DSpace Repository :: Browsing by Author "Westermann, Rüdiger"

Browsing by Author "Westermann, Rüdiger"

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Analytic Ray Splitting for Controlled Precision DVR
(The Eurographics Association, 2021) Weiss, Sebastian; Westermann, Rüdiger; Agus, Marco and Garth, Christoph and Kerren, Andreas
For direct volume rendering of post-classified data, we propose an algorithm that analytically splits a ray through a cubical cell at the control points of a piecewise-polynomial transfer function. This splitting generates segments over which the variation of the optical properties is described by piecewise cubic functions. This allows using numerical quadrature rules with controlled precision to obtain an approximation with prescribed error bounds. The proposed splitting scheme can be used to find all piecewise linear or monotonic segments along a ray, and it can thus be used to improve the accuracy of direct volume rendering, scale-invariant volume rendering, and multi-isosurface rendering.
Cluster-based Analysis of Multi-Parameter Distributions in Cloud Simulation Ensembles
(The Eurographics Association, 2019) Kumpf, Alexander; Stumpfegger, Josef; Westermann, Rüdiger; Schulz, Hans-Jörg and Teschner, Matthias and Wimmer, Michael
The proposed approach enables a comparative visual exploration of multi-parameter distributions in time-varying 3D ensemble simulations. To investigate whether dominant trends in such distributions occur, we consider the simulation elements in each dataset-per ensemble member and time step-as elements in the multi-dimensional parameter space, and use t-SNE to project these elements into 2D space. To find groups of elements with similar parameter values in each time step, the resulting projections are clustered via k-Means. Since elements with similar data values can be disconnected in one single projection, we compute an ensemble of projections using multiple t-SNE runs and use evidence accumulation to determine sets of elements that are stably clustered together. We build upon per-cluster multi-parameter distribution functions to quantify cluster similarity, and merge clusters in different ensemble members. By applying the proposed approach to a time-varying ensemble, the temporal development of clusters, and in particular their stability over time can be analyzed. We apply this approach to analyze a time-varying ensemble of 3D cloud simulations. The visualizations via t-SNE, parallel coordinate plots and scatter plot matrices show dependencies between the simulation results and the simulation parameters used to generate the ensemble, and they provide insight into the temporal ensemble variability regarding the major trends in the multi-parameter distributions.
Clustering Ensembles of 3D Jet-Stream Core Lines
(The Eurographics Association, 2019) Kern, Michael; Westermann, Rüdiger; Schulz, Hans-Jörg and Teschner, Matthias and Wimmer, Michael
The extraction of a jet-stream core line in a wind field results in many disconnected line segments of arbitrary topology. In an ensemble of wind fields, these structures show high variation, coincide only partly, and almost nowhere agree in all ensemble members. In this paper, we shed light on the use of clustering for visualizing an ensemble of jet-stream core lines. Since classical approaches for clustering 3D line sets fail due to the mentioned properties, we analyze different strategies and compare them to each other: We cluster the 3D scalar fields from which jet-stream core lines are extracted. We cluster on a closest-point representation of each set of core lines. These representations are derived from the extracted line geometry and can be used independently of the line orientation and topology. We cluster on the 3D line set using the Hausdorff distance as similarity metric. In the resulting clusters, we visualize core lines from the most representative ensemble member. We further compute ridges in a single 3D visitation map that is build from the ensemble of core lines, and we extract the most central core line from the ensemble closest-point representation. These ''averages'' are compared to the clustering results, and they are put into relation to ground truth jet-stream core lines at the predicted lead time.
Efficient High-Quality Rendering of Ribbons and Twisted Lines
(The Eurographics Association, 2022) Neuhauser, Christoph; Wang, Junpeng; Kern, Michael; Westermann, Rüdiger; Bender, Jan; Botsch, Mario; Keim, Daniel A.
