Streamline Variability Plots for Characterizing the Uncertainty in Vector Field Ensembles.

We present a new method to visualize from an ensemble of flow fields the statistical properties of streamlines passing through a selected location. We use principal component analysis to transform the set of streamlines into a low-dimensional Euclidean space. In this space the streamlines are clustered into major trends, and each cluster is in turn approximated by a multivariate Gaussian distribution. This yields a probabilistic mixture model for the streamline distribution, from which confidence regions can be derived in which the streamlines are most likely to reside. This is achieved by transforming the Gaussian random distributions from the low-dimensional Euclidean space into a streamline distribution that follows the statistical model, and by visualizing confidence regions in this distribution via iso-contours. We further make use of the principal component representation to introduce a new concept of streamline-median, based on existing median concepts in multidimensional Euclidean spaces. We demonstrate the potential of our method in a number of real-world examples, and we compare our results to alternative clustering approaches for particle trajectories as well as curve boxplots.

A computational tool for preoperative breast augmentation planning in aesthetic plastic surgery.

Breast augmentation was the most commonly performed cosmetic surgery procedure in 2011 in the United States. Although aesthetically pleasing surgical results can only be achieved if the correct breast implant is selected from a large variety of different prosthesis sizes and shapes available on the market, surgeons still rely on visual assessment and other subjective approaches for operative planning because of lacking objective evaluation tools. In this paper, we present the development of a software prototype for augmentation mammaplasty simulation solely based on 3-D surface scans, from which patient-specific finite-element models are generated in a semiautomatic process. The finite-element model is used to preoperatively simulate the expected breast shapes using physical soft-tissue mechanics. Our approach uses a novel mechanism based on so-called displacement templates, which, for a specific implant shape and position, describe the respective internal body forces. Due to a highly efficient numerical solver we can provide immediate visual feedback of the simulation results, and thus, the software prototype can be integrated smoothly into the medical workflow. The clinical value of the developed 3-D computational tool for aesthetic breast augmentation surgery planning is demonstrated in patient-specific use cases.

Flux-freezing breakdown in high-conductivity magnetohydrodynamic turbulence.

The idea of 'frozen-in' magnetic field lines for ideal plasmas is useful to explain diverse astrophysical phenomena, for example the shedding of excess angular momentum from protostars by twisting of field lines frozen into the interstellar medium. Frozen-in field lines, however, preclude the rapid changes in magnetic topology observed at high conductivities, as in solar flares. Microphysical plasma processes are a proposed explanation of the observed high rates, but it is an open question whether such processes can rapidly reconnect astrophysical flux structures much greater in extent than several thousand ion gyroradii. An alternative explanation is that turbulent Richardson advection brings field lines implosively together from distances far apart to separations of the order of gyroradii. Here we report an analysis of a simulation of magnetohydrodynamic turbulence at high conductivity that exhibits Richardson dispersion. This effect of advection in rough velocity fields, which appear non-differentiable in space, leads to line motions that are completely indeterministic or 'spontaneously stochastic', as predicted in analytical studies. The turbulent breakdown of standard flux freezing at scales greater than the ion gyroradius can explain fast reconnection of very large-scale flux structures, both observed (solar flares and coronal mass ejections) and predicted (the inner heliosheath, accretion disks, γ-ray bursts and so on). For laminar plasma flows with smooth velocity fields or for low turbulence intensity, stochastic flux freezing reduces to the usual frozen-in condition.

Interactive separating streak surfaces.

