VISUALIZATION: Feature Driven Simplification and Visualization of Vector Fields

为了理解大型矢量场，科学家通常会尝试简化和可视化数据。一般来说，有两种方法用于可视化向量场特征提取技术和通用可视化技术，它们提供互补的优势。基于特征的方法提取重要的特征，如拓扑结构（临界点和临界曲线）、附着线或分离线、旋涡、分叉或激波，并试图给出矢量场的简化视图。首先，太多的特征可能会使可视化混乱。因此，有必要修剪虚假和不重要的功能。第二，功能可视化本身可能无法提供一个全面的数据视图。这可以通过使用流行的通用可视化技术（如流线，线积分卷积（LIC）和流表面）来弥补。然而，大多数使用这种方法的尝试在简化或压缩方法的早期破坏了潜在的重要特征，正如我们在我们的初步工作中所证明的那样。因此，需要将特征简化过程与底层向量场的简化联系起来，以便产生一致的可视化。我们建议为2D矢量场开发受控的特征简化和保留算法，通过去除噪声和利用特征来去除不重要的特征并保留重要的特征，驱动的相似性度量来度量和控制简化过程，所提出的算法将同时简化特征和底层向量场，以产生一致的可视化。我们将这些算法扩展到3D和图像相关的向量场。其他挑战包括：（i）基于更复杂的3D特征（例如3D分离和附着线、涡流和冲击波区域）的性质设计有效的算法和结构相似性度量，以及（ii）随着时间的推移跟踪简化的特征，因为可能发生分叉。我们还将量化和可视化由于简化的不确定性或损失，以便让科学家更好地了解在简化过程中丢失或妥协的内容。我们将把我们的算法应用于计算流体动力学和环境数据。我们期望在这个项目中开发的算法和技术将适用于各种学科，包括航空学，气象学，海洋学，环境科学，天文学，地理信息科学，计算机图形学和计算机辅助几何设计。

In order to understand large vector fields, scientists typically attempt to simplify and visualize the data. Broadly speaking, there are two methods for visualizing vector field feature extraction techniques and general visualization techniques, that offer complementary advantages. Feature based techniques extract important features such as topology (critical point and critical curves), attachment or separation lines, vortices, bifurcations or shock waves, and attempt to present a simplified view of the vector field.There are two main dificulties with this approach. First, too many features may clutter the visualization. Therefore, there is a need to prune spurious and insignificant features.Second, feature visualization alone may fail to provide a comprehensive view of the data. This can be remedied by using popular general visualization techniques such as streamlines, line integral convolution (LIC), and stream surfaces.However, most attempts using this approach destroy the underlying important features early in thesimplification or compression approach, as we have demonstrated in our preliminary work. Therefore,there is a need to tie the feature simplification process with the simplification of the underlying vector field in order to produce consistent visualization.In this work, we propose to develop controlled feature simplification and preservation algorithmsfor 2D vector fields that remove insignificant features and preserve important ones by removing noise and by utilizing feature-driven similarity metrics to measure and control the simplificationprocess.The proposed algorithms will simplify the features and the underlying vector field simulatneouslyin order to produce consistent visualization. We will extend these algorithms to 3D and ime-dependent vector fields. Additional challenges include: (i) designing efficient algorithms and structure-similarity metrics based on the properties of more complex 3D features such as the 3D separation and attachement lines, vortices and shock wave regions, and (ii) tracking simplied features over time as bifurcations may take place. We will also quantify and visualize the uncertainty or loss due to simplification in order to give a better sense to the scientist as to what is lost or compromised during the simplification process.We will apply our algorithms to computational fluid dynamics and environmental data. We expect that the algorithms and techniques developed in this project will be applicable to a wide variety of disciplines including aeronautics, meteorology, oceanography, environmental sciences, astronomy, geographic information sciences, computer graphics, and computer-aided geometric design.