Alex Pang

APPROACHES TO UNCERTAINTY VISUALIZATION

Visualized data often have dubious origins and quality. Different forms of uncertainty and errors are also introduced as the data are derived, transformed, interpolated, and finally rendered. In the absence of integrated presentation of data and uncertainty, the analysis of the visualization is incomplete at best and often leads to inaccurate or incorrect conclusions. This paper surveys techniques for presenting data together with uncertainty. These uncertainty visualization techniques present data in such a manner that users are made aware of the locations and degree of uncertainties in their data so as to make more informed analyses and decisions. The techniques include adding glyphs, adding geometry, modifying geometry, modifying attributes, animation, sonification, and psycho-visual approaches. We present our results in uncertainty visualization for environmental visualization, surface interpolation, global illumination with radiosity, flow visualization, and figure animation. We also present a classification of the possibilities in uncertainty visualization, and locate our contributions within this classification.

Glyphs for visualizing uncertainty in vector fields

Environmental data have inherent uncertainty which is often ignored in visualization. Meteorological stations and doppler radars, including their time series averages, have a wealth of uncertainty information that traditional vector visualization methods such as meteorological wind barbs and arrow glyphs simply ignore. We have developed a new vector glyph to visualize uncertainty in winds and ocean currents. Our approach is to include uncertainty in direction and magnitude, as well as the mean direction and length, in vector glyph plots. Our glyph shows the variation in uncertainty, and provides fair comparisons of data from instruments, models, and time averages of varying certainty. We also define visualizations that incorporate uncertainty in an unambiguous manner as verity visualization. We use both quantitative and qualitative methods to compare our glyphs to traditional ones. Subjective comparison tests with experts are provided, as well as objective tests, where the information density of our new glyphs and traditional glyphs are compared. The design of the glyph and numerous examples using environmental data are given. We show enhanced visualizations, data together with their uncertainty information, that may improve understanding of environmental vector field data quality.

A flow-guided streamline seeding strategy

The paper presents a seed placement strategy for streamlines based on flow features in the dataset. The primary goal of our seeding strategy is to capture flow patterns in the vicinity of critical points in the flow field, even as the density of streamlines is reduced. Secondary goals are to place streamlines such that there is sufficient coverage in non-critical regions, and to vary the streamline placements and lengths so that the overall presentation is aesthetically pleasing (avoid clustering of streamlines, avoid sharp discontinuities across several streamlines, etc.). The procedure is straightforward and non-iterative. First, critical points are identified. Next, the flow field is segmented into regions, each containing a single critical point. The critical point in each region is then seeded with a template depending on the type of critical point. Finally, additional seed points are randomly distributed around the field using a Poisson disk distribution to minimize closely spaced seed points. The main advantage of this approach is that it does not miss the features around critical points. Since the strategy is not image-guided, and hence not view dependent, significant savings are possible when examining flow fields from different viewpoints, especially for 3D flow fields.

UFLOW: visualizing uncertainty in fluid flow

Uncertainty or errors are introduced in fluid flow data as the data is acquired, transformed and rendered. Although researchers are aware of these uncertainties, little has been done to incorporate them in the existing visualization systems for fluid flow. In the absence of integrated presentation of data and its associated uncertainty, the analysis of the visualization is incomplete at best and may lead to inaccurate or incorrect conclusions. The article presents UFLOW-a system for visualizing uncertainty in fluid flow. Although there are several sources of uncertainties in fluid flow data, in this work, we focus on uncertainty arising from the use of different numerical algorithms for computing particle traces in a fluid flow. The techniques that we have employed to visualize uncertainty in fluid flow include uncertainty glyphs, flow envelopes, animations, priority sequences, twirling batons of trace viewpoints, and rakes. These techniques are effective in making the users aware of the effects of different integration methods and their sensitivity, especially near critical points in the flow field.

Visualizing scalar volumetric data with uncertainty

Abstract Increasingly, more importance is placed on the uncertainty information of data being displayed. This paper focuses on techniques for visualizing 3D scalar data sets with corresponding uncertainty information at each point which is also represented as a scalar value. In Djurcilov (in: D. Ebert, J.M. Favre, R. Peikert (Eds.), Data Visualization 2001, Springer, Berlin, 2001), we presented two general methods (inline DVR approach and a post-processing approach) for carrying out this task. The first method involves incorporating the uncertainty information directly into the volume rendering equation. The second method involves post-processing information of volume rendered images to composite uncertainty information. Here, we provide further improvements to those techniques primarily by showing the depth cues for the uncertainty, and also better transfer function selections.

Strategy for seeding 3D streamlines

This paper presents a strategy for seeding streamlines in 3D flow fields. Its main goal is to capture the essential flow patterns and to provide sufficient coverage in the field while reducing clutter. First, critical points of the flow field are extracted to identify regions with important flow patterns that need to be presented. Different seeding templates are then used around the vicinity of the different critical points. Because there is significant variability in the flow pattern even for the same type of critical point, our template can change shape depending on how far the critical point is from transitioning into another type of critical point. To accomplish this, we introduce the /spl alpha/-/spl beta/ map of 3D critical points. Next, we use Poisson seeding to populate the empty regions. Finally, we filter the streamlines based on their geometric and spatial properties. Altogether, this multi-step strategy reduces clutter and yet captures the important 3D flow features.

Collaborative 3D visualization with CSpray

CSpray lets small groups of geographically distributed scientists share data and interactively create visualizations. It features different information-sharing levels, a session manager, and 3D visualization aids.

Visualizing spatial multivalue data

We introduce multivalue data as a new data type in the context of scientific visualization. While this data type has existed in other fields, the visualization community has largely ignored it. Formally, a multivalue datum is a collection of values about a single variable. Multivalue data sets can be defined for multiple dimensions. A spatial multivalue data set consists of a multivalue datum at each physical location in the domain. The time dimension is equally valid. This leads to spatio-temporal multivalue data sets where there is time varying, multidimensional data with a multivalue datum at each location and time. The spatial multivalue data type captures multiple instances of the same variable at each location in space. Visualizing spatial multivalue data sets is a new challenge.

Comparative flow visualization

There are many situations where one needs to compare two or more data sets. It may be to compare different models, different resolutions, differences in algorithms, different experimental results, etc. There is therefore a need for comparative visualization tools to help analyze the differences. This paper focuses on comparative visualization tools for analyzing flow or vector data sets. The techniques presented allow one to compare individual streamlines and stream ribbons as well as a dense field of streamlines. These comparison methods can also be used to study differences in vortex cores that are represented as polylines.

Topological Lines in 3D Tensor Fields

Visualization of 3D tensor fields continues to be a major challenge in terms of providing intuitive and uncluttered images that allow the users to better understand their data. The primary focus of this paper is on finding a formulation that lends itself to a stable numerical algorithm for extracting stable and persistent topological features from 2nd order real symmetric 3D tensors. While features in 2D tensors can be identified as either wedge or trisector points, in 3D, the corresponding stable features are lines, not just points. These topological feature lines provide a compact representation of the 3D tensor field and are essential in helping scientists and engineers understand their complex nature. Existing techniques work by finding degenerate points and are not numerically stable, and worse, produce both false positive and false negative feature points. This work seeks to address this problem with a robust algorithm that can extract these features in a numerically stable, accurate, and complete manner.