SetCoLa: High‐Level Constraints for Graph Layout

Constraints enable flexible graph layout by combining the ease of automatic layout with customizations for a particular domain. However, constraint‐based layout often requires many individual constraints defined over specific nodes and node pairs. In addition to the effort of writing and maintaining a large number of similar constraints, such constraints are specific to the particular graph and thus cannot generalize to other graphs in the same domain. To facilitate the specification of customized and generalizable constraint layouts, we contribute SetCoLa: a domain‐specific language for specifying high‐level constraints relative to properties of the backing data. Users identify node sets based on data or graph properties and apply high‐level constraints within each set. Applying constraints to node sets rather than individual nodes reduces specification effort and facilitates reapplication of customized layouts across distinct graphs. We demonstrate the conciseness, generalizability, and expressiveness of SetCoLa on a series of real‐world examples from ecological networks, biological systems, and social networks.     

A Random Sampling O(n) Force‐calculation Algorithm for Graph Layouts

This paper proposes a linear‐time repulsive‐force‐calculation algorithm with sub‐linear auxiliary space requirements, achieving an asymptotic improvement over the Barnes‐Hut and Fast Multipole Method force‐calculation algorithms. The algorithm, named random vertex sampling (RVS), achieves its speed by updating a random sample of vertices at each iteration, each with a random sample of repulsive forces. This paper also proposes a combination algorithm that uses RVS to derive an initial layout and then applies Barnes‐Hut to refine the layout. An evaluation of RVS and the combination algorithm compares their speed and quality on 109 graphs against a Barnes‐Hut layout algorithm. The RVS algorithm performs up to 6.1 times faster on the tested graphs while maintaining comparable layout quality. The combination algorithm also performs faster than Barnes‐Hut, but produces layouts that are more symmetric than using RVS alone. Data and code: https://osf.io/nb7m8/     

V‐Awake: A Visual Analytics Approach for Correcting Sleep Predictions from Deep Learning Models

The usage of deep learning models for tagging input data has increased over the past years because of their accuracy and high‐performance. A successful application is to score sleep stages. In this scenario, models are trained to predict the sleep stages of individuals. Although their predictive accuracy is high, there are still mis classifications that prevent doctors from properly diagnosing sleep‐related disorders. This paper presents a system that allows users to explore the output of deep learning models in a real‐life scenario to spot and analyze faulty predictions. These can be corrected by users to generate a sequence of sleep stages to be examined by doctors. Our approach addresses a real‐life scenario with absence of ground truth. It differs from others in that our goal is not to improve the model itself, but to correct the predictions it provides. We demonstrate that our approach is effective in identifying faulty predictions and helping users to fix them in the proposed use case.     

VIAN: A Visual Annotation Tool for Film Analysis

While color plays a fundamental role in film design and production, existing solutions for film analysis in the digital humanities address perceptual and spatial color information only tangentially. We introduce VIAN, a visual film annotation system centered on the semantic aspects of film color analysis. The tool enables expert‐assessed labeling, curation, visualization and Classification of color features based on their perceived context and aesthetic quality. It is the first of its kind that incorporates foreground‐background information made possible by modern deep learning segmentation methods. The proposed tool seamlessly integrates a multimedia data management system, so that films can undergo a full color‐oriented analysis pipeline.     

An Approximate Parallel Vectors Operator for Multiple Vector Fields

The Parallel Vectors (PV) Operator extracts the locations of points where two vector fields are parallel. In general, these features are line structures. The PV operator has been used successfully for a variety of problems, which include finding vortex‐core lines or extremum lines. We present a new generic feature extraction method for multiple 3D vector fields: The Approximate Parallel Vectors (APV) Operator extracts lines where all fields are approximately parallel. The definition of the APV operator is based on the application of PV for two vector fields that are derived from the given set of fields. The APV operator enables the direct visualization of features of vector field ensembles without processing fields individually and without causing visual clutter. We give a theoretical analysis of the APV operator and demonstrate its utility for a number of ensemble data.     

