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Item Analysis of Vortex Merge Graphs(The Eurographics Association, 2012) Kasten, Jens; Zoufahl, Andre; Hege, Hans-Christian; Hotz, Ingrid; Michael Goesele and Thorsten Grosch and Holger Theisel and Klaus Toennies and Bernhard PreimWe propose an analysis framework to investigate different flow quantities such as vorticity, λ<sub>2</sub> or the acceleration magnitude along vortex merge graphs and within their regions of influence. The explicit extraction of vortex merge graphs enables the application of statistical tools to investigate the vortex core lines themselves. The analysis tool provides common plots as scatter plots and parallel coordinates to explore the correlation of different quantities. An abstract representation of the vortex merge graph highlights birth, death and merges of vortices. Interactive picking of substructures supports a closer insepection of single vortices and their evolution. A further step integrates the regions of influence into the statistical analysis. Minima, maxima, median, mean and other percentiles of the measures along the vortex merge graph and its regions are visualized. The usability of the framework is demonstrated using a simulated flow data set of a mixing layer and a jet.Item Synaptic Connectivity in Anatomically Realistic Neural Networks: Modeling and Visual Analysis(The Eurographics Association, 2012) Dercksen, Vincent J.; Egger, Robert; Hege, Hans-Christian; Oberlaender, Marcel; Timo Ropinski and Anders Ynnerman and Charl Botha and Jos RoerdinkThe structural organization of neural circuitry is an important determinant of brain function. Thus, knowing the brain's wiring (the connectome) is key to understanding how it works. For example, understanding how sensory information is translated into behavior requires a comprehensive view of the microcircuits performing this translation at the level of individual neurons and synapses. Obtaining a wiring diagram, however, is nontrivial due to size, complexity and accessibility of the involved brain regions. Even when such data were available, it were difficult to analyze. Here we describe how a network of around 0.5 million neurons and their synaptic connections, representing the vibrissal area of the rat primary somatosensory cortex, can be reconstructed. Furthermore, we present a framework for visual exploration of synaptic connectivity between (groups of) neurons within this model. It includes, first, the Cortical Column Connectivity Viewer (CCCV) that provides a hybrid abstract/spatial representation of the connections between neurons of different cell types and/or in different cortical columns. Second, it comprises a 3D view of cell type-specific synapse positions on selected morphologies. This framework is thus an effective tool to visually explore structural organization principles at the population, individual neuron and synapse levels.Item Hardware-Accelerated Point-Based Rendering of Complex Scenes(The Eurographics Association, 2002) Coconu, Liviu; Hege, Hans-Christian; P. Debevec and S. GibsonHigh quality point rendering methods have been developed in the last years. A common drawback of these approaches is the lack of hardware support. We propose a novel point rendering technique that yields good image quality while fully making use of hardware acceleration. Previous research revealed various advantages and drawbacks of point rendering over traditional rendering. Thus, a guideline in our algorithm design has been to allow both primitive types simultaneously and dynamically choose the best suited for rendering. An octree-based spatial representation, containing both triangles and sampled points, is used for level-of-detail and visibility calculations. Points in each block are stored in a generalized layered depth image. McMillan s algorithm is extended and hierarchically applied in the octree to warp overlapping Gaussian fuzzy splats in occlusion-compatible order and hence z-buffer tests are avoided. We show how to use off-the-shelf hardware to draw elliptical Gaussian splats oriented according to normals and to perform texture filtering. The result is a hybrid polygon-point system with increased efficiency compared to previous approaches.Item 3D Strokes on Visible Structures in Direct Volume Rendering(The Eurographics Association, 2013) Wiebel, Alexander; Preis, Philipp; Vos, Frans M.; Hege, Hans-Christian; Mario Hlawitschka and Tino WeinkaufIn this paper we describe VisiTrace, a novel technique to draw 3D lines in direct volume rendered images. It allows to draw strokes in the 2D space of the screen to produce 3D lines that run on top or in the center of structures visible in the rendering. It is able to ignore structures that shortly occlude the structure that has been visible at the start of the stroke. For this purpose a shortest path algorithm finding the optimal curve in a specially designed graph is employed. We demonstrate the usefulness of the technique by applying it to image data from medicine and engineering, and show how it can be used to mark structures in the example data, and to automatically obtain good views toward these structures enabling faster navigation in the rendering.Item Nonparametric Models for Uncertainty Visualization(The Eurographics Association and Blackwell Publishing Ltd., 2013) Pöthkow, Kai; Hege, Hans-Christian; B. Preim, P. Rheingans, and H. TheiselAn uncertain (scalar, vector, tensor) field is usually perceived as a discrete random field with a priori unknown probability distributions. To compute derived probabilities, e.g. for the occurrence of certain features, an appropriate probabilistic model has to be selected. The majority of previous approaches in uncertainty visualization were restricted to Gaussian fields. In this paper we extend these approaches to nonparametric models, which are much more flexible, as they can represent various types of distributions, including multimodal and skewed ones. We present three examples of nonparametric representations: (a) empirical