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.     

Robust Reference Frame Extraction from Unsteady 2D Vector Fields with Convolutional Neural Networks

Robust feature extraction is an integral part of scientific visualization. In unsteady vector field analysis, researchers recently directed their attention towards the computation of near‐steady reference frames for vortex extraction, which is a numerically challenging endeavor. In this paper, we utilize a convolutional neural network to combine two steps of the visualization pipeline in an end‐to‐end manner: the filtering and the feature extraction. We use neural networks for the extraction of a steady reference frame for a given unsteady 2D vector field. By conditioning the neural network to noisy inputs and resampling artifacts, we obtain numerically stabler results than existing optimization‐based approaches. Supervised deep learning typically requires a large amount of training data. Thus, our second contribution is the creation of a vector field benchmark data set, which is generally useful for any local deep learning‐based feature extraction. Based on Vatistas velocity profile, we formulate a parametric vector field mixture model that we parameterize based on numerically‐computed example vector fields in near‐steady reference frames. Given the parametric model, we can efficiently synthesize thousands of vector fields that serve as input to our deep learning architecture. The proposed network is evaluated on an unseen numerical fluid flow simulation.     

Interactive Volumetric Visual Analysis of Glycogen‐derived Energy Absorption in Nanometric Brain Structures

Digital acquisition and processing techniques are changing the way neuroscience investigation is carried out. Emerging applications range from statistical analysis on image stacks to complex connectomics visual analysis tools targeted to develop and test hypotheses of brain development and activity. In this work, we focus on neuroenergetics, a field where neuroscientists analyze nanoscale brain morphology and relate energy consumption to glucose storage in form of glycogen granules. In order to facilitate the understanding of neuroenergetic mechanisms, we propose a novel customized pipeline for the visual analysis of nanometric‐level reconstructions based on electron microscopy image data. Our framework supports analysis tasks by combining i) a scalable volume visualization architecture able to selectively render image stacks and corresponding labelled data, ii) a method for highlighting distance‐based energy absorption probabilities in form of glow maps, and iii) a hybrid connectivitybased and absorption‐based interactive layout representation able to support queries for selective analysis of areas of interest and potential activity within the segmented datasets. This working pipeline is currently used in a variety of studies in the neuroenergetics domain. Here, we discuss a test case in which the framework was successfully used by domain scientists for the analysis of aging effects on glycogen metabolism, extracting knowledge from a series of nanoscale brain stacks of rodents somatosensory cortex.     

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.     

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.     

An Analysis of Region Clustered BVH Volume Rendering on GPU

We present a Direct Volume Rendering method that makes use of newly available Nvidia graphics hardware for Bounding Volume Hierarchies. Using BVHs for DVR has been overlooked in recent research due to build times potentially impeding interactive rates. We indicate that this is not necessarily the case, especially when a clustering algorithm is applied before the BVH build to reduce leaf‐node complexity. Our results show substantial render time improvements for full‐resolution DVR on GPU in comparison to a recent state‐of‐the‐art approach for empty‐space‐skipping. Furthermore, the use of a BVH for DVR allows seamless integration into popular surface‐based path‐tracing technologies like Nvidia's OptiX.     

Hierarchical Functional Maps between Subdivision Surfaces

We propose a novel approach for computing correspondences between subdivision surfaces with different control polygons. Our main observation is that the multi‐resolution spectral basis functions that are open used for computing a functional correspondence can be compactly represented on subdivision surfaces, and therefore can be efficiently computed. Furthermore, the reconstruction of a pointwise map from a functional correspondence also greatly benefits from the subdivision structure. Leveraging these observations, we suggest a hierarchical pipeline for functional map inference, allowing us to compute correspondences between surfaces at fine subdivision levels, with hundreds of thousands of polygons, an order of magnitude faster than existing correspondence methods. We demonstrate the applicability of our results by transferring high‐resolution sculpting displacement maps and textures between subdivision models.     