An Interactive Visualization System for Large Sets of Phase Space Trajectories

We introduce a visual analysis system with GPU acceleration techniques for large sets of trajectories from complex dynamical systems. The approach is based on an interactive Boolean combination of subsets into a Focus+Context phase‐space visualization. We achieve high performance through efficient bitwise algorithms utilizing runtime generated GPU shaders and kernels. This enables a higher level of interactivity for visualizing the large multivariate trajectory data. We explain how our design meets a set of carefully considered analysis requirements, provide performance results, and demonstrate utility through case studies with many‐particle simulation data from two application areas.     

Towards Glyphs for Uncertain Symmetric Second‐Order Tensors

Measured data often incorporates some amount of uncertainty, which is generally modeled as a distribution of possible samples. In this paper, we consider second‐order symmetric tensors with uncertainty. In the 3D case, this means the tensor data consists of 6 coefficients – uncertainty, however, is encoded by 21 coefficients assuming a multivariate Gaussian distribution as model. The high dimension makes the direct visualization of tensor data with uncertainty a difficult problem, which was until now unsolved. The contribution of this paper consists in the design of glyphs for uncertain second‐order symmetric tensors in 2D and 3D. The construction consists of a standard glyph for the mean tensor that is augmented by a scalar field that represents uncertainty. We show that this scalar field and therefore the displayed glyph encode the uncertainty comprehensively, i.e., there exists a bijective map between the glyph and the parameters of the distribution. Our approach can extend several classes of existing glyphs for symmetric tensors to additionally encode uncertainty and therefore provides a possible foundation for further uncertain tensor glyph design. For demonstration, we choose the well‐known superquadric glyphs, and we show that the uncertainty visualization satisfies all their design constraints.     

Efficient Optimal Overlap Removal: Algorithms and Experiments

Motivated by visualizing spatial data using proportional symbols, we study the following problem: given a set of overlapping squares of varying sizes, minimally displace the squares as to remove the overlap while maintaining the orthogonal order on their centers. Though this problem is NP‐hard, we show that rotating the squares by 45 degrees into diamonds allows for a linear or convex quadratic program. It is thus efficiently solvable even for relatively large instances. This positive result and the flexibility offered by constraint programming allow us to study various trade‐offs for overlap removal. Specifically, we model and evaluate through computational experiments the relations between displacement, scale and order constraints for static data, and between displacement and temporal coherence for time‐varying data. Finally, we also explore the generalization of our methodology to other shapes.     

Optimizing Stepwise Animation in Dynamic Set Diagrams

A set diagram represents the membership relation among data elements. It is often visualized as secondary information on top of primary information, such as the spatial positions of elements on maps and charts. Visualizing the temporal evolution of such set diagrams as well as their primary features is quite important; however, conventional approaches have only focused on the temporal behavior of the primary features and do not provide an effective means to highlight notable transitions within the set relationships. This paper presents an approach for generating a stepwise animation between set diagrams by decomposing the entire transition into atomic changes associated with individual data elements. The key idea behind our approach is to optimize the ordering of the atomic changes such that the synthesized animation minimizes unwanted set occlusions by considering their depth ordering and reduces the gaze shift between two consecutive stepwise changes. Experimental results and a user study demonstrate that the proposed approach effectively facilitates the visual identification of the detailed transitions inherent in dynamic set diagrams.     

IGM‐Vis: Analyzing Intergalactic and Circumgalactic Medium Absorption Using Quasar Sightlines in a Cosmic Web Context

We introduce IGM‐Vis, a novel astrophysics visualization and data analysis application for investigating galaxies and the gas that surrounds them in context with their larger scale environment, the Cosmic Web. Environment is an important factor in the evolution of galaxies from actively forming stars to quiescent states with little, if any, discernible star formation activity. The gaseous halos of galaxies (the circumgalactic medium, or CGM) play a critical role in their evolution, because the gas necessary to fuel star formation and any gas expelled from widely observed galactic winds must encounter this interface region between galaxies and the intergalactic medium (IGM). We present a taxonomy of tasks typically employed in IGM/CGM studies informed by a survey of astrophysicists at various career levels, and demonstrate how these tasks are facilitated via the use of our visualization software. Finally, we evaluate the effectiveness of IGM‐Vis through two in‐depth use cases that depict real‐world analysis sessions that use IGM/CGM data.     

