META: Multifield Extension of Topological Analysis

物理学家、工程师和临床医生依靠可视化来洞察扫描和模拟产生的数据。自20世纪80年代以来，美国国家科学基金会的一份有影响力的报告引入了使用图形来理解大量数值数据的方法，可视化技术在以重大突破为标志的浪潮中取得了进展，包括：用于解释标量场的“行进立方体”及其导数，用于固有体积数据的体绘制，以及用于理解流结构的矢量场拓扑。然而，现有的可视化技术仅限于数据、温度、压力、速度、涡度、切变、燃烧速率、降雨量等个别属性。在信息可视化中确实存在多变量(多场)数据的技术，其中广泛使用平行坐标、蜘蛛图等。但这些工具对科学数据集用处不大，因为对数据的解释与物理空间/时间密切相关，或者与科学数据集的规模密切相关，科学数据集的规模通常以千兆字节或兆兆字节来衡量。关键问题是，到目前为止，我们还缺乏任何合适的数学和计算模型来进行多场分析。需要数学来解释理解多个场如何交互的确切含义；需要计算模型来解释如何将这种交互映射为可以从大量数据高效生成的视觉表示。多场分析技术将在依赖(科学)可视化的各种应用领域带来巨大好处，包括航空航天、材料工程、气候学和气象学、天体物理学、放射学和外科手术规划。它将带来新的科学见解，并为工业界提供新的工具，通过这些工具来发展竞争优势。申请者最近的工作取得了突破性成果。“联合等高线网络”是一个新的抽象概念，在提供多个领域所需的数学和计算机器方面有着巨大的希望。JCN起源于计算拓扑学，这一领域在过去十年中通过发现和解释数据中的结构对可视化做出了重大贡献。拓扑为识别数据中的功能和转换提供了严格的基础，最终用户在了解原始问题时对这些功能和转换特别感兴趣。拓扑模型在简化和呈现海量数据集方面也是必不可少的，因为我们解释数据的能力必须通过屏幕空间(通常约为200万像素)的瓶颈和人类视觉系统的千兆字节限制。联合等值线网络第一次展示了如何将拓扑分析从一个领域推广到多个领域，以及重要的是，如何有效地这样做，并以一种适应并行化的方式扩大到处理海量数据集。这项提议将通过发展多领域分析的数学理论，产生理解多领域行为所需的数学理论和视觉抽象来兑现最初的承诺。为了实现这一目标，我们将与可视化和计算拓扑领域的其他国际领先者密切合作，以解决具体问题，例如基于JCN的简化和渲染技术，以及用于指导分析的用户界面，以适应特定应用的需求。为了确保研究具有最大可能的影响，我们将把我们的软件嵌入到最广泛使用的可视化工具包中，致力于确保实施是可靠和可维护的，并将培训最终用户应用程序。

Physical scientists, engineers and clinicians rely on visualization to obtain insight into data arising from scans and simulation. Since the 1980s, when an influential US NSF report ushered in the use of graphics to make sense of large volumes of numerical data, visualization techniques have advanced in surges marked by major breakthroughs, including: "marching cubes" and its derivatives for interpreting scalar fields, volume rendering for inherently volumetric data; and vector field topology for understanding the structure of flow. However, existing visualization techniques are limited to individual properties of data, temperature, pressure, velocity, vorticity, shear, combustion rate, rainfall, and so on. Techniques for multivariate (multifield) data do exist in information visualization, where parallel coordinates, spider plots etc are widely used. But these tools are of little use for scientific datasets, where the interpretation of data is intimately tied to physical space/time, or to the scale of scientific datasets, which is routinely measured in gigabytes or terabytes. The key problem is that, until now, we have lacked any suitable mathematical and computational model for multifield analysis. The mathematics is needed to explain what exactly it means to understand how multiple fields interact; the computational model is needed to explain how this interaction can be mapped into visual representations that can be generated efficiently from large volumes of data. Techniques for multifield analysis would be of enormous benefit right across the diverse range of application domains that rely on (scientific) visualization, including aerospace, materials engineering, climatology and meterology, astrophysics, radiology and surgical planning. It would enable new scientific insight, and provide industry with new tools through which to develop competitive advantage.Recent work by the applicants has achieved a breakthrough result. The "Joint Contour Net" is a new abstraction that hold great promise in providing the mathematical and computational machinery needed for multifields. The origins of the JCN are in computational topology, a field that, over the last decade, has made major contributions to visualization through finding and explaining structure within data. Topology provides a rigorous foundation for identifying features and transitions within data, and these are of particular interest to end users in understanding the original problem. Topological models are also essential in simplifying and presenting massive datasets, as our ability to interpret data has to pass through the bottleneck of screen space (typically around 2M pixels) and the gigabyte limits of the human visual system. The Joint Contour Net provides a first glimpse of how to generalise topological analysis from one field to many fields, and importantly, how to do so efficiently, and in a way that accommodates parallelisation to scale up to processing massive datasets.This proposal will deliver on the initial promise by developing the mathematical theory for multifield analysis, generating the and the visual abstractions needed to understand multifield behaviour. To achieve this, we will work closely with other international leaders in visualization and computational topology to address specific issues, such as simplification and rendering techniques based on JCNs, and user interfaces for steering analysis that are adapted to the needs of particular applications. To ensure the research has the maximum possible reach, we will embed our software into the most widely used visualization toolkits, with dedicated effort to ensure that the implementation is robust and maintainable, and courses to train end-users in its application.