Vector Field Visualization of Advective‐Diffusive Flows

We propose a framework for unified visualization of advective and diffusive concentration fluxes, which play a key role in many phenomena like, e.g. Marangoni convection and microscopic mixing. The main idea is the decomposition of fluxes into their concentration and velocity parts. Using this flux decomposition, we are able to convey advective‐diffusive concentration transport using integral lines. In order to visualize superimposed flux effects, we introduce a new graphical metaphor, the stream feather, which adds extensions to stream tubes pointing in the directions of deviating fluxes. The resulting unified visualization of macroscopic advection and microscopic diffusion allows for deeper insight into complex flow scenarios that cannot be achieved with current volume and surface rendering techniques alone. Our approach for flux decomposition and visualization of advective‐diffusive flows can be applied to any kind of (simulation) data if velocity and concentration data are available. We demonstrate that our techniques can easily be integrated into Smoothed Particle Hydrodynamics (SPH) based simulations.     

Space‐Time Bifurcation Lines for Extraction of 2D Lagrangian Coherent Structures

We present a novel and efficient technique to extract Lagrangian coherent structures in two‐dimensional time‐dependent vector fields. We show that this can be achieved by employing bifurcation line extraction in the space‐time representation of the vector field, and generating space‐time bifurcation manifolds therefrom. To show the utility and applicability of our approach, we provide an evaluation of existing extraction techniques for Lagrangian coherent structures, and compare them to our approach.     

Visualization of Coherent Structures of Light Transport

Inspired by vector field topology, an established tool for the extraction and identification of important features of flows and vector fields, we develop means for the analysis of the structure of light transport. For that, we derive an analogy to vector field topology that defines coherent structures in light transport. We also introduce Finite‐Time Path Deflection (FTPD), a scalar quantity that represents the deflection characteristic of all light transport paths passing through a given point in space. For virtual scenes, the FTPD can be computed directly using path‐space Monte Carlo integration. We visualize the FTPD field for several example scenes and discuss the revealed structures. Lastly, we show that the coherent regions visualized by the FTPD are closely related to the coherent regions in our new topologically‐motivated analysis of light transport. FTPD visualizations are thus also visualizations of the structure of light transport.     

Illustrative Visualization of Mesoscale Ocean Eddies

Feature‐based time‐varying volume visualization is combined with illustrative visualization to tell the story of how mesoscale ocean eddies form in the Gulf Stream and transport heat and nutrients across the ocean basin. The internal structure of these three‐dimensional eddies and the kinematics with which they move are critical to a full understanding of ocean eddies. In this work, we apply a feature‐based method to track instances of ocean eddies through the time steps of a high‐resolution multi‐decadal regional ocean model and generate a series of eddy paths which reflect the life cycle of individual eddy instances. Based on the computed metadata, several important geometric and physical properties of eddy are computed. Illustrative visualization techniques, including visual effectiveness enhancement, focus+context, and smart visibility, are combined with the extracted volume features to explore eddy characteristics at different levels. An evaluation by domain experts indicates that combining our feature‐based techniques with illustrative visualization techniques provides an insight into the role eddies play in ocean circulation. The domain experts expressed a preference for our methods over existing tools.     

Transductive 3D Shape Segmentation using Sparse Reconstruction

We propose a transductive shape segmentation algorithm, which can transfer prior segmentation results in database to new shapes without explicitly specification of prior category information. Our method first partitions an input shape into a set of segmentations as a data preparation, and then a linear integer programming algorithm is used to select segments from them to form the final optimal segmentation. The key idea is to maximize the segment similarity between the segments in the input shape and the segments in database, where the segment similarity is computed through sparse reconstruction error. The segment‐level similarity enables to handle a large amount of shapes with significant topology or shape variations with a small set of segmented example shapes. Experimental results show that our algorithm can generate high quality segmentation and semantic labeling results in the Princeton segmentation benchmark.     

