Uncertainty and Error Analysis in the Visualization of Multidimensional and Ensemble Datasets.

다국어 초록 (Multilingual Abstract)

Analysis and quantification of uncertainty have become an integral part of the modern day data analysis and visualization frameworks. Varied amounts of uncertainty are introduced throughout the different stages of the visualization pipeline. While visualizing the scientific data sets, it is now imperative to provide an estimation of the associated uncertainty such that the users can readily assess the reliability of the visualization tools. Quantification of uncertainty is non-trivial for scalar data sets and this problem becomes even harder while handling multivariate and vector data sets. In this dissertation, several techniques are presented that identify, utilize and quantify uncertainty for multi-dimensional data sets. These techniques can be broadly classified into two groups: a) analysis of the existence of relationships and features and b) identification and analysis of error in flow visualization tools. The first category of studies use multivariate and ensemble datasets for analyzing relationship uncertainties. The second category of studies primarily use vector fields to demonstrate streamlines and stream surface for error analysis.
In the analysis stage, we initially present an information theoretic framework towards the exploration of uncertainty in the relationships of multivariate datasets. We show that, in a multivariate system, variables can show interdependence on each other and information theoretic distance can be effectively used to find a hierarchical grouping of these variables. Using information content as the importance measure, salient variables are identified to start the variable exploration process. Specific mutual information is used for classifying the isosurfaces of one variable such that they reveal uncertainty regarding the other selected variables. Feedback from the ocean scientists establishes the superiority of this system over the existing techniques. From multivariate relationships, next we discuss the uncertainty in the relationship between ensemble output and input parameters and further propose models for output error estimation. In this case, we show how a spatial and temporal analysis can help in revealing the sensitivity of the input parameters in a multi-resolution ensemble data set. We employ spatial clustering and temporal aggregation to create an interactive tool for exploration of uncertain sensitivity information. A Bayes' rule-based error estimation approach is provided with another interactive tool for spatio-temporal multi-resolution error exploration. From relationship analysis, we next analyze the uncertainties in feature detection where the feature is a vortex. Vortices are very important features of the flow field but detection of these are not free of uncertainties. Although there are several vortex detection techniques available, they have varying amounts of robustness while detecting these features which in turn introduces uncertainty. Another source of uncertainty is the selection of threshold values for the local point based methods. Here, we use the logistic function to model the threshold selection uncertainty and use multiple uncertain existing detectors to combine them into a more robust vortex detection scheme. Measuring against the domain expert's vortex labels, our proposed method shows higher accuracy compared to the existing vortex methods.
Next, we focus on the visualization tools: streamlines and stream surfaces. For streamlines, we analyze and quantify the error in streamline generation and propose an implicit streamline strategy that scales well with good load balancing. We use a flux-based approach to generate the local streamlines and then use a parallel flux-offset propagation technique to create a scalar field from a given large two-dimensional vector field. Using this field, isocontour extraction strategy is used for final streamline visualization. This method exhibits much improved performance compared to the existing techniques. Finally, we work with stream surfaces that are popular flow visualization tools and propose four different techniques to quantify the visualization errors. Our proposed techniques provide a trade-off between computation speed and accuracy and we select three popular existing stream surface generation methods to study their behaviors. Using our proposed methods, a comprehensive report is generated to explore how the quality of stream surfaces change depending on the selection of algorithms, and choices of parameters and data complexity.