2D标量场临界点在参数和非参数概率模型下的不确定性可视化
Uncertainty Visualization of Critical Points of 2D Scalar Fields for Parametric and Nonparametric Probabilistic Models
AI总结：
本文提出一种端到端框架，通过推导闭式和半解析解计算2D不确定标量场临界点的不确定性，利用VTK-m并行加速并集成至ParaView，实现了比传统MC采样更高效准确的近实时可视化。
摘要：
本文提出了一种新颖的端到端框架，用于对2D不确定标量场中的临界点不确定性进行闭式计算和可视化。临界点是用于标量场可视化和分析的基本拓扑描述符。然而，数据中固有的不确定性（例如观测和实验数据、模拟中的近似以及压缩）会导致临界点位置的不确定性。因此，鉴于其对下游数据分析任务的影响，临界点位置的不确定性不容忽视。在本研究中，我们将临界点的不确定性作为用概率分布建模的数据不确定性的函数进行研究。尽管先前的研宄使用蒙特卡洛（MC）采样技术来量化临界点的不确定性，但它们通常计算成本高昂，且很少用于生产级可视化软件。因此，我们提出一个新的端到端框架来应对这些挑战，该框架包含三方面的贡献。首先，我们以闭式形式推导出临界点的不确定性，这比传统的MC采样方法更准确且更高效。具体而言，我们为具有有限支撑的参数模型（如均匀分布、Epanechnikov分布）和非参数模型（如直方图）提供了闭式和半解析（闭式与MC方法的混合）解。其次，我们使用VTK-m库的并行实现加速了临界点概率计算，该库具有平台可移植性。最后，我们展示了将我们的实现与ParaView软件系统集成，以展示真实数据集的近实时结果。
英文摘要：
This paper presents a novel end-to-end framework for closed-form computation and visualization of critical point uncertainty in 2D uncertain scalar fields. Critical points are fundamental topological descriptors used in the visualization and analysis of scalar fields. The uncertainty inherent in data (e.g., observational and experimental data, approximations in simulations, and compression), however, creates uncertainty regarding critical point positions. Uncertainty in critical point positions, therefore, cannot be ignored, given their impact on downstream data analysis tasks. In this work, we study uncertainty in critical points as a function of uncertainty in data modeled with probability distributions. Although Monte Carlo (MC) sampling techniques have been used in prior studies to quantify critical point uncertainty, they are often expensive and are infrequently used in production-quality visualization software. We, therefore, propose a new end-to-end framework to address these challenges that comprises a threefold contribution. First, we derive the critical point uncertainty in closed form, which is more accurate and efficient than the conventional MC sampling methods. Specifically, we provide the closed-form and semianalytical (a mix of closed-form and MC methods) solutions for parametric (e.g., uniform, Epanechnikov) and nonparametric models (e.g., histograms) with finite support. Second, we accelerate critical point probability computations using a parallel implementation with the VTK-m library, which is platform portable. Finally, we demonstrate the integration of our implementation with the ParaView software system to demonstrate near-real-time results for real datasets.
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