Pathline glyphs

Visualization of pathlines is common and highly relevant for the analysis of unsteady flow. However, pathlines can intersect, leading to visual clutter and perceptual issues. This makes it intrinsically difficult to provide expressive visualizations of the entire domain by an arrangement of multiple pathlines, in contrast to well‐established streamline placement techniques. We present an approach to reduce these problems. It is inspired by glyph‐based visualization and small multiples: we partition the domain into cells, each corresponding to a downscaled version of the entire domain. Inside these cells, a single downscaled pathline is drawn. On the overview scale, our pathline glyphs lead to emergent visual patterns that provide insight into time‐dependent flow behavior. Zooming‐in allows us to analyze individual pathlines in detail and compare neighboring lines. The overall approach is complemented with a context‐preserving zoom lens and interactive pathline‐based exploration. While we primarily target the visualization of 2D flow, we also address the extension to 3D. Our evaluation includes several examples, comparison to other flow visualization techniques, and a user study with domain experts.     

Photoelasticity Raycasting

We present a novel physically‐based method to visualize stress tensor fields. By incorporating photoelasticity into traditional raycasting and extending it with reflection and refraction, taking into account polarization, we obtain the virtual counterpart to traditional experimental polariscopes. This allows us to provide photoelastic analysis of stress tensor fields in arbitrary domains. In our model, the optical material properties, such as stress‐optic coefficient and refractive index, can either be chosen in compliance with the subject under investigation, or, in case of stress problems that do not model optical properties or that are not transparent, be chosen according to known or even new transparent materials. This enables direct application of established polariscope methodology together with respective interpretation. Using a GPU‐based implementation, we compare our technique to experimental data, and demonstrate its utility with several simulated datasets.     

Extracting Features from Time‐Dependent Vector Fields Using Internal Reference Frames

Extracting features from complex, time‐dependent flow fields remains a significant challenge despite substantial research efforts, especially because most flow features of interest are defined with respect to a given reference frame. Pathline‐based techniques, such as the FTLE field, are complex to implement and resource intensive, whereas scalar transforms, such as λ₂, often produce artifacts and require somewhat arbitrary thresholds. Both approaches aim to analyze the flow in a more suitable frame, yet neither technique explicitly constructs one. This paper introduces a new data‐driven technique to compute internal reference frames for large‐scale complex flows. More general than uniformly moving frames, these frames can transform unsteady fields, which otherwise require substantial processing of resources, into a sequence of individual snapshots that can be analyzed using the large body of steady‐flow analysis techniques. Our approach is simple, theoretically well‐founded, and uses an embarrassingly parallel algorithm for structured as well as unstructured data. Using several case studies from fluid flow and turbulent combustion, we demonstrate that internal frames are distinguished, result in temporally coherent structures, and can extract well‐known as well as notoriously elusive features one snapshot at a time.     

Adjoint Map Representation for Shape Analysis and Matching

In this paper, we propose to consider the adjoint operators of functional maps, and demonstrate their utility in several tasks in geometry processing. Unlike a functional map, which represents a correspondence simply using the pull‐back of function values, the adjoint operator reflects both the map and its distortion with respect to given inner products. We argue that this property of adjoint operators and especially their relation to the map inverse under the choice of different inner products, can be useful in applications including bi‐directional shape matching, shape exploration, and pointwise map recovery among others. In particular, in this paper, we show that the adjoint operators can be used within the cycle‐consistency framework to encode and reveal the presence or lack of consistency between distortions in a collection, in a way that is complementary to the previously used purely map‐based consistency measures. We also show how the adjoint can be used for matching pairs of shapes, by accounting for maps in both directions, can help in recovering point‐to‐point maps from their functional counterparts, and describe how it can shed light on the role of functional basis selection.     

InSpectr: Multi‐Modal Exploration,Visualization, and Analysis of Spectral Data

This paper addresses the increasing demand in industry for methods to analyze and visualize multimodal data involving a spectral modality. Two data modalities are used: high‐resolution X‐ray computed tomography (XCT) for structural characterization and low‐resolution X‐ray fluorescence (XRF) spectral data for elemental decomposition. We present InSpectr, an integrated tool for the interactive exploration and visual analysis of multimodal, multiscalar data. The tool has been designed around a set of tasks identified by domain experts in the fields of XCT and XRF. It supports registered single scalar and spectral datasets optionally coupled with element maps and reference spectra. InSpectr is instantiating various linked views for the integration of spatial and non‐spatial information to provide insight into an industrial component's structural and material composition: views with volume renderings of composite and individual 3D element maps visualize global material composition; transfer functions defined directly on the spectral data and overlaid pie‐chart glyphs show elemental composition in 2D slice‐views; a representative aggregated spectrum and spectra density histograms are introduced to provide a global overview in the spectral view. Spectral magic lenses, spectrum probing and elemental composition probing of points using a pie‐chart view and a periodic table view aid the local material composition analysis. Two datasets are investigated to outline the usefulness of the presented techniques: a 3D virtually created phantom with a brass metal alloy and a real‐world 2D water phantom with insertions of gold, barium, and gadolinium. Additionally a detailed user evaluation of the results is provided.     

