III: Small: Uncertainty Quantification and Propagation Analysis in The Visualization Pipeline

存在不确定性的决策是一个臭名昭著的问题，在复杂的环境中做出理性的选择往往需要分析和预测。随着用于数据可视化和分析的计算工具在各种决策场景中的流行，在量化、传播和理解不确定性方面出现了新的挑战。该项目研究了数据不确定性与数据分析过程的相互作用，因为不同的特征被提取和可视化。当数据在可视化管道的各个阶段传播时，它解决了在分析和量化不确定性时出现的基本挑战。这种不确定性感知框架允许在成像管道中进行端到端灵敏度分析，其中数据采集中的不确定性在整个合成过程中传播。不确定性量化在集成仿真和可视化、成像逆问题和大规模数据可视化等应用领域中出现的问题推动了研究的开展。该项目通过为研究生提供研究培训和指导其他受训者，拓宽了计算机科学教育。为了通过可视化管道对不确定性的传播进行建模，该项目开发了一个统计呈现框架，其中每个数据点都是一个随机变量，其分布表征了该点存在的不确定性。该项目解决了成像和可视化中出现的挑战，其中数据转换（例如，数据过滤、重建、分类和等值面提取）导致对不确定性的非线性转换。随着不确定性在可视化过程中的传播，这些随机变量分布上的非线性变换会不断累积。这个项目开发了新的方法来描述这些变换，这些变换在各种可视化算法中都很常见。这个项目的发展使不确定性作为一个一流的对象，能够在直接和间接可视化范例中呈现的关键数据转换中集成。此外，由于这些数据转换在广泛的数据处理操作中无处不在，该项目为各种数据分析和可视化系统中的不确定性量化提供了可能性。由此产生的算法、软件和出版物可通过项目网站（http://www.cise.ufl.edu/~entezari/research/uqp/）访问。

Decision making in presence of uncertainty is a notorious problem where making rational choices often requires analysis and prediction in complex environments. With the prevalence of computational tools for data visualization and analysis that are employed in diverse decision making scenarios, new challenges arise in quantifying, propagating and understanding uncertainty. This project investigates the interaction of data uncertainty with the data analysis process as different features are extracted and visualized. It addresses fundamental challenges that arise in analysis and quantification of uncertainty as the data propagates throughout various stages of the visualization pipeline. This uncertainty-aware framework allows for an end-to-end sensitivity analysis in imaging pipeline where the uncertainties in data acquisition are propagated throughout the synthesis process. The research is driven by problems that arise in uncertainty quantification in a number of application domains including: ensemble simulation and visualization, inverse problems in imaging, and large-scale data visualization. The project broadens the computer science education by providing research training for graduate students and mentoring other trainees. To model the propagation of uncertainty through the visualization pipeline, this project develops a statistical rendering framework in which each data point is a random variable whose distribution characterizes the uncertainty present at that point. The project addresses challenges that arise in imaging and visualization where data transformations (e.g., data filtering, reconstruction, classification, and isosurface extraction) lead to non-linear transformation on the uncertainty. These non-linear transformations on the distribution of random variables accumulate as the uncertainty propagates through the visualization process. This project develops novel approaches for characterizing these transformations that are common to various visualization algorithms. The developments in this project enable the integration of uncertainty, as a first class object, within the key data transformations present in direct and indirect visualization paradigms. Moreover, due to the ubiquity of these data transformations in a wide range of data processing operators, this project opens possibilities for uncertainty quantification in a diverse set of data analysis and visualization systems. The resulting algorithms, software and publications are made accessible via the project web site (http://www.cise.ufl.edu/~entezari/research/uqp/).