Exploring Flow Fields Using Space-Filling Analysis of Streamlines.

Large scale scientific simulations frequently use streamline based techniques to visualize flow fields. As the shape of a streamline is often related to some underlying property of the field, it is important to identify streamlines (or their parts) with unique geometric features. In this paper, we introduce a metric, called the box counting ratio, which measures the geometric complexity of streamlines by measuring their space-filling capacity at different scales. We propose a novel interactive visualization framework which utilizes this metric to extract, organize and visualize features of varying density and complexity hidden in large numbers of streamlines. The proposed framework extracts complex regions of varying density from the streamlines, and organizes and presents them on an interactive 2D information space, allowing user selection and visualization of streamlines. We also extend this framework to support exploration using an ensemble of measures including box counting ratio. Our framework allows the user to easily visualize and interact with features otherwise hidden in large vector field data. We strengthen our claims with case studies using combustion and climate simulation data sets.

Efficient local statistical analysis via integral histograms with discrete wavelet transform.

Histograms computed from local regions are commonly used in many visualization applications, and allowing the user to query histograms interactively in regions of arbitrary locations and sizes plays an important role in feature identification and tracking. Computing histograms in regions with arbitrary location and size, nevertheless, can be time consuming for large data sets since it involves expensive I/O and scan of data elements. To achieve both performance- and storage-efficient query of local histograms, we present a new algorithm called WaveletSAT, which utilizes integral histograms, an extension of the summed area tables (SAT), and discrete wavelet transform (DWT). Similar to SAT, an integral histogram is the histogram computed from the area between each grid point and the grid origin, which can be be pre-computed to support fast query. Nevertheless, because one histogram contains multiple bins, it will be very expensive to store one integral histogram at each grid point. To reduce the storage cost for large integral histograms, WaveletSAT treats the integral histograms of all grid points as multiple SATs, each of which can be converted into a sparse representation via DWT, allowing the reconstruction of axis-aligned region histograms of arbitrary sizes from a limited number of wavelet coefficients. Besides, we present an efficient wavelet transform algorithm for SATs that can operate on each grid point separately in logarithmic time complexity, which can be extended to parallel GPU-based implementation. With theoretical and empirical demonstration, we show that WaveletSAT can achieve fast preprocessing and smaller storage overhead than the conventional integral histogram approach with close query performance.

Feature tracking and visualization of the Madden-Julian oscillation in climate simulation.

The Madden-Julian oscillation (MJO) is one of the less understood aspects of tropical meteorology. It plays a significant role in tropical intraseasonal variations in rain, temperature, and winds over the Indian and Pacific Oceans. Researchers have developed an integrated analysis and visualization tool for MJO episodes simulated by a high-resolution regional model. To distinguish the MJO from other weather phenomena, the tool uses domain knowledge to track the MJO and find the globally optimized properties in the data. To visualize large-scale events in space and time, the tool integrates different visualization components such as a Hovmöller diagram and virtual globe. By linking the visualization components on a Web-based interface, the tool lets scientists more easily identify cloud and environmental processes associated with the MJO's onset and eastward propagation.

Load-balanced parallel streamline generation on large scale vector fields.

Because of the ever increasing size of output data from scientific simulations, supercomputers are increasingly relied upon to generate visualizations. One use of supercomputers is to generate field lines from large scale flow fields. When generating field lines in parallel, the vector field is generally decomposed into blocks, which are then assigned to processors. Since various regions of the vector field can have different flow complexity, processors will require varying amounts of computation time to trace their particles, causing load imbalance, and thus limiting the performance speedup. To achieve load-balanced streamline generation, we propose a workload-aware partitioning algorithm to decompose the vector field into partitions with near equal workloads. Since actual workloads are unknown beforehand, we propose a workload estimation algorithm to predict the workload in the local vector field. A graph-based representation of the vector field is employed to generate these estimates. Once the workloads have been estimated, our partitioning algorithm is hierarchically applied to distribute the workload to all partitions. We examine the performance of our workload estimation and workload-aware partitioning algorithm in several timings studies, which demonstrates that by employing these methods, better scalability can be achieved with little overhead.

An information-theoretic framework for flow visualization.

The process of visualization can be seen as a visual communication channel where the input to the channel is the raw data, and the output is the result of a visualization algorithm. From this point of view, we can evaluate the effectiveness of visualization by measuring how much information in the original data is being communicated through the visual communication channel. In this paper, we present an information-theoretic framework for flow visualization with a special focus on streamline generation. In our framework, a vector field is modeled as a distribution of directions from which Shannon's entropy is used to measure the information content in the field. The effectiveness of the streamlines displayed in visualization can be measured by first constructing a new distribution of vectors derived from the existing streamlines, and then comparing this distribution with that of the original data set using the conditional entropy. The conditional entropy between these two distributions indicates how much information in the original data remains hidden after the selected streamlines are displayed. The quality of the visualization can be improved by progressively introducing new streamlines until the conditional entropy converges to a small value. We describe the key components of our framework with detailed analysis, and show that the framework can effectively visualize 2D and 3D flow data.

Visualization and exploration of temporal trend relationships in multivariate time-varying data.

We present a new algorithm to explore and visualize multivariate time-varying data sets. We identify important trend relationships among the variables based on how the values of the variables change over time and how those changes are related to each other in different spatial regions and time intervals. The trend relationships can be used to describe the correlation and causal effects among the different variables. To identify the temporal trends from a local region, we design a new algorithm called SUBDTW to estimate when a trend appears and vanishes in a given time series. Based on the beginning and ending times of the trends, their temporal relationships can be modeled as a state machine representing the trend sequence. Since a scientific data set usually contains millions of data points, we propose an algorithm to extract important trend relationships in linear time complexity. We design novel user interfaces to explore the trend relationships, to visualize their temporal characteristics, and to display their spatial distributions. We use several scientific data sets to test our algorithm and demonstrate its utilities.