Quality Metrics for Information Visualization

The visualization community has developed to date many intuitions and understandings of how to judge the quality of views in visualizing data. The computation of a visualization's quality and usefulness ranges from measuring clutter and overlap, up to the existence and perception of specific (visual) patterns. This survey attempts to report, categorize and unify the diverse understandings and aims to establish a common vocabulary that will enable a wide audience to understand their differences and subtleties. For this purpose, we present a commonly applicable quality metric formalization that should detail and relate all constituting parts of a quality metric. We organize our corpus of reviewed research papers along the data types established in the information visualization community: multi‐ and high‐dimensional, relational, sequential, geospatial and text data. For each data type, we select the visualization subdomains in which quality metrics are an active research field and report their findings, reason on the underlying concepts, describe goals and outline the constraints and requirements. One central goal of this survey is to provide guidance on future research opportunities for the field and outline how different visualization communities could benefit from each other by applying or transferring knowledge to their respective subdomain. Additionally, we aim to motivate the visualization community to compare computed measures to the perception of humans.     

Comparative Blood Flow Visualization for Cerebral Aneurysm Treatment Assessment

A pathological vessel dilation in the brain, termed cerebral aneurysm, bears a high risk of rupture, and is associated with a high mortality. In recent years, incidental findings of unruptured aneurysms have become more frequent, mainly due to advances in medical imaging. The pathological condition is often treated with a stent that diverts the blood flow from the aneurysm sac back to the original vessel. Prior to treatment, neuroradiologists need to decide on the optimal stent configuration and judge the long‐term rupture risk, for which blood flow information is essential. Modern patient‐specific simulations can model the hemodynamics for various stent configurations, providing important indicators to support the decision‐making process. However, the necessary visual analysis of these data becomes tedious and time‐consuming, because of the abundance of information. We introduce a comprehensive comparative visualization that integrates morphology with blood flow indicators to facilitate treatment assessment. To deal with the visual complexity, we propose a details‐on‐demand approach, combining established medical visualization techniques with innovative glyphs inspired by information visualization concepts. In an evaluation we have obtained informal feedback from domain experts, gauging the value of our visualization.     

Visual Debugging Techniques for Reactive Data Visualization

Interaction is critical to effective visualization, but can be difficult to author and debug due to dependencies among input events, program state, and visual output. Recent advances leverage reactive semantics to support declarative design and avoid the “spaghetti code” of imperative event handlers. While reactive programming improves many aspects of development, textual specifications still fail to convey the complex runtime dynamics. In response, we contribute a set of visual debugging techniques to reveal the runtime behavior of reactive visualizations. A timeline view records input events and dynamic variable updates, allowing designers to replay and inspect the propagation of values step‐by‐step. On‐demand annotations overlay the output visualization to expose relevant state and scale mappings in‐situ. Dynamic tables visualize how backing datasets change over time. To evaluate the effectiveness of these techniques, we study how first‐time Vega users debug interactions in faulty, unfamiliar specifications; with no prior knowledge, participants were able to accurately trace errors through the specification.     

Stability of Dissipation Elements: A Case Study in Combustion

Recently, dissipation elements have been gaining popularity as a mechanism for measurement of fundamental properties of turbulent flow, such as turbulence length scales and zonal partitioning. Dissipation elements segment a domain according to the source and destination of streamlines in the gradient flow field of a scalar function f : → ?. They have traditionally been computed by numerically integrating streamlines from the center of each voxel in the positive and negative gradient directions, and grouping those voxels whose streamlines terminate at the same extremal pair. We show that the same structures map well to combinatorial topology concepts developed recently in the visualization community. Namely, dissipation elements correspond to sets of cells of the Morse‐Smale complex. The topology‐based formulation enables a more exploratory analysis of the nature of dissipation elements, in particular, in understanding their stability with respect to small scale variations. We present two examples from combustion science that raise significant questions about the role of small scale perturbation and indeed the definition of dissipation elements themselves.     