Streak surfaces are among the most important features to support 3D unsteady flow exploration, but they are also among the computationally most demanding. Furthermore, to enable a feature driven analysis of the flow, one is mainly interested in streak surfaces that show separation profiles and thus detect unstable manifolds in the flow. The computation of such separation surfaces requires to place seeding structures at the separation locations and to let the structures move correspondingly to these locations in the unsteady flow. Since only little knowledge exists about the time evolution of separating streak surfaces, at this time, an automated exploration of 3D unsteady flows using such surfaces is not feasible. Therefore, in this paper we present an interactive approach for the visual analysis of separating streak surfaces. Our method draws upon recent work on the extraction of Lagrangian coherent structures (LCS) and the real-time visualization of streak surfaces on the GPU. We propose an interactive technique for computing ridges in the finite time Lyapunov exponent (FTLE) field at each time step, and we use these ridges as seeding structures to track streak surfaces in the time-varying flow. By showing separation surfaces in combination with particle trajectories, and by letting the user interactively change seeding parameters such as particle density and position, visually guided exploration of separation profiles in 3D is provided. To the best of our knowledge, this is the first time that the reconstruction and display of semantic separable surfaces in 3D unsteady flows can be performed interactively, giving rise to new possibilities for gaining insight into complex flow phenomena.

Sample-based surface coloring.

In this paper, we present a sample-based approach for surface coloring, which is independent of the original surface resolution and representation. To achieve this, we introduce the Orthogonal Fragment Buffer (OFB)-an extension of the Layered Depth Cube-as a high-resolution view-independent surface representation. The OFB is a data structure that stores surface samples at a nearly uniform distribution over the surface, and it is specifically designed to support efficient random read/write access to these samples. The data access operations have a complexity that is logarithmic in the depth complexity of the surface. Thus, compared to data access operations in tree data structures like octrees, data-dependent memory access patterns are greatly reduced. Due to the particular sampling strategy that is employed to generate an OFB, it also maintains sample coherence, and thus, exhibits very good spatial access locality. Therefore, OFB-based surface coloring performs significantly faster than sample-based approaches using tree structures. In addition, since in an OFB, the surface samples are internally stored in uniform 2D grids, OFB-based surface coloring can efficiently be realized on the GPU to enable interactive coloring of high-resolution surfaces. On the OFB, we introduce novel algorithms for color painting using volumetric and surface-aligned brushes, and we present new approaches for particle-based color advection along surfaces in real time. Due to the intermediate surface representation we choose, our method can be used to color polygonal surfaces as well as any other type of surface that can be sampled.

Interactive streak surface visualization on the GPU.

In this paper we present techniques for the visualization of unsteady flows using streak surfaces, which allow for the first time an adaptive integration and rendering of such surfaces in real-time. The techniques consist of two main components, which are both realized on the GPU to exploit computational and bandwidth capacities for numerical particle integration and to minimize bandwidth requirements in the rendering of the surface. In the construction stage, an adaptive surface representation is generated. Surface refinement and coarsening strategies are based on local surface properties like distortion and curvature. We compare two different methods to generate a streak surface: a) by computing a patch-based surface representation that avoids any interdependence between patches, and b) by computing a particle-based surface representation including particle connectivity, and by updating this connectivity during particle refinement and coarsening. In the rendering stage, the surface is either rendered as a set of quadrilateral surface patches using high-quality point-based approaches, or a surface triangulation is built in turn from the given particle connectivity and the resulting triangle mesh is rendered. We perform a comparative study of the proposed techniques with respect to surface quality, visual quality and performance by visualizing streak surfaces in real flows using different rendering options.

Direct volume editing.

In this work we present basic methodology for interactive volume editing on GPUs, and we demonstrate the use of these methods to achieve a number of different effects. We present fast techniques to modify the appearance and structure of volumetric scalar fields given on Cartesian grids. Similar to 2D circular brushes as used in surface painting we present 3D spherical brushes for intuitive coloring of particular structures in such fields. This paint metaphor is extended to allow the user to change the data itself, and the use of this functionality for interactive structure isolation, hole filling, and artefact removal is demonstrated. Building on previous work in the field we introduce high-resolution selection volumes, which can be seen as a resolution-based focus+context metaphor. By utilizing such volumes we present a novel approach to interactive volume editing at sub-voxel accuracy. Finally, we introduce a fast technique to paste textures onto iso-surfaces in a 3D scalar field. Since the texture resolution is independent of the volume resolution, this technique allows structure-aligned textures containing appearance properties or textual information to be used for volume augmentation and annotation.