AI 中文总结
该研究提出了一种感知不确定性的雅可比集计算方法，基于多元正态分布的不确定性模型分析传播不确定性，结合专用视觉映射叠加，经解析数据集验证后应用于流体动力学和天气集合场景。
AI 中文摘要
我们提出了一种感知不确定性的雅可比集计算方法。雅可比集是一种拓扑描述子，用于捕获两个标量场的梯度对齐情况，例如可用于多场可视化。我们采用并重新表述了一种现有计算方法，该方法依赖于在给定三角剖分上基于边识别雅可比集边。我们对不确定性可视化的扩展基于一种通用的、空间一致的双标量场不确定性模型，该模型基于多元正态分布。我们分析地传播不确定性，从而将原始雅可比集计算提升到可处理不确定输入的水平。此外，我们提出了一种视觉映射叠加，专门设计用于显示雅可比集以及不同方面的不确定性信息。我们在一个解析数据集上针对蒙特卡洛方法验证了该不确定性模型和感知不确定性方法，并将其应用于流体动力学和天气集合的两个用例。
英文摘要
We present an uncertainty-aware Jacobi set computation method. In general, Jacobi sets are topological descriptors that capture the gradient alignments of two scalar fields, as, e.g., used for multi-field visualization. We adopt and reformulate an existing computational approach that relies on an edge-based identification of Jacobi set edges on a given triangulation. Our extension to uncertainty visualization builds upon a versatile, spatially coherent uncertainty model for pairs of scalar fields based on multivariate normal distributions. We propagate the uncertainty analytically, thereby lifting the original Jacobi set computation to uncertain inputs. Furthermore, we present an overlay of visual mappings specifically designed to show the Jacobi sets along with different facets of uncertainty information. Both the uncertainty model and uncertainty-aware method are validated against a Monte Carlo approach on an analytic dataset and applied to two use cases from fluid dynamics and weather ensembles.
Comments11 pages, 6 figures