Visualizing the Phase Space of Heterogeneous Inertial Particles in 2D Flows

In many scientific disciplines, the motion of finite‐sized objects in fluid flows plays an important role, such as in brownout engineering, sediment transport, oceanology or meteorology. These finite‐sized objects are called inertial particles and, in contrast to traditional tracer particles, their motion depends on their current position, their own particle velocity, the time and their size. Thus, the visualization of their motion becomes a high‐dimensional problem that entails computational and perceptual challenges. So far, no visualization explored and visualized the particle trajectories under variation of all seeding parameters. In this paper, we propose three coordinated views that visualize the different aspects of the high‐dimensional space in which the particles live. We visualize the evolution of particles over time, showing that particles travel different distances in the same time, depending on their size. The second view provides a clear illustration of the trajectories of different particle sizes and allows the user to easily identify differences due to particle size. Finally, we embed the trajectories in the space‐velocity domain and visualize their distance to an attracting manifold using ribbons. In all views, we support interactive linking and brushing, and provide abstraction through density volumes that are shown by direct volume rendering and isosurface slabs. Using our method, users gain deeper insights into the dynamics of inertial particles in 2D fluids, including size‐dependent separation, preferential clustering and attraction. We demonstrate the effectiveness of our method in multiple steady and unsteady 2D flows.     

Baseball Timeline: Summarizing Baseball Plays Into a Static Visualization

In sports, Play Diagrams are the standard way to represent and convey information. They are widely used by coaches, managers, journalists and fans in general. There are situations where diagrams may be hard to understand, for example, when several actions are packed in a certain region of the field or there are just too many actions to be transformed in a clear depiction of the play. The representation of how actions develop through time, in particular, may be hardly achieved on such diagrams. The time, and the relationship among the actions of the players through time, is critical on the depiction of complex plays. In this context, we present a study on how player actions may be clearly depicted on 2D diagrams. The study is focused on Baseball plays, a sport where diagrams are heavily used to summarize the actions of the players. We propose a new and simple approach to represent spatiotemporal information in the form of a timeline. We designed our visualization with a requirement driven approach, conducting interviews and fulfilling the needs of baseball experts and expert‐fans. We validate our approach by presenting a detailed analysis of baseball plays and conducting interviews with four domain experts.     

Bladder Runner: Visual Analytics for the Exploration of RT‐Induced Bladder Toxicity in a Cohort Study

We present the Bladder Runner, a novel tool to enable detailed visual exploration and analysis of the impact of bladder shape variation on the accuracy of dose delivery, during the course of prostate cancer radiotherapy (RT). Our tool enables the investigation of individual patients and cohorts through the entire treatment process, and it can give indications of RT‐induced complications for the patient. In prostate cancer RT treatment, despite the design of an initial plan prior to dose administration, bladder toxicity remains very common. The main reason is that the dose is delivered in multiple fractions over a period of weeks, during which, the anatomical variation of the bladder – due to differences in urinary filling – causes deviations between planned and delivered doses. Clinical researchers want to correlate bladder shape variations to dose deviations and toxicity risk through cohort studies, to understand which specific bladder shape characteristics are more prone to side effects. This is currently done with Dose‐Volume Histograms (DVHs), which provide limited, qualitative insight. The effect of bladder variation on dose delivery and the resulting toxicity cannot be currently examined with the DVHs. To address this need, we designed and implemented the Bladder Runner, which incorporates visualization strategies in a highly interactive environment with multiple linked views. Individual patients can be explored and analyzed through the entire treatment period, while inter‐patient and temporal exploration, analysis and comparison are also supported. We demonstrate the applicability of our presented tool with a usage scenario, employing a dataset of 29 patients followed through the course of the treatment, across 13 time points. We conducted an evaluation with three clinical researchers working on the investigation of RT‐induced bladder toxicity. All participants agreed that Bladder Runner provides better understanding and new opportunities for the exploration and analysis of the involved cohort data.     