Route‐Aware Edge Bundling for Visualizing Origin‐Destination Trails in Urban Traffic

Origin‐destination (OD) trails describe movements across space. Typical visualizations thereof use either straight lines or plot the actual trajectories. To reduce clutter inherent to visualizing large OD datasets, bundling methods can be used. Yet, bundling OD trails in urban traffic data remains challenging. Two specific reasons hereof are the constraints implied by the underlying road network and the difficulty of finding good bundling settings. To cope with these issues, we propose a new approach called Route Aware Edge Bundling (RAEB). To handle road constraints, we first generate a hierarchical model of the road‐and‐trajectory data. Next, we derive optimal bundling parameters, including kernel size and number of iterations, for a user‐selected level of detail of this model, thereby allowing users to explicitly trade off simplification vs accuracy. We demonstrate the added value of RAEB compared to state‐of‐the‐art trail bundling methods on both synthetic and real‐world traffic data for tasks that include the preservation of road network topology and the support of multiscale exploration.     

Quantitative and Qualitative Analysis of the Perception of Semi‐Transparent Structures in Direct Volume Rendering

Direct Volume Rendering (DVR) provides the possibility to visualize volumetric data sets as they occur in many scientific disciplines. With DVR semi‐transparency is facilitated to convey the complexity of the data. Unfortunately, semi‐transparency introduces challenges in spatial comprehension of the data, as the ambiguities inherent to semi‐transparent representations affect spatial comprehension. Accordingly, many techniques have been introduced to enhance the spatial comprehension of DVR images. In this paper, we present our findings obtained from two evaluations investigating the perception of semi‐transparent structures from volume rendered images. We have conducted a user evaluation in which we have compared standard DVR with five techniques previously proposed to enhance the spatial comprehension of DVR images. In this study, we investigated the perceptual performance of these techniques and have compared them against each other in a large‐scale quantitative user study with 300 participants. Each participant completed micro‐tasks designed such that the aggregated feedback gives insight on how well these techniques aid the user to perceive depth and shape of objects. To further clarify the findings, we conducted a qualitative evaluation in which we interviewed three experienced visualization researchers, in order to find out if we can identify the benefits and shortcomings of the individual techniques.     

Compacting Voxelized Polyhedra via Tree Stacking

Volume compaction is a geometric problem that aims to reduce the volume of a polyhedron via shape transform. Compactable structures are easier to transport and in some cases easier to manufacture, therefore, they are commonly found in our daily life (e.g. collapsible containers) and advanced technology industries (e.g., the recent launch of 60 Starlink satellites compacted in a single rocket by SpaceX). It is known in the literature that finding a universal solution to compact an arbitrary 3D shape is computationally challenging. Previous approaches showed that stripifying mesh surface can lead to optimal compaction, but the resulting structures were often impractical. In this paper, we propose an algorithm that cuts the 3D orthogonal polyhedron, tessellated by thick square panels, into a tree structure that can be transformed into compact piles by folding and stacking. We call this process tree stacking. Our research found that it is possible to decompose the problem into a pipeline of several solvable local optimizations. We also provide an efficient algorithm to check if the solution exists by avoiding the computational bottleneck of the pipeline. Our results show that tree stacking can efficiently generate stackable structures that have better folding accuracy and similar compactness comparing to the most compact stacking using strips.     

Visual Exploration of Dynamic Multichannel EEG Coherence Networks

Electroencephalography (EEG) coherence networks represent functional brain connectivity, and are constructed by calculating the coherence between pairs of electrode signals as a function of frequency. Visualization of such networks can provide insight into unexpected patterns of cognitive processing and help neuroscientists to understand brain mechanisms. However, visualizing dynamic EEG coherence networks is a challenge for the analysis of brain connectivity, especially when the spatial structure of the network needs to be taken into account. In this paper, we present a design and implementation of a visualization framework for such dynamic networks. First, requirements for supporting typical tasks in the context of dynamic functional connectivity network analysis were collected from neuroscience researchers. In our design, we consider groups of network nodes and their corresponding spatial location for visualizing the evolution of the dynamic coherence network. We introduce an augmented timeline‐based representation to provide an overview of the evolution of functional units (FUs) and their spatial location over time. This representation can help the viewer to identify relations between functional connectivity and brain regions, as well as to identify persistent or transient functional connectivity patterns across the whole time window. In addition, we introduce the time‐annotated FU map representation to facilitate comparison of the behaviour of nodes between consecutive FU maps. A colour coding is designed that helps to distinguish distinct dynamic FUs. Our implementation also supports interactive exploration. The usefulness of our visualization design was evaluated by an informal user study. The feedback we received shows that our design supports exploratory analysis tasks well. The method can serve as a first step before a complete analysis of dynamic EEG coherence networks.     

