In biology, we are often confronted with information-rich, large-scale trajectory data, but exploring and communicating patterns in such data can be a cumbersome task. Ideally, the data should be wrapped with an interactive visualisation in one concise packet that makes it straightforward to create and test hypotheses collaboratively. To address these challenges, we have developed a tool, linus, which makes the process of exploring and sharing 3D trajectories as easy as browsing a website. We provide a python script that reads trajectory data, enriches them with additional features such as edge bundling or custom axes, and generates an interactive web-based visualisation that can be shared online. linus facilitates the collaborative discovery of patterns in complex trajectory data.

In this study we compared various neural network types for the task of automatic infant vocalization classification, i.e convolutional, recurrent and fully-connected networks as well as combinations of thereof. The goal was to first determine the optimal configuration for each network type to then identify the type with the highest overall performance. This investigation helps to employ neural networks more effectively to infant vocalization classification tasks, which typically offer low amounts of training data. To this end, we defined a unified neural network architecture scheme for audio classification from which we derived various network types. For each type we performed a semi-random hyperparameter search which employed regression trees to both focus the search space as well as derive insights on the most influential parameters. We finally compared the test performances of the best performing configurations in an contest-like setup. Our key findings are: (1) Networks with convolutional stages reached the highest performance, regardless of being combined with fully-connected or recurrent layers. (2) The most influential architectural hyperparameter for all types were the integration operations for reducing tensor dimensionality between network stages. The best performing configurations reached test performances of 75% unweighted average recall, surpassing previously published benchmarks.

Vector field topology is one of the most powerful flow visualization tools, because it can break down huge amounts of data into a compact, sparse, and easy to read description with little information loss. It suffers from one main drawback though: The definition of critical points, which is the foundation of vector field topology, is highly dependent on the frame of reference. In this paper we propose to consider every point as a critical point and locally adjust the frame of reference to the most persistent ones, that means the extrema of the determinant of the Jacobian. The result is not the extraction of one well-suited frame of reference, but the simultaneous visualization of the dominating frames of reference in the different areas of the flow field. Each of them could individually be perceived by an observer traveling along these critical points. We show all important ones at once.

Abstract This paper presents the state of the art in the area of topology‐based visualization. It describes the process and results of an extensive annotation for generating a definition and terminology for the field. The terminology enabled a typology for topological models which is used to organize research results and the state of the art. Our report discusses relations among topological models and for each model describes research results for the computation, simplification, visualization, and application. The paper identifies themes common to subfields, current frontiers, and unexplored territory in this research area.

Hierarchical fiber clustering is a promising way to analyze brain connectivity. A disadvantage of hierarchical fiber clustering is its difficult visualization. The simple presentation as a 2D tree is visually too complex because of the amount of several thousand leaves. We present a framework that allows the modification of the dendrogram visualization in a flexible way. The modified dendrogram visualization can convey additional information that grants an easier orientation within the hierarchical clustering. Besides the interaction with the dendrogram itself, it is also possible to make use of a 3D view and a clustering preview. To illustrate potential use cases, we present two usage examples that show the versatility of our framework.

Linear approximation plays an important role in many areas employing numerical algorithms. Particularly in the field of vector field visualization, it is the basis of widely used techniques. In this paper, we introduce two methods to extract areas in two- and three-dimensional vector fields that are connected to linear flow behavior. We propose a region-growing algorithm that extracts the linear neighborhood for a certain position. The region is characterized by linear flow behavior up to a user-defined approximation threshold. While this first method computes the size of a region given the mentioned threshold, our second method computes the quality of a linear approximation given a user-defined n-ring neighborhood. The scalar field resulting from the second method is, therefore, called affine linear approximation error. Isosurfaces of this field show regions of close-to-linear and non-linear flow behavior. We demonstrate the expressiveness and discuss the properties of the extracted regions using analytical examples and several datasets from the domain of computational fluid dynamics (CFD).

Abstract Particle swarm optimization (PSO) is a metaheuristic that has been applied successfully to many continuous and combinatorial optimization problems, e.g., in the fields of economics, engineering, and natural sciences. In PSO, a swarm of particles moves within a search space in order to find an optimal solution. Unfortunately, it is hard to understand in detail why and how changes in the design of PSO algorithms affect the optimization behavior. Visualizing the particle states could provide substantially better insight into PSO algorithms. Though in case of combinatorial optimization problems, it often raises the problem of illustrating the states within the discrete search space that cannot be embedded spatially. We propose a visualization approach to depict the optimization problem topologically using a landscape metaphor. This visualization is augmented by an illustration of the time‐dependent states of the particles. Thus, the user of dPSO‐Vis is able to analyze the swarm's behavior within the search space. In principle, our method can be used for any optimization algorithm where a swarm of individuals searches within a discrete search space. Our approach is verified with a case study for the PSO algorithm HelixPSO that predicts the secondary structure of RNA molecules.

Rendering large numbers of dense line bundles in three dimensions is a common need for many visualization techniques, including streamlines and fiber tractography. Unfortunately, depiction of spatial relations inside these line bundles is often difficult but critical for understanding the represented structures. Many approaches evolved for solving this problem by providing special illumination models or tube-like renderings. Although these methods improve spatial perception of individual lines or related sets of lines, they do not solve the problem for complex spatial relations between dense bundles of lines. In this paper, we present a novel approach that improves spatial and structural perception of line renderings by providing a novel ambient occlusion approach suited for line rendering in real time.