Flat twisting ribbons are often used for visualizing twists along lines in 3D space. Flat ribbons can disappear when looking at them under oblique angles, and they introduce flickering due to aliasing during animations. We demonstrate that this limitation can be overcome by procedurally rendering generalized cylinders with elliptic profiles. By adjusting the length of the cylinder's semi-minor axis, the ribbon thickness can be controlled so that it always remains visible. The proposed rendering approach further enables the visualization of twists via the projection of a line spiralling around the cylinder's center line. In contrast to texture mapping, this keeps the line width fixed, regardless of the strength of the twist, and provides efficient control over the spiralling frequency and coloring between the twisting lines. The proposed rendering approach can be performed efficiently on recent GPUs by exploiting programmable pulling, mesh shaders and hardware-accelerated ray tracing.
Evaluation of Volume Representation Networks for Meteorological Ensemble Compression
(The Eurographics Association, 2022) Höhlein, Kevin; Weiss, Sebastian; Necker, Tobias; Weissmann, Martin; Miyoshi, Takemasa; Westermann, Rüdiger; Bender, Jan; Botsch, Mario; Keim, Daniel A.
Recent studies have shown that volume scene representation networks constitute powerful means to transform 3D scalar fields into extremely compact representations, from which the initial field samples can be randomly accessed. In this work, we evaluate the capabilities of such networks to compress meteorological ensemble data, which are comprised of many separate weather forecast simulations. We analyze whether these networks can effectively exploit similarities between the ensemble members, and how alternative classical compression approaches perform in comparison. Since meteorological ensembles contain different physical parameters with various statistical characteristics and variations on multiple scales of magnitude, we analyze the impact of data normalization schemes on learning quality. Along with an evaluation of the trade-offs between reconstruction quality and network model parameterization, we compare compression ratios and reconstruction quality for different model architectures and alternative compression schemes.
A Globally Conforming Lattice Structure for 2D Stress Tensor Visualization
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Wang, Junpeng; Wu, Jun; Westermann, Rüdiger; Viola, Ivan and Gleicher, Michael and Landesberger von Antburg, Tatiana
We present a visualization technique for 2D stress tensor fields based on the construction of a globally conforming lattice. Conformity ensures that the lattice edges follow the principal stress directions and the aspect ratio of lattice elements represents the stress anisotropy. Since such a lattice structure cannot be space-filling in general, it is constructed from multiple intersecting lattice beams. Conformity at beam intersections is ensured via a constrained optimization problem, by computing the aspect ratio of elements at intersections so that their edges meet when continued along the principal stress lines. In combination with a coloring scheme that encodes relative stress magnitudes, a global visualization is achieved. By introducing additional constraints on the positional variation of the beam intersections, coherent visualizations are achieved when external loads or material parameters are changed. In a number of experiments using non-trivial scenarios, we demonstrate the capability of the proposed visualization technique to show the global and local structure of a given stress field.
Interactive Visual Exploration of Line Clusters
(The Eurographics Association, 2018) Kanzler, Mathias; Westermann, Rüdiger; Beck, Fabian and Dachsbacher, Carsten and Sadlo, Filip
We propose a visualization approach to interactively explore the structure of clusters of lines in 3D space. We introduce cluster consistency fields to indicate the local consistency of the lines in a cluster depending on line density and dispersion of line directions. Via brushing the user can select a focus region where lines are shown, and the consistency fields are used to automatically control the density of displayed lines according to information content. The brush is automatically continued along the gradient of the consistency field towards high information regions, or along a derived mean direction field to reveal major pathways. For a given line clustering, visualizations of cluster hulls are added to preserve context information.