ClustMe: A Visual Quality Measure for Ranking Monochrome Scatterplots based on Cluster Patterns

We propose ClustMe, a new visual quality measure to rank monochrome scatterplots based on cluster patterns. ClustMe is based on data collected from a human‐subjects study, in which 34 participants judged synthetically generated cluster patterns in 1000 scatterplots. We generated these patterns by carefully varying the free parameters of a simple Gaussian Mixture Model with two components, and asked the participants to count the number of clusters they could see (1 or more than 1). Based on the results, we form ClustMe by selecting the model that best predicts these human judgments among 7 different state‐of‐the‐art merging techniques (Demp ). To quantitatively evaluate ClustMe, we conducted a second study, in which 31 human subjects ranked 435 pairs of scatterplots of real and synthetic data in terms of cluster patterns complexity. We use this data to compare ClustMe's performance to 4 other state‐of‐the‐art clustering measures, including the well‐known Clumpiness scagnostics. We found that of all measures, ClustMe is in strongest agreement with the human rankings.     

Spatio‐Temporal Contours from Deep Volume Raycasting

We visualize contours for spatio‐temporal processes to indicate where and when non‐continuous changes occur or spatial bounds are encountered. All time steps are comprised densely in one visualization, with contours allowing to efficiently analyze processes in the data even in case of spatial or temporal overlap. Contours are determined on the basis of deep raycasting that collects samples across time and depth along each ray. For each sample along a ray, its closest neighbors from adjacent rays are identified, considering time, depth, and value in the process. Large distances are represented as contours in image space, using color to indicate temporal occurrence. This contour representation can easily be combined with volume rendering‐based techniques, providing both full spatial detail for individual time steps and an outline of the whole time series in one view. Our view‐dependent technique supports efficient progressive computation, and requires no prior assumptions regarding the shape or nature of processes in the data. We discuss and demonstrate the performance and utility of our approach via a variety of data sets, comparison and combination with an alternative technique, and feedback by a domain scientist.     

A General Illumination Model for Molecular Visualization

Several visual representations have been developed over the years to visualize molecular structures, and to enable a better understanding of their underlying chemical processes. Today, the most frequently used atom‐based representations are the Space‐filling, the Solvent Excluded Surface, the Balls‐and‐Sticks, and the Licorice models. While each of these representations has its individual benefits, when applied to large‐scale models spatial arrangements can be difficult to interpret when employing current visualization techniques. In the past it has been shown that global illumination techniques improve the perception of molecular visualizations; unfortunately existing approaches are tailored towards a single visual representation. We propose a general illumination model for molecular visualization that is valid for different representations. With our illumination model, it becomes possible, for the first time, to achieve consistent illumination among all atom‐based molecular representations. The proposed model can be further evaluated in real‐time, as it employs an analytical solution to simulate diffuse light interactions between objects. To be able to derive such a solution for the rather complicated and diverse visual representations, we propose the use of regression analysis together with adapted parameter sampling strategies as well as shape parametrization guided sampling, which are applied to the geometric building blocks of the targeted visual representations. We will discuss the proposed sampling strategies, the derived illumination model, and demonstrate its capabilities when visualizing several dynamic molecules.     

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.     

