Energy‐scale Aware Feature Extraction for Flow Visualization

In the visualization of flow simulation data, feature detectors often tend to result in overly rich response, making some sort of filtering or simplification necessary to convey meaningful images. In this paper we present an approach that builds upon a decomposition of the flow field according to dynamical importance of different scales of motion energy. Focusing on the high‐energy scales leads to a reduction of the flow field while retaining the underlying physical process. The presented method acknowledges the intrinsic structures of the flow according to its energy and therefore allows to focus on the energetically most interesting aspects of the flow. Our analysis shows that this approach can be used for methods based on both local feature extraction and particle integration and we provide a discussion of the error caused by the approximation. Finally, we illustrate the use of the proposed approach for both a local and a global feature detector and in the context of numerical flow simulations.     

Visualization and Analysis of Eddies in a Global Ocean Simulation

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.     

Toward a Lagrangian Vector Field Topology

In this paper we present an extended critical point concept which allows us to apply vector field topology in the case of unsteady flow. We propose a measure for unsteadiness which describes the rate of change of the velocities in a fluid element over time. This measure allows us to select particles for which topological properties remain intact inside a finite spatio‐temporal neighborhood. One benefit of this approach is that the classification of critical points based on the eigenvalues of the Jacobian remains meaningful. In the steady case the proposed criterion reduces to the classical definition of critical points. As a first step we show that finding an optimal Galilean frame of reference can be obtained implicitly by analyzing the acceleration field. In a second step we show that this can be extended by switching to the Lagrangian frame of reference. This way the criterion can detect critical points moving along intricate trajectories. We analyze the behavior of the proposed criterion based on two analytical vector fields for which a correct solution is defined by their inherent symmetries and present results for numerical vector fields.     

COPERNICUS: Context‐Preserving Engine for Route Navigation with Interactive User‐modifiable Scaling

In this paper, we present an automated system for generating context‐preserving route maps that depict navigation routes as a path between nodes and edges inside a topographic network. Our application identifies relevant context information to support navigation and orientation, and generates customizable route maps according to design principles that communicate all relevant context information clearly visible on one single page. Interactive scaling allows seamless transition between the original undistorted map and our new map design, and supports user‐specified scaling of regions of interest to create personalized driving directions according to the drivers needs.     

Defocus Magnification

A blurry background due to shallow depth of field is often desired for photographs such as portraits, but, unfortunately, small point-and-shoot cameras do not permit enough defocus because of the small diameter of their lenses. We present an image-processing technique that increases the defocus in an image to simulate the shallow depth of field of a lens with a larger aperture. Our technique estimates the spatially-varying amount of blur over the image, and then uses a simple image-based technique to increase defocus. We first estimate the size of the blur kernel at edges and then propagate this defocus measure over the image. Using our defocus map, we magnify the existing blurriness, which means that we blur blurry regions and keep sharp regions sharp. In contrast to more difficult problems such as depth from defocus, we do not require precise depth estimation and do not need to disambiguate textureless regions.     

Dental Inlay and Onlay Construction by Iterative Laplacian Surface Editing

We propose a new method for automatic construction of inlays and onlays. Mesh models from a small tooth library are adapted to the remaining healthy surface of the patient's tooth. In the area above the cavity, the general morphology of the model tooth (fissures, cusp tips, etc) is preserved, but precisely adjusted to the intra‐oral situation. Our approach uses iterative Laplacian Surface Editing to deform the model tooth. This allows the automatic generation of highly individual, functional and anatomically correct inlays/onlays, without having to resort to a large library of different tooth shapes.     

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.     

Visualisation of Sensor Data from Animal Movement

A new area of biological research is identifying and grouping patterns of behaviour in wild animals by analysing data obtained through the attachment of tri-axial accelerometers. As these recording devices become smaller and less expensive their use has increased. Currently acceleration data are visualised as 2D time series plots, and analyses are based on summary statistics and the application of Fourier transforms. We develop alternate visualisations of this data so as to analyse, explore and present new patterns of animal behaviour. Our visualisations include interactive spherical scatterplots, spherical histograms, clustering methods, and feature-based state diagrams of the data. We study the application of these visualisation methods to accelerometry data from animal movement. The reaction of biologists to these visualisations is also reported.     

