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Automatic detection of relevant structures in scientific data sets is still one of the big challenges in visualization. Techniques based on information theory have shown to be a promising direction to automatically highlight interesting subsets of a time-dependent data set. The methods that have been proposed so far, however, were restricted to the Eulerian view. In the Eulerian description of motion, a position fixed in space is observed over time. In fluid dynamics, however, not only the site-specific analysis of the flow is of interest, but also the temporal evolution of particles that are advected through the domain by the flow. This second description of motion is called the Lagrangian perspective. To support these two different frames of reference widely used in CFD research, we extend the notion of local statistical complexity (LSC) to make them applicable to Lagrangian and Eulerian flow descriptions. Thus, coherent structures can be identified by highlighting positions that either feature unusual temporal dynamics at a fixed position or that hold a particle that experiences such dynamics while passing through the position. A new area of application is opened by LagrangianLSC, which can be applied to short pathlines running through each position in the data set, as well as to individual pathlines computed for longer time intervals. Coloring the pathline according to the local complexity helps to detect extraordinary dynamics while the particle passes through the domain. The two techniques are explained and compared using different fluid flow examples.

Over the past decades, scientific visualization has helped tremendously to easily generate meaningful representations of complicated data sets. However, with data correlated over many dimensions and millions of points, only few of the standard techniques are directly applicable. Unsteady multifield visualizations require effective reduction of the data to be displayed. From a huge amount of information, scientists must be able to extract the most informative parts. ?-machines, a concept based on information theory, can handle this task. They're a finitestate machine representation of a system's dynamics, which can be represented as a directed graph (see Figure 1). The nodes encode the local dynamics given as a spatiotemporal stochastic pattern, and the edges indicate the flow's evolution. ?-machines consist of causal states and transitions between them. Several enhancements to the fundamental ?-machine representation can help users identify interesting time intervals, analyze the evolution of unusual local dynamics, and track features over time.

The visualization and exploration of multivariate data is still a challenging task. Methods either try to visualize all variables simultaneously at each position using glyph-based approaches or use linked views for the interaction between attribute space and physical domain such as brushing of scatterplots. Most visualizations of the attribute space are either difficult to understand or suffer from visual clutter. We propose a transformation of the high-dimensional data in attribute space to 2D that results in a point cloud, called attribute cloud, such that points with similar multivariate attributes are located close to each other. The transformation is based on ideas from multivariate density estimation and manifold learning. The resulting attribute cloud is an easy to understand visualization of multivariate data in two dimensions. We explain several techniques to incorporate additional information into the attribute cloud, that help the user get a better understanding of multivariate data. Using different examples from fluid dynamics and climate simulation, we show how brushing can be used to explore the attribute cloud and find interesting structures in physical space.

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.

Modern unsteady (multi-)field visualizations require an effective reduction of the data to be displayed. From a huge amount of information the most informative parts have to be extracted. Instead of the fuzzy application dependent notion of feature, a new approach based on information theoretic concepts is introduced in this paper to detect important regions. This is accomplished by extending the concept of local statistical complexity from finite state cellular automata to discretized (multi-)fields. Thus, informative parts of the data can be highlighted in an application-independent, purely mathematical sense. The new measure can be applied to unsteady multifields on regular grids in any application domain. The ability to detect and visualize important parts is demonstrated using diffusion, flow, and weather simulations.

In this paper, we present a novel three-stage process to visualize the structure of point clouds in arbitrary dimensions. To get insight into the structure and complexity of a data set, we would most preferably just look into it, e.g. by plotting its corresponding point cloud. Unfortunately, for orthogonal scatter plots, this only works up to three dimensions, and other visualizations, like parallel coordinates or scatterplot matrices, also have problems handling many dimensions and visual overlap of data entities.

Sound is an integral part of most movies and videos. In many situations, viewers of a video are unable to hear the sound track, for example, when watching it in a fast forward mode, viewing it by hearing-impaired viewers or when the plot is given as a storyboard. In this paper, we present an automated visualization solution to such problems. The system first detects the common components (such as music, speech, rain, explosions, and so on) from a sound track, then maps them to a collection of programmable visual metaphors, and generates a composite visualization. This form of sound visualization, which is referred to as SoundRiver, can be also used to augment various forms of video abstraction and annotated key frames and to enhance graphical user interfaces for video handling software. The SoundRiver conveys more semantic information to the viewer than traditional graphical representations of sound illustration, such as phonoautographs, spectrograms or artistic audiovisual animations.

Due to its nonlinear nature, the climate system shows quite high natural variability on different time scales, including multiyear oscillations such as the El Ni˜no Southern Oscillation phenomenon. Beside a shift of the mean states and of extreme values of climate variables, climate change may also change the frequency or the spatial patterns of these natural climate variations. Wavelet analysis is a well established tool to investigate variability in the frequency domain. However, due to the size and complexity of the analysis results, only few time series are commonly analyzed concurrently. In this paper we will explore different techniques to visually assist the user in the analysis of variability and variability changes to allow for a holistic analysis of a global climate model data set consisting of several variables and extending over 250 years. Our new framework and data from the IPCC AR4 simulations with the coupled climate model ECHAM5/MPI-OM are used to explore the temporal evolution of El Ni˜no due to climate change.

We present a method to extract and visualize vortices that originate from bounding walls of three-dimensional time- dependent flows. These vortices can be detected using their footprint on the boundary, which consists of critical points in the wall shear stress vector field. In order to follow these critical points and detect their transformations, affected regions of the surface are parameterized. Thus, an existing singularity tracking algorithm devised for planar settings can be applied. The trajectories of the singularities are used as a basis for seeding particles. This leads to a new type of streak line visualization, in which particles are released from a moving source. These generalized streak lines visualize the particles that are ejected from the wall. We demonstrate the usefulness of our method on several transient fluid flow datasets from computational fluid dynamics simulations.