge no automated ridge detection approach has been applied to jet-stream core detection. In this work, we -a team of visualization scientists and meteorologists-propose a method that exploits directional information in the wind field to extract core lines in a robust and numerically less involved manner than traditional 3D ridge detection. For the first time, we apply the extracted 3D core lines to meteorological analysis, considering real-world case studies and demonstrating our method's benefits for weather forecasting and meteorological research.

Visual Analysis of Inclusion Dynamics in Two-Phase Flow.

In single-phase flow visualization, research focuses on the analysis of vector field properties. In two-phase flow, in contrast, analysis of the phase components is typically of major interest. So far, visualization research of two-phase flow concentrated on proper interface reconstruction and the analysis thereof. In this paper, we present a novel visualization technique that enables the investigation of complex two-phase flow phenomena with respect to the physics of breakup and coalescence of inclusions. On the one hand, we adapt dimensionless quantities for a localized analysis of phase instability and breakup, and provide detailed inspection of breakup dynamics with emphasis on oscillation and its interplay with rotational motion. On the other hand, we present a parametric tightly linked space-time visualization approach for an effective interactive representation of the overall dynamics. We demonstrate the utility of our approach using several two-phase CFD datasets.

Topological Analysis of Inertial Dynamics.

Traditional vector field visualization has a close focus on velocity, and is typically constrained to the dynamics of massless particles. In this paper, we present a novel approach to the analysis of the force-induced dynamics of inertial particles. These forces can arise from acceleration fields such as gravitation, but also be dependent on the particle dynamics itself, as in the case of magnetism. Compared to massless particles, the velocity of an inertial particle is not determined solely by its position and time in a vector field. In contrast, its initial velocity can be arbitrary and impacts the dynamics over its entire lifetime. This leads to a four-dimensional problem for 2D setups, and a six-dimensional problem for the 3D case. Our approach avoids this increase in dimensionality and tackles the visualization by an integrated topological analysis approach. We demonstrate the utility of our approach using a synthetic time-dependent acceleration field, a system of magnetic dipoles, and N-body systems both in 2D and 3D.

Interactive Progressive Visualization with Space-Time Error Control.

We present a novel scheme for progressive rendering in interactive visualization. Static settings with respect to a certain image quality or frame rate are inherently incapable of delivering both high frame rates for rapid changes and high image quality for detailed investigation. Our novel technique flexibly adapts by steering the visualization process in three major degrees of freedom: when to terminate the refinement of a frame in the background and start a new one, when to display a frame currently computed, and how much resources to consume. We base these decisions on the correlation of the errors due to insufficient sampling and response delay, which we estimate separately using fast yet expressive heuristics. To automate the configuration of the steering behavior, we employ offline video quality analysis. We provide an efficient implementation of our scheme for the application of volume raycasting, featuring integrated GPU-accelerated image reconstruction and error estimation. Our implementation performs an integral handling of the changes due to camera transforms, transfer function adaptations, as well as the progression of the data to in time. Finally, the overall technique is evaluated with an expert study.

Low-Pass Filtered Volumetric Shadows.

We present a novel and efficient method to compute volumetric soft shadows for interactive direct volume visualization to improve the perception of spatial depth. By direct control of the softness of volumetric shadows, disturbing visual patterns due to hard shadows can be avoided and users can adapt the illumination to their personal and application-specific requirements. We compute the shadowing of a point in the data set by employing spatial filtering of the optical depth over a finite area patch pointing toward each light source. Conceptually, the area patch spans a volumetric region that is sampled with shadow rays; afterward, the resulting optical depth values are convolved with a low-pass filter on the patch. In the numerical computation, however, to avoid expensive shadow ray marching, we show how to align and set up summed area tables for both directional and point light sources. Once computed, the summed area tables enable efficient evaluation of soft shadows for each point in constant time without shadow ray marching and the softness of the shadows can be controlled interactively. We integrated our method in a GPU-based volume renderer with ray casting from the camera, which offers interactive control of the transfer function, light source positions, and viewpoint, for both static and time-dependent data sets. Our results demonstrate the benefit of soft shadows for visualization to achieve user-controlled illumination with many-point lighting setups for improved perception combined with high rendering speed.

Escape Maps.

We present a technique to visualize the streamline-based mapping between the boundary of a simply-connected subregion of arbitrary 3D vector fields. While the streamlines are seeded on one part of the boundary, the remaining part serves as escape border. Hence, the seeding part of the boundary represents a map of streamline behavior, indicating if streamlines reach the escape border or not. Since the resulting maps typically exhibit a very fine and complex structure and are thus not amenable to direct sampling, our approach instead aims at topologically consistent extraction of their boundary. We show that isocline surfaces of the projected vector field provide a robust basis for stream-surface-based extraction of these boundaries. The utility of our technique is demonstrated in the context of transport processes using vector field data from different domains.

Ambient volume scattering.

We present ambient scattering as a preintegration method for scattering on mesoscopic scales in direct volume rendering. Far-range scattering effects usually provide negligible contributions to a given location due to the exponential attenuation with increasing distance. This motivates our approach to preintegrating multiple scattering within a finite spherical region around any given sample point. To this end, we solve the full light transport with a Monte-Carlo simulation within a set of spherical regions, where each region may have different material parameters regarding anisotropy and extinction. This precomputation is independent of the data set and the transfer function, and results in a small preintegration table. During rendering, the look-up table is accessed for each ray sample point with respect to the viewing direction, phase function, and material properties in the spherical neighborhood of the sample. Our rendering technique is efficient and versatile because it readily fits in existing ray marching algorithms and can be combined with local illumination and volumetric ambient occlusion. It provides interactive volumetric scattering and soft shadows, with interactive control of the transfer function, anisotropy parameter of the phase function, lighting conditions, and viewpoint. A GPU implementation demonstrates the benefits of ambient scattering for the visualization of different types of data sets, with respect to spatial perception, high-quality illumination, translucency, and rendering speed.