Characterizing the interplay between the vortices and forces acting on a wind turbine's blades in a qualitative and quantitative way holds the potential for significantly improving large wind turbine design. This paper introduces an integrated pipeline for highly effective wind and force field analysis and visualization. We extract vortices induced by a turbine's rotation in a wind field, and characterize vortices in conjunction with numerically simulated forces on the blade surfaces as these vortices strike another turbine's blades downstream. The scientifically relevant issue to be studied is the relationship between the extracted, approximate locations on the blades where vortices strike the blades and the forces that exist in those locations. This integrated approach is used to detect and analyze turbulent flow that causes local impact on the wind turbine blade structure. The results that we present are based on analyzing the wind and force field data sets generated by numerical simulations, and allow domain scientists to relate vortex-blade interactions with power output loss in turbines and turbine life expectancy. Our methods have the potential to improve turbine design to save costs related to turbine operation and maintenance.

Scientific data sets generated by numerical simulations or experimental measurements often contain a substantial amount of noise. Smoothing the data removes noise but can have potentially drastic effects on the qualitative nature of the data, thereby influencing its characterization and visualization via topological analysis, for example. We propose a method to track topological changes throughout the smoothing process. As a preprocessing step, we oversmooth the data and collect a list of topological events, specifically the creation and destruction of extremal points. During rendering, it is possible to select the number of topological events by interactively manipulating a merging parameter. The result that a specific amount of smoothing has on the topology of the data is illustrated using a topology-derived transfer function that relates region connectivity of the smoothed data to the original regions of the unsmoothed data. This approach enables visual as well as quantitative analysis of the topological effects of smoothing.

Abstract Studying transformation in a chemical system by considering its energy as a function of coordinates of the system's components provides insight and changes our understanding of this process. Currently, a lack of effective visualization techniques for high‐dimensional energy functions limits chemists to plot energy with respect to one or two coordinates at a time. In some complex systems, developing a comprehensive understanding requires new visualization techniques that show relationships between all coordinates at the same time. We propose a new visualization technique that combines concepts from topological analysis, multi‐dimensional scaling, and graph layout to enable the analysis of energy functions for a wide range of molecular structures. We demonstrate our technique by studying the energy function of a dimer of formic and acetic acids and a LTA zeolite structure, in which we consider diffusion of methane.

Abstract We present analysis and visualization of flow data from a high‐resolution simulation of the dynamical behavior of the global ocean. Of particular scientific interest are coherent vortical features called mesoscale eddies. We first extract high‐vorticity features using a metric from the oceanography community called the Okubo‐Weiss parameter. We then use a new circularity criterion to differentiate eddies from other non‐eddy features like meanders in strong background currents. From these data, we generate visualizations showing the three‐dimensional structure and distribution of ocean eddies. Additionally, the characteristics of each eddy are recorded to form an eddy census that can be used to investigate correlations among variables such as eddy thickness, depth, and location. From these analyses, we gain insight into the role eddies play in large‐scale ocean circulation.

We consider the problem of extracting discrete two-dimensional vortices from a turbulent flow. In our approach we use a reference model describing the expected physics and geometry of an idealized vortex. The model allows us to derive a novel correlation between the size of the vortex and its strength, measured as the square of its strain minus the square of its vorticity. For vortex detection in real models we use the strength parameter to locate potential vortex cores, then measure the similarity of our ideal analytical vortex and the real vortex core for different strength thresholds. This approach provides a metric for how well a vortex core is modeled by an ideal vortex. Moreover, this provides insight into the problem of choosing the thresholds that identify a vortex. By selecting a target coefficient of determination (i.e., statistical confidence), we determine on a per-vortex basis what threshold of the strength parameter would be required to extract that vortex at the chosen confidence. We validate our approach on real data from a global ocean simulation and derive from it a map of expected vortex strengths over the global ocean.

Understanding fluid flow data, especially vortices, is still a challenging task. Sophisticated visualization tools help to gain insight. In this paper, we present a novel approach for the interactive comparison of scalar fields using isosurfaces, and its application to fluid flow datasets. Features in two scalar fields are defined by largest contour segmentation after topological simplification. These features are matched using a volumetric similarity measure based on spatial overlap of individual features. The relationships defined by this similarity measure are ranked and presented in a thumbnail gallery of feature pairs and a graph representation showing all relationships between individual contours. Additionally, linked views of the contour trees are provided to ease navigation. The main render view shows the selected features overlapping each other. Thus, by displaying individual features and their relationships in a structured fashion, we enable exploratory visualization of correlations between similar structures in two scalar fields. We demonstrate the utility of our approach by applying it to a number of complex fluid flow datasets, where the emphasis is put on the comparison of vortex related scalar quantities.

Tensors occur in many areas of science and engineering. Especially, they are used to describe charge, mass and energy transport (i.e. electrical conductivity tensor, diffusion tensor, thermal conduction tensor resp.) If the locale transport pattern is complicated, usual second order tensor representation is not sufficient. So far, there are no appropriate visualization methods for this case. We point out similarities of symmetric higher order tensors and spherical harmonics. A spherical harmonic representation is used to improve tensor glyphs. This paper unites the definition of streamlines and tensor lines and generalizes tensor lines to those applications where second order tensors representations fail. The algorithm is tested on the tractography problem in diffusion tensor magnetic resonance imaging (DT-MRI) and improved for this special application.