Learning Generic Local Shape Properties for Adaptive Super-Sampling
(The Eurographics Association, 2022) Reinbold, Christian; Westermann, Rüdiger; Pelechano, Nuria; Vanderhaeghe, David
We propose a novel encoder/decoder-based neural network architecture that learns view-dependent shape and appearance of geometry represented by voxel representations. Since the network is trained on local geometry patches, it generalizes to arbitrary models. A geometry model is first encoded into a sparse voxel octree of features learned by a network, and this model representation can then be decoded by another network in-turn for the intended task. We utilize the network for adaptive supersampling in ray-tracing, to predict super-sampling patterns when seeing coarse-scale geometry. We discuss and evaluate the proposed network design, and demonstrate that the decoder network is compact and can be integrated seamlessly into on-chip ray-tracing kernels. We compare the results to previous screen-space super-sampling strategies as well as non-network-based world-space approaches.
Learning Multiple-Scattering Solutions for Sphere-Tracing of Volumetric Subsurface Effects
(The Eurographics Association and John Wiley & Sons Ltd., 2021) Leonard, Ludwic; Höhlein, Kevin; Westermann, Rüdiger; Mitra, Niloy and Viola, Ivan
Accurate subsurface scattering solutions require the integration of optical material properties along many complicated light paths. We present a method that learns a simple geometric approximation of random paths in a homogeneous volume with translucent material. The generated representation allows determining the absorption along the path as well as a direct lighting contribution, which is representative of all scatter events along the path. A sequence of conditional variational auto-encoders (CVAEs) is trained to model the statistical distribution of the photon paths inside a spherical region in the presence of multiple scattering events. A first CVAE learns how to sample the number of scatter events, occurring on a ray path inside the sphere, which effectively determines the probability of this ray to be absorbed. Conditioned on this, a second model predicts the exit position and direction of the light particle. Finally, a third model generates a representative sample of photon position and direction along the path, which is used to approximate the contribution of direct illumination due to in-scattering. To accelerate the tracing of the light path through the volumetric medium toward the solid boundary, we employ a sphere-tracing strategy that considers the light absorption and can perform a statistically accurate next-event estimation. We demonstrate efficient learning using shallow networks of only three layers and no more than 16 nodes. In combination with a GPU shader that evaluates the CVAEs' predictions, performance gains can be demonstrated for a variety of different scenarios. We analyze the approximation error that is introduced by the data-driven scattering simulation and shed light on the major sources of error.
Neural Fields for Interactive Visualization of Statistical Dependencies in 3D Simulation Ensembles
(The Eurographics Association, 2023) Farokhmanesh, Fatemeh; Höhlein, Kevin; Neuhauser, Christoph; Necker, Tobias; Weissmann, Martin; Miyoshi, Takemasa; Westermann, Rüdiger; Guthe, Michael; Grosch, Thorsten
We present neural dependence fields (NDFs) - the first neural network that learns to compactly represent and efficiently reconstruct the statistical dependencies between the values of physical variables at different spatial locations in large 3D simulation ensembles. Going beyond linear dependencies, we consider mutual information as an exemplary measure of non-linear dependence. We demonstrate learning and reconstruction with a large weather forecast ensemble comprising 1000 members, each storing multiple physical variables at a 250×352×20 simulation grid. By circumventing compute-intensive statistical estimators at runtime, we demonstrate significantly reduced memory and computation requirements for reconstructing the major dependence structures. This enables embedding the estimator into a GPU-accelerated direct volume renderer and interactively visualizing all mutual dependencies for a selected domain point.