Aesthetic Rating and Color Suggestion for Color Palettes

A model to rate color combinations that considers human aesthetic preferences is proposed. The proposed method does not assume that a color palette has a specific number of colors, i.e., input is not restricted to a two‐, three‐, or five‐color palettes. We extract features from a color palette whose size does not depend on the number of colors in the palette. The proposed rating prediction model is trained using a human color preference dataset. The model allows a user to extend a color palette, e.g., from three colors to five or seven colors, while retaining color harmony. In addition, we present a color search scheme for a given palette and a customized version of the proposed model for a specific color tone. We demonstrate that the proposed model can also be applied to various palette‐based applications.     

An Objective Deghosting Quality Metric for HDR Images

Reconstructing high dynamic range (HDR) images of a complex scene involving moving objects and dynamic backgrounds is prone to artifacts. A large number of methods have been proposed that attempt to alleviate these artifacts, known as HDR deghosting algorithms. Currently, the quality of these algorithms are judged by subjective evaluations, which are tedious to conduct and get quickly outdated as new algorithms are proposed on a rapid basis. In this paper, we propose an objective metric which aims to simplify this process. Our metric takes a stack of input exposures and the deghosting result and produces a set of artifact maps for different types of artifacts. These artifact maps can be combined to yield a single quality score. We performed a subjective experiment involving 52 subjects and 16 different scenes to validate the agreement of our quality scores with subjective judgements and observed a concordance of almost 80%. Our metric also enables a novel application that we call as hybrid deghosting, in which the output of different deghosting algorithms are combined to obtain a superior deghosting result.     

Methods for Compensating Contrast Effects in Information Visualization

Color, as one of the most effective visual variables, is used in many techniques to encode and group data points according to different features. Relations between features and groups appear as visual patterns in the visualization. However, optical illusions may bias the perception at the first level of the analysis process. For instance, in pixel‐based visualizations contrast effects make pixels appear brighter if surrounded by a darker area, which distorts the encoded metric quantity of the data points. Even if we are aware of these perceptual issues, our visual cognition system is not able to compensate these effects accurately. To overcome this limitation, we present a color optimization algorithm based on perceptual metrics and color perception models to reduce physiological contrast or color effects. We evaluate our technique with a user study and find that the technique doubles the accuracy of users comparing and estimating color encoded data values. Since the presented technique can be used in any application without adaption to the visualization itself, we are able to demonstrate its effectiveness on data visualizations in different domains.     

Sparse Inertial Poser: Automatic 3D Human Pose Estimation from Sparse IMUs

We address the problem of making human motion capture in the wild more practical by using a small set of inertial sensors attached to the body. Since the problem is heavily under‐constrained, previous methods either use a large number of sensors, which is intrusive, or they require additional video input. We take a different approach and constrain the problem by: (i) making use of a realistic statistical body model that includes anthropometric constraints and (ii) using a joint optimization framework to fit the model to orientation and acceleration measurements over multiple frames. The resulting tracker Sparse Inertial Poser (SIP) enables motion capture using only 6 sensors (attached to the wrists, lower legs, back and head) and works for arbitrary human motions. Experiments on the recently released TNT15 dataset show that, using the same number of sensors, SIP achieves higher accuracy than the dataset baseline without using any video data. We further demonstrate the effectiveness of SIP on newly recorded challenging motions in outdoor scenarios such as climbing or jumping over a wall.     

Sparse representation of terrains for procedural modeling

In this paper, we present a simple and efficient method to represent terrains as elevation functions built from linear combinations of landform features (atoms). These features can be extracted either from real world data‐sets or procedural primitives, or from any combination of multiple terrain models. Our approach consists in representing the elevation function as a sparse combination of primitives, a concept which we call Sparse Construction Tree, which blends the different landform features stored in a dictionary. The sparse representation allows us to represent complex terrains using combinations of atoms from a small dictionary, yielding a powerful and compact terrain representation and synthesis tool. Moreover, we present a method for automatically learning the dictionary and generating the Sparse Construction Tree model. We demonstrate the efficiency of our method in several applications: inverse procedural modeling of terrains, terrain amplification and synthesis from a coarse sketch.