A time-dependent vector field topology based on streak surfaces.

It was shown recently how the 2D vector field topology concept, directly applicable to stationary vector fields only, can be generalized to time-dependent vector fields by replacing the role of stream lines by streak lines. The present paper extends this concept to 3D vector fields. In traditional 3D vector field topology separatrices can be obtained by integrating stream lines from 0D seeds corresponding to critical points. We show that in our new concept, in contrast, 1D seeding constructs are required for computing streak-based separatrices. In analogy to the 2D generalization we show that invariant manifolds can be obtained by seeding streak surfaces along distinguished path surfaces emanating from intersection curves between codimension-1 ridges in the forward and reverse finite-time Lyapunov exponent (FTLE) fields. These path surfaces represent a time-dependent generalization of critical points and convey further structure in time-dependent topology of vector fields. Compared to the traditional approach based on FTLE ridges, the resulting streak manifolds ease the analysis of Lagrangian coherent structures (LCS) with respect to visual quality and computational cost, especially when time series of LCS are computed. We exemplify validity and utility of the new approach using both synthetic examples and computational fluid dynamics results.

Hierarchical line integration.

This paper presents an acceleration scheme for the numerical computation of sets of trajectories in vector fields or iterated solutions in maps, possibly with simultaneous evaluation of quantities along the curves such as integrals or extrema. It addresses cases with a dense evaluation on the domain, where straightforward approaches are subject to redundant calculations. These are avoided by first calculating short solutions for the whole domain. From these, longer solutions are then constructed in a hierarchical manner until the designated length is achieved. While the computational complexity of the straightforward approach depends linearly on the length of the solutions, the computational cost with the proposed scheme grows only logarithmically with increasing length. Due to independence of subtasks and memory locality, our algorithm is suitable for parallel execution on many-core architectures like GPUs. The trade-offs of the method--lower accuracy and increased memory consumption--are analyzed, including error order as well as numerical error for discrete computation grids. The usefulness and flexibility of the scheme are demonstrated with two example applications: line integral convolution and the computation of the finite-time Lyapunov exponent. Finally, results and performance measurements of our GPU implementation are presented for both synthetic and simulated vector fields from computational fluid dynamics.

Coherent Structures of Characteristic Curves in Symmetric Second Order Tensor Fields.

This paper generalizes the concept of Lagrangian coherent structures, which is known for its potential to visualize coherent regions in vector fields and to distinguish them from each other. In particular, we extend the concept of the flow map to generic mappings of coordinates. As the major application of this generalization, we present a semiglobal method for visualizing coherent structures in symmetric second order tensor fields. We demonstrate the usefulness by examples from DT-MRI, uncovering anatomical structures in linearly anisotropic regions not amenable to local feature criteria. To further exemplify the suitability of our concept, we also present its application to stress tensor fields. Last, an accelerated implementation utilizing GPUs is presented.

Parallel vectors criteria for unsteady flow vortices.

Feature-based flow visualization is naturally dependent on feature extraction. To extract flow features, often higher-order properties of the flow data are used such as the Jacobian or curvature properties, implicitly describing the flow features in terms of their inherent flow characteristics (e.g., collinear flow and vorticity vectors). In this paper we present recent research which leads to the (not really surprising) conclusion that feature extraction algorithms need to be extended to a time-dependent analysis framework (in terms of time derivatives) when dealing with unsteady flow data. Accordingly, we present two extensions of the parallel vectors based vortex extraction criteria to the time-dependent domain and show the improvements of feature-based flow visualization in comparison to the steady versions of this extraction algorithm both in the context of a high-resolution dataset, i.e., a simulation specifically designed to evaluate our new approach, as well as for a real-world dataset from a concrete application.

Efficient visualization of lagrangian coherent structures by filtered AMR ridge extraction.

This paper presents a method for filtered ridge extraction based on adaptive mesh refinement. It is applicable in situations where the underlying scalar field can be refined during ridge extraction. This requirement is met by the concept of Lagrangian coherent structures which is based on trajectories started at arbitrary sampling grids that are independent of the underlying vector field. The Lagrangian coherent structures are extracted as ridges in finite Lyapunov exponent fields computed from these grids of trajectories. The method is applied to several variants of finite Lyapunov exponents, one of which is newly introduced. High computation time due to the high number of required trajectories is a main drawback when computing Lyapunov exponents of 3-dimensional vector fields. The presented method allows a substantial speed-up by avoiding the seeding of trajectories in regions where no ridges are present or do not satisfy the prescribed filter criteria such as a minimum finite Lyapunov exponent.

Visualization tools for vorticity transport analysis in incompressible flow.

Vortices are undesirable in many applications while indispensable in others. It is therefore of common interest to understand their mechanisms of creation. This paper aims at analyzing the transport of vorticity inside incompressible flow. The analysis is based on the vorticity equation and is performed along pathlines which are typically started in upstream direction from vortex regions. Different methods for the quantitative and explorative analysis of vorticity transport are presented and applied to CFD simulations of water turbines. Simulation quality is accounted for by including the errors of meshing and convergence into analysis and visualization. The obtained results are discussed and interpretations with respect to engineering questions are given.