distributions, (b) histograms and (c) kernel density estimates (KDE). While the first is a direct representation of the ensemble data, the latter two use reconstructed probability density functions of continuous random variables. For KDE we propose an approach to compute valid consistent marginal distributions and to efficiently capture correlations using a principal component transformation. Furthermore, we use automatic bandwidth selection, obtaining a model for probabilistic local feature extraction. The methods are demonstrated by computing probabilities of level crossings, critical points and vortex cores in simulated biofluid dynamics and climate data.Item Terrain Rendering using Spherical Clipmaps(The Eurographics Association, 2006) Clasen, Malte; Hege, Hans-Christian; Beatriz Sousa Santos and Thomas Ertl and Ken JoyWe describe a terrain rendering algorithm for spherical terrains based on clipmaps. It leverages the high geometry throughput of current GPU to render large static triangle sets. The vertices are displaced by a height map texture. Our main contribution is mapping of texture coordinates to calculate the height map sample position based on the static vertex offset and the variable view position.Item Galilean Invariant Extraction and Iconic Representation of Vortex Core Lines(The Eurographics Association, 2005) Sahner, Jan; Weinkauf, Tino; Hege, Hans-Christian; Ken Brodlie and David Duke and Ken JoyWhile vortex region quantities are Galilean invariant, most methods for extracting vortex cores depend on the frame of reference. We present an approach to extracting vortex core lines independently of the frame of reference by extracting ridge and valley lines of Galilean invariant vortex region quantities. We discuss a generalization of this concept leading to higher dimensional features. For the visualization of extracted line features we use an iconic representation indicating their scale and extent. We apply our approach to datasets from numerical simulations and experimental measurements.Item Atomic Accessibility Radii for Molecular Dynamics Analysis(The Eurographics Association, 2018) Lindow, Norbert; Baum, Daniel; Hege, Hans-Christian; Jan Byska and Michael Krone and Björn SommerIn molecular structure analysis and visualization, the molecule's atoms are often modeled as hard spheres parametrized by their positions and radii. While the atom positions result from experiments or molecular simulations, for the radii typically values are taken from literature. Most often, van der Waals (vdW) radii are used, for which diverse values exist. As a consequence, different visualization and analysis tools use different atomic radii, and the analyses are less objective than often believed. Furthermore, for the geometric accessibility analysis of molecular structures, vdW radii are not well suited. The reason is that during the molecular dynamics simulation, depending on the force field and the kinetic energy in the system, non-bonded atoms can come so close to each other that their vdW spheres intersect. In this paper, we introduce a new kind of atomic radius, called 'atomic accessibility radius', that better characterizes the accessibility of an atom in a given molecular trajectory. The new radii reflect the movement possibilities of atoms in the simulated physical system. They are computed by solving a linear program that maximizes the radii of the atoms under the constraint that non-bonded spheres do not intersect in the considered molecular trajectory. Using this data-driven approach, the actual accessibility of atoms can be visualized more precisely.Item Visibility-Driven Depth Determination of Surface Patches in Direct Volume Rendering(The Eurographics Association, 2014) Stoppel, Sergej; Hege, Hans-Christian; Wiebel, Alexander; N. Elmqvist and M. Hlawitschka and J. KennedyThis paper presents an algorithm called surfseek for selecting surfaces on the most visible features in directvolume rendering (DVR). The algorithm is based on a previously published technique (WYSIWYP) for picking 3Dlocations in DVR. The new algorithm projects a surface patch on the DVR image, consisting of multiple rays. Foreach ray the algorithm uses WYSIWYP or a variant of it to find the candidates for the most visible locations alongthe ray. Using these candidates the algorithm constructs a graph and computes a minimum cut on this graph.The minimum cut represents a visible and typically rather smooth surface. In the last step the selected surface isdisplayed. We provide examples for results using artificially generated and real-world data sets.Item Probabilistic Local Features in Uncertain Vector Fields with Spatial Correlation(The Eurographics Association and Blackwell Publishing Ltd., 2012) Petz, Christoph; Pöthkow, Kai; Hege, Hans-Christian; S. Bruckner, S. Miksch, and H. PfisterIn this paper methods for extraction of local features in crisp vector fields are extended to uncertain fields. While in a crisp field local features are either present or absent at some location, in an uncertain field they are present with some probability. We model sampled uncertain vector fields by discrete Gaussian random fields with empirically estimated spatial correlations. The variability of the random fields in a spatial neighborhood is characterized by marginal distributions. Probabilities for the presence of local features are formulated in terms of low-dimensional integrals over such marginal distributions. Specifically, we define probabilistic equivalents for critical points and vortex cores. The probabilities are computed by Monte Carlo integration. For identification of critical points and cores of swirling motion we employ the Poincaré index and the criterion by Sujudi and Haimes. In contrast to previous global methods we take a local perspective and directly extract features in divergence-free fields as well. The method is able to detect saddle points in a straight forward way and works on various grid types. It is demonstrated by applying it to simulated unsteady flows of biofluid and climate dynamics.