Uncertainty Visualization And Analysis

Data visualization aims at generating visual representations of data by exploiting shape, glyph, color, texture and so on. It is an important tool for users to understand the intrinsic structures and analyze interesting patterns within a dataset. Scientific visualization and information visualization are two conventional branches for the data visualization research. Recently, as the importance of data analysis by utilizing visualization techniques increases, visual analytics becomes a new branch for data visualization.When the states and outcomes of an object cannot be precisely described, uncertainty is produced. It is a crucial component of data. Different from data conflict and data error, which are induced by incorrect experimental setups, uncertainty inevitably spreads throughout the entire data visualization pipeline including acquisition, transformation, and visualization. Uncertainty has a significant impact on the reliability of the resulting visualization. It might cause wrong decisions made by users. In order to enable visualization to be a promising decision making tool, uncertainty should be clearly presented in the resulting visualizations.In this dissertation, we focus on modeling, quantifying, visualizing, and alleviating uncertain-ties introduced into different stages of the data visualization pipeline. The main contributions of this dissertation are summarized as follows:·We propose a uncertainty-aware multidimensional ensemble data visualization and explo-ration solution. Ensemble data are widely used in many numerical simulation applications to study uncertainties caused by simulation models and parameters. Challenges for analyzing a multidimensional ensemble dataset include both the uncertainty with respect to each variable of data objects and the high dimensionality. In this work, we first employ the kernel density estimation to reconstruct the high-dimensional distribution of each ensemble data object. Both differences between ensemble means and differences between ensemble distributions are leveraged to characterize the dissimilarity relationship between any two ensemble data objects. Afterwards, all ensemble data objects are projected onto a 2D visual plane with an enhanced Laplacian-based projection method. The low-dimensional layouts allow users to study the intrinsic structures and distribution patterns within the dataset. We also introduce two measures to quantify the overall uncertainty and distribution for an ensemble data object. Additionally, we develop a visual exploration system equipped with a set of visualization and interaction tools.·We propose a two-phase projection technique for visually exploring differences among curve-based fiber models. Fiber tracking is commonly used to transform a complex tensor field into a fiber model that consists of a bunch of 3D curves. In order to visually discovering and exploring differences among complex fiber models, we first register all fiber models into a common space. Then the two-phase projection method based on LMDS is exploited to project each fiber model onto the 2D visual plane. Kernel density estimation is further utilized to enhance the perceptual quality of the low-dimensional layout such that a set of signature maps are generated. To assist users identify regions of differences (RoD) among these signature maps, we harness the region growing algorithm to segment the thresholded variance map. We design the DiffRadar representation to show the detailed quantitative fiber metric differences within a RoD. In addition, we implement a visual difference exploration interface that follows the Juxtaposition and Explicit Encoding comparison schemes.·We propose a new visual abstraction and exploration technique for multi-class scatterplots based on a novel hierarchical multi-class blue noise sampling technique. This new sampling method cannot only reduce the number of shown data points but also preserves the relative density features among data classes. As such, the understanding and recognition uncertainty caused by limited screen space or point drawn orders can be alleviated. To enhance the perceptual quality of the abstracted set of data points, we formulate a point color optimization model and introduce two additional point shape designs that can encode local trends.