Procedural Modeling of a Building from a Single Image

Creating a virtual city is demanded for computer games, movies, and urban planning, but it takes a lot of time to create numerous 3D building models. Procedural modeling has become popular in recent years to overcome this issue, but creating a grammar to get a desired output is difficult and time consuming even for expert users. In this paper, we present an interactive tool that allows users to automatically generate such a grammar from a single image of a building. The user selects a photograph and highlights the silhouette of the target building as input to our method. Our pipeline automatically generates the building components, from large‐scale building mass to fine‐scale windows and doors geometry. Each stage of our pipeline combines convolutional neural networks (CNNs) and optimization to select and parameterize procedural grammars that reproduce the building elements of the picture. In the first stage, our method jointly estimates camera parameters and building mass shape. Once known, the building mass enables the rectification of the façades, which are given as input to the second stage that recovers the façade layout. This layout allows us to extract individual windows and doors that are subsequently fed to the last stage of the pipeline that selects procedural grammars for windows and doors. Finally, the grammars are combined to generate a complete procedural building as output. We devise a common methodology to make each stage of this pipeline tractable. This methodology consists in simplifying the input image to match the visual appearance of synthetic training data, and in using optimization to refine the parameters estimated by CNNs. We used our method to generate a variety of procedural models of buildings from existing photographs.     

Elastic Correspondence between Triangle Meshes

We propose a novel approach for shape matching between triangular meshes that, in contrast to existing methods, can match crease features. Our approach is based on a hybrid optimization scheme, that solves simultaneously for an elastic deformation of the source and its projection on the target. The elastic energy we minimize is invariant to rigid body motions, and its non‐linear membrane energy component favors locally injective maps. Symmetrizing this model enables feature aligned correspondences even for non‐isometric meshes. We demonstrate the advantage of our approach over state of the art methods on isometric and non‐isometric datasets, where we improve the geodesic distance from the ground truth, the conformal and area distortions, and the mismatch of the mean curvature functions. Finally, we show that our computed maps are applicable for surface interpolation, consistent cross‐field computation, and consistent quadrangular remeshing of a set of shapes.     

Topology Preserving Simplification of Medial Axes in 3D Models

We propose an efficient method for topology‐preserving simplification of medial axes of 3D models. Existing methods either cannot preserve the topology during medial axes simplification or have the problem of being geometrically inaccurate or computationally expensive. To tackle these issues, we restrict our topology‐checking to the areas around the topological holes to avoid unnecessary checks in other areas. Our algorithm can keep high precision even when the medial axis is simplified to be in very few vertices. Furthermore, we parallelize the medial axes simplification procedure to enhance the performance significantly. Experimental results show that our method can preserve the topology with highly efficient performance, much superior to the existing methods in terms of topology preservation, accuracy and performance.     

Adaptive Temporal Sampling for Volumetric Path Tracing of Medical Data

Monte‐Carlo path tracing techniques can generate stunning visualizations of medical volumetric data. In a clinical context, such renderings turned out to be valuable for communication, education, and diagnosis. Because a large number of computationally expensive lighting samples is required to converge to a smooth result, progressive rendering is the only option for interactive settings: Low‐sampled, noisy images are shown while the user explores the data, and as soon as the camera is at rest the view is progressively refined. During interaction, the visual quality is low, which strongly impedes the user's experience. Even worse, when a data set is explored in virtual reality, the camera is never at rest, leading to constantly low image quality and strong flickering. In this work we present an approach to bring volumetric Monte‐Carlo path tracing to the interactive domain by reusing samples over time. To this end, we transfer the idea of temporal antialiasing from surface rendering to volume rendering. We show how to reproject volumetric ray samples even though they cannot be pinned to a particular 3D position, present an improved weighting scheme that makes longer history trails possible, and define an error accumulation method that downweights less appropriate older samples. Furthermore, we exploit reprojection information to adaptively determine the number of newly generated path tracing samples for each individual pixel. Our approach is designed for static, medical data with both volumetric and surface‐like structures. It achieves good‐quality volumetric Monte‐Carlo renderings with only little noise, and is also usable in a VR context.     

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.