Hunting High and Low: Visualising Shifting Correlations in Financial Markets

The analysis of financial assets’ correlations is fundamental to many aspects of finance theory and practice, especially modern portfolio theory and the study of risk. In order to manage investment risk, in‐depth analysis of changing correlations is needed, with both high and low correlations between financial assets (and groups thereof) important to identify. In this paper, we propose a visual analytics framework for the interactive analysis of relations and structures in dynamic, high‐dimensional correlation data. We conduct a series of interviews and review the financial correlation analysis literature to guide our design. Our solution combines concepts from multi‐dimensional scaling, weighted complete graphs and threshold networks to present interactive, animated displays which use proximity as a visual metaphor for correlation and animation stability to encode correlation stability. We devise interaction techniques coupled with context‐sensitive auxiliary views to support the analysis of subsets of correlation networks. As part of our contribution, we also present behaviour profiles to help guide future users of our approach. We evaluate our approach by checking the validity of the layouts produced, presenting a number of analysis stories, and through a user study. We observe that our solutions help unravel complex behaviours and resonate well with study participants in addressing their needs in the context of correlation analysis in finance.     

Visualization of Equivalence in 2D Bivariate Fields

In this paper, we show how the equivalence property leads to the novel concept of equivalent regions in mappings from ?ⁿ to ?ⁿ. We present a technique for obtaining these regions both in the domain and the codomain of such a mapping, and determine their correspondence. This enables effective investigation of variation equivalence within mappings, and between mappings in terms of comparative visualization. We implement our approach for n = 2, and demonstrate its utility using different examples.     

The Dependent Vectors Operator

In this paper, we generalize the parallel vectors operator due to Peikert and Roth to arbitrary dimension, i.e., to four‐dimensional fields and beyond. Whereas the original operator tested for parallelism of two (derived) 2D or 3D vector fields, we reformulate the concept in terms of linear dependency of sets of vector fields, and propose a generic technique to extract and filter the solution manifolds. We exemplify our approach for vortex cores, bifurcations, and ridges as well as valleys in higher dimensions.     

Visualization of 4D Vector Field Topology

In this paper, we present an approach to the topological analysis of four‐dimensional vector fields. In analogy to traditional 2D and 3D vector field topology, we provide a classification and visual representation of critical points, together with a technique for extracting their invariant manifolds. For effective exploration of the resulting four‐dimensional structures, we present a 4D camera that provides concise representation by exploiting projection degeneracies, and a 4D clipping approach that avoids self‐intersection in the 3D projection. We exemplify the properties and the utility of our approach using specific synthetic cases.     

Design and Automated Generation of Japanese Picture Puzzles

We introduce the generalized nonogram, an extension of the well‐known nonogram or Japanese picture puzzle. It is not based on a regular square grid but on a subdivision (arrangement) with differently shaped cells, bounded by straight lines or curves. To generate a good, clear puzzle from a filled line drawing, the arrangement that is formed for the puzzle must meet a number of criteria. Some of these relate to the puzzle and some to the geometry. We give an overview of these criteria and show that a puzzle can be generated by an optimization method like simulated annealing. Experimentally, we analyze the convergence of the method and the remaining penalty score on several input pictures along with various other design options.     

Core Lines in 3D Second‐Order Tensor Fields

Vortices are important features in vector fields that show a swirling behavior around a common core. The concept of a vortex core line describes the center of this swirling behavior. In this work, we examine the extension of this concept to 3D second‐order tensor fields. Here, a behavior similar to vortices in vector fields can be observed for trajectories of the eigenvectors. Vortex core lines in vector fields were defined by Sujudi and Haimes to be the locations where stream lines are parallel to an eigenvector of the Jacobian. We show that a similar criterion applied to the eigenvector trajectories of a tensor field yields structurally stable lines that we call tensor core lines. We provide a formal definition of these structures and examine their mathematical properties. We also present a numerical algorithm for extracting tensor core lines in piecewise linear tensor fields. We find all intersections of tensor core lines with the faces of a dataset using a simple and robust root finding algorithm. Applying this algorithm to tensor fields obtained from structural mechanics simulations shows that it is able to effectively detect and visualize regions of rotational or hyperbolic behavior of eigenvector trajectories.