Parameterized Splitting of Summed Volume Tables
(The Eurographics Association and John Wiley & Sons Ltd., 2021) Reinbold, Christian; Westermann, Rüdiger; Borgo, Rita and Marai, G. Elisabeta and Landesberger, Tatiana von
Summed Volume Tables (SVTs) allow one to compute integrals over the data values in any cubical area of a three-dimensional orthogonal grid in constant time, and they are especially interesting for building spatial search structures for sparse volumes. However, SVTs become extremely memory consuming due to the large values they need to store; for a dataset of n values an SVT requires O(nlogn) bits. The 3D Fenwick tree allows recovering the integral values in O(log3 n) time, at a memory consumption ofO(n) bits.We propose an algorithm that generates SVT representations that can flexibly trade speed for memory: From similar characteristics as SVTs, over equal memory consumption as 3D Fenwick trees at significantly lower computational complexity, to even further reduced memory consumption at the cost of raising computational complexity. For a 641x9601x9601 binary dataset, the algorithm can generate an SVT representation that requires 27.0 GB and 46 . 8 data fetch operations to retrieve an integral value, compared to 27.5 GB and 1521 . 8 fetches by 3D Fenwick trees, a decrease in fetches of 97%. A full SVT requires 247.6GB and 8 fetches per integral value. We present a novel hierarchical approach to compute and store intermediate prefix sums of SVTs, so that any prescribed memory consumption between O(n) bits and O(nlogn) bits is achieved. We evaluate the performance of the proposed algorithm in a number of examples considering large volume data, and we perform comparisons to existing alternatives.
Spatiotemporal Variance-Guided Filtering for Motion Blur
(ACM Association for Computing Machinery, 2022) Oberberger, Max; Chajdas, Matthäus G.; Westermann, Rüdiger; Josef Spjut; Marc Stamminger; Victor Zordan
Adding motion blur to a scene can help to convey the feeling of speed even at low frame rates. Monte Carlo ray tracing can compute accurate motion blur, but requires a large number of samples per pixel to converge. In comparison, rasterization, in combination with a post-processing filter, can generate fast, but not accurate motion blur from a single sample per pixel. We build upon a recent path tracing denoiser and propose its variant to simulate ray-traced motion blur, enabling fast and high-quality motion blur from a single sample per pixel. Our approach creates temporally coherent renderings by estimating the motion direction and variance locally, and using these estimates to guide wavelet filters at different scales. We compare image quality against brute force Monte Carlo methods and current post-processing motion blur. Our approach achieves real-time frame rates, requiring less than 4ms for full-screen motion blur at a resolution of 1920 × 1080 on recent graphics cards.
Triplanar Displacement Mapping for Terrain Rendering
(The Eurographics Association, 2020) Weiss, Sebastian; Bayer, Florian; Westermann, Rüdiger; Wilkie, Alexander and Banterle, Francesco
Heightmap-based terrain representations are common in computer games and simulations. However, adding geometric details to such a representation during rendering on the GPU is difficult to achieve. In this paper, we propose a combination of triplanar mapping, displacement mapping, and tessellation on the GPU, to create extruded geometry along steep faces of heightmap-based terrain fields on-the-fky during rendering. The method allows rendering geometric details such as overhangs and boulders, without explicit triangulation. We further demonstrate how to handle collisions and shadows for the enriched geometry.
Visualizing the Stability of 2D Point Sets from Dimensionality Reduction Techniques
(© 2020 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2020) Reinbold, Christian; Kumpf, Alexander; Westermann, Rüdiger; Benes, Bedrich and Hauser, Helwig
We use ‐order Voronoi diagrams to assess the stability of ‐neighbourhoods in ensembles of 2D point sets, and apply it to analyse the robustness of a dimensionality reduction technique to variations in its input configurations. To measure the stability of ‐neighbourhoods over the ensemble, we use cells in the ‐order Voronoi diagrams, and consider the smallest coverings of corresponding points in all point sets to identify coherent point subsets with similar neighbourhood relations. We further introduce a pairwise similarity measure for point sets, which is used to select a subset of representative ensemble members via the PageRank algorithm as an indicator of an individual member's value. The stability information is embedded into the ‐order Voronoi diagrams of the representative ensemble members to emphasize coherent point subsets and simultaneously indicate how stable they lie together in all point sets. We use the proposed technique for visualizing the robustness of t‐distributed stochastic neighbour embedding and multi‐dimensional scaling applied to high‐dimensional data in neural network layers and multi‐parameter cloud simulations.

Browsing by Author "Westermann, Rüdiger"

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