三维对称二阶张量场集合中退化张量的不确定性可视化探索
Exploring Uncertainty Visualization for Degenerate Tensors in 3D Symmetric Second-Order Tensor Field Ensembles
AI总结：
本文探索了三维对称二阶张量场集合中退化张量位置的不确定性可视化新方法，基于张量模式分析其实用性并提出多种可视化策略，有效传达了退化张量信息。
摘要：
对称二阶张量在各类科学和工程领域至关重要，因为它们能够表示诸如材料应力或脑组织中的扩散过程等属性。近年来，人们引入并改进了多种方法，利用拓扑特征（如退化张量位置，即张量具有重复特征值，或法向曲面）来分析这些场。传统上，对此类特征的识别仅限于单一张量场。然而，为了考虑模拟和测量中的不确定性与变异性，创建张量场集合已成为常见做法。在本研究中，我们探索了描述和可视化三维对称二阶张量场集合中退化张量位置的新方法。我们以张量模式为基础，分析其在表征退化张量位置不确定性方面的实用性，随后提出多种可视化策略以有效传达退化张量信息。我们在合成数据集和模拟数据集上演示了这些技术。结果表明，不同不确定性描述之间的相互作用能够有效传达有关退化张量位置的信息。
英文摘要：
Symmetric second-order tensors are fundamental in various scientific and engineering domains, as they can represent properties such as material stresses or diffusion processes in brain tissue. In recent years, several approaches have been introduced and improved to analyze these fields using topological features, such as degenerate tensor locations, i.e., the tensor has repeated eigenvalues, or normal surfaces. Traditionally, the identification of such features has been limited to single tensor fields. However, it has become common to create ensembles to account for uncertainties and variability in simulations and measurements. In this work, we explore novel methods for describing and visualizing degenerate tensor locations in 3D symmetric second-order tensor field ensembles. We base our considerations on the tensor mode and analyze its practicality in characterizing the uncertainty of degenerate tensor locations before proposing a variety of visualization strategies to effectively communicate degenerate tensor information. We demonstrate our techniques for synthetic and simulation data sets. The results indicate that the interplay of different descriptions for uncertainty can effectively convey information on degenerate tensor locations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