Visual Analysis and Semantic Exploration of Urban LIDAR Change Detection

Many previous approaches to detecting urban change from LIDAR point clouds interpolate the points into rasters, perform pixel‐based image processing to detect changes, and produce 2D images as output. We present a method of LIDAR change detection that maintains accuracy by only using the raw, irregularly spaced LIDAR points, and extracts relevant changes as individual 3D models. We then utilize these models, alongside existing GIS data, within an interactive application that allows the chronological exploration of the changes to an urban environment. A three‐tiered level‐of‐detail system maintains a scale‐appropriate, legible visual representation across the entire range of view scales, from individual changes such as buildings and trees, to groups of changes such as new residential developments, deforestation, and construction sites, and finally to larger regions such as neighborhoods and districts of a city that are emerging or undergoing revitalization. Tools are provided to assist the visual analysis by urban planners and historians through semantic categorization and filtering of the changes presented.     

A Hidden‐picture Puzzles Generator

A hidden‐picture puzzle contains objects hidden in a background image, in such a way that each object fits closely into a local region of the background. Our system converts image of the background and objects into line drawing, and then finds places in which to hide transformed versions of the objects using rotation‐invariant shape context matching. During the hiding process, each object is subjected to a slight deformation to enhance its similarity to the background. The results were assessed by a panel of puzzle‐solvers.     

Volume Deformations in Grid-Less Flow Simulations

This paper presents a novel method for the extraction and visualization of volume deformations in grid-less point based flow simulations. Our primary goals are the segmentation of different paths through a mixing device and the visualization of ellipsoidal particle deformations. The main challenges are the numerically efficient processing of deformation tensors and the robust integration of stream- and streaklines at boundaries of the dataset such that closed segments are obtained. Our results show two- and three-dimensional particle deformations as well as the segmentation of volumes in stationary fields and areas in time-dependent datasets taking consistent paths through a mixing device.     

A Maximum Enhancing Higher‐Order Tensor Glyph

Glyphs are a fundamental tool in tensor visualization, since they provide an intuitive geometric representation of the full tensor information. The Higher‐Order Maximum Enhancing (HOME) glyph, a generalization of the second‐order tensor ellipsoid, was recently shown to emphasize the orientational information in the tensor through a pointed shape around maxima. This paper states and formally proves several important properties of this novel glyph, presents its first three‐dimensional implementation, and proposes a new coloring scheme that reflects peak direction and sharpness. Application to data from High Angular Resolution Diffusion Imaging (HARDI) shows that the method allows for interactive data exploration and confirms that the HOME glyph conveys fiber spread and crossings more effectively than the conventional polar plot.     

Lagrangian Visualization of Flow‐Embedded Surface Structures

The notions of Finite‐Time Lyapunov Exponent (FTLE) and Lagrangian Coherent Structures provide a strong framework for the analysis and visualization of complex technical flows. Their definition is simple and intuitive, and they are built on a deep theoretical foundation. We apply these concepts to enable the analysis of flows in the immediate vicinity of the boundaries of flow‐embedded objects by limiting the Lagrangian analysis to surfaces closely neighboring these boundaries. To this purpose, we present an approach to approximate FTLE fields over such surfaces. Furthermore, we achieve an effective depiction of boundary‐related flow structures such as separation and attachment over object boundaries and specific insight into the surrounding flow using several specifically chosen visualization techniques. We document the applicability of our methods by presenting a number of application examples.     

Embedded Implicit Stand-Ins for Animated Meshes: A Case of Hybrid Modelling

In this paper, we address shape modelling problems, encountered in computer animation and computer games development that are difficult to solve just using polygonal meshes. Our approach is based on a hybrid-modelling concept that combines polygonal meshes with implicit surfaces. A hybrid model consists of an animated polygonal mesh and an approximation of this mesh by a convolution surface stand-in that is embedded within it or is attached to it. The motions of both objects are synchronised using a rigging skeleton. We model the interaction between an animated mesh object and a viscoelastic substance, which is normally represented in an implicit form. Our approach is aimed at achieving verisimilitude rather than physically based simulation. The adhesive behaviour of the viscous object is modelled using geometric blending operations on the corresponding implicit surfaces. Another application of this approach is the creation of metamorphosing implicit surface parts that are attached to an animated mesh. A prototype implementation of the proposed approach and several examples of modelling and animation with near real-time preview times are presented.     

Topology‐based Visualization of Transformation Pathways in Complex Chemical Systems

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.     

Automatic Detection and Visualization of Distinctive Structures in 3D Unsteady Multi‐fields

Current unsteady multi‐field simulation data‐sets consist of millions of data‐points. To efficiently reduce this enormous amount of information, local statistical complexity was recently introduced as a method that identifies distinctive structures using concepts from information theory. Due to high computational costs this method was so far limited to 2D data. In this paper we propose a new strategy for the computation that is substantially faster and allows for a more precise analysis. The bottleneck of the original method is the division of spatio‐temporal configurations in the field (light‐cones) into different classes of behavior. The new algorithm uses a density‐driven Voronoi tessellation for this task that more accurately captures the distribution of configurations in the sparsely sampled high‐dimensional space. The efficient computation is achieved using structures and algorithms from graph theory. The ability of the method to detect distinctive regions in 3D is illustrated using flow and weather simulations.     

Dynamic Multi‐View Exploration of Shape Spaces

Statistical shape modeling is a widely used technique for the representation and analysis of the shapes and shape variations present in a population. A statistical shape model models the distribution in a high dimensional shape space, where each shape is represented by a single point. We present a design study on the intuitive exploration and visualization of shape spaces and shape models. Our approach focuses on the dual‐space nature of these spaces. The high‐dimensional shape space represents the population, whereas object space represents the shape of the 3D object associated with a point in shape space. A 3D object view provides local details for a single shape. The high dimensional points in shape space are visualized using a 2D scatter plot projection, the axes of which can be manipulated interactively. This results in a dynamic scatter plot, with the further extension that each point is visualized as a small version of the object shape that it represents. We further enhance the population‐object duality with a new type of view aimed at shape comparison. This new “shape evolution view” visualizes shape variability along a single trajectory in shape space, and serves as a link between the two spaces described above. Our three‐view exploration concept strongly emphasizes linked interaction between all spaces. Moving the cursor over the scatter plot or evolution views, shapes are dynamically interpolated and shown in the object view. Conversely, camera manipulation in the object view affects the object visualizations in the other views. We present a GPU‐accelerated implementation, and show the effectiveness of the three‐view approach using a number of real‐world cases. In these, we demonstrate how this multi‐view approach can be used to visually explore important aspects of a statistical shape model, including specificity, compactness and reconstruction error.     

Flow‐Based Automatic Generation of Hybrid Picture Mazes

A method for automatically generating a picture maze from two different images is introduced throughout this paper. The process begins with the extraction of salient contours and edge tangent flow information from the primary image in order to build the overall maze. Thus, mazes with passages flowing in the main edge directions and walls that effectively represent an abstract version of the primary image can be successfully created. Furthermore, our proposed approach makes possible the use of their solution path as a means of illustrating the main features of the secondary image, while attempting to keep its image motif concealed until the maze has been finally solved. The contour features and intensity of the secondary image are also incorporated into our method in order to determine the areas of the maze to be shaded by allowing the solution path to go through them. Moreover, an experiment has been conducted to confirm that solution paths can be successfully hidden from the participants in the mazes generated using our method.     

Diffusion‐Based Snow Cover Generation

We present a method to generate snow covers on complex scene geometries. Both volumetric snow shapes and photorealistic texturing are computed. We formulate snow accumulation as a diffusive distribution process on a ground scene. Our theoretical framework is motivated by models for granular material deposition. With the framework we can capture the most relevant features of natural snow cover geometries in a concise local computation scheme. Snow bridges and overhangs are also included. Snow surface texture coordinates are computed to create realistic ground–snow interfaces. Several example scenes and a supplementary snow cover growth animation demonstrate the method's efficiency.