Vector Field Decompositions using Multiscale Poisson Kernel
Vector Field Decompositions using Multiscale Poisson Kernel
复制标题
使用多尺度泊松核的矢量场分解
DOI：
10.1109/tvcg.2020.2984413
复制
发表时间：
2020
影响因子：
5.2
通讯作者：
Bremer, Peer-Timo
中科院分区：
文献类型：
--
作者：
Bhatia, Harsh;Kirby, Robert M.;Pascucci, Valerio;Bremer, Peer-Timo
使用尺度空间提取多尺度特征是分析标量场的基本方法之一。然而，矢量场的类似技术并不常见，尽管众所周知，例如湍流包含不同尺度的嵌套涡流级联。挑战在于，与尺度空间相关的想法是基于迭代平滑数据以提取逐渐更大尺度的特征，这使得提取重叠特征变得困难。相反，我们将矢量场中影响的空间区域视为尺度，并引入一种矢量场多尺度分析的新方法。我们不是平滑流动，而是使用自然的亥姆霍兹-霍奇分解，使用逐渐变大的邻域将其分成小规模和大规模组件。我们的方法通过从大规模效应（例如背景流）中提取局部流动行为（例如小漩涡）来创建特征的自然分离。我们在大规模湍流上展示了我们的技术，并展示了无法使用最先进的技术提取的多尺度特征。
Extraction of multiscale features using scale-space is one of the fundamental approaches to analyze scalar fields. However, similar techniques for vector fields are much less common, even though it is well known that, for example, turbulent flows contain cascades of nested vortices at different scales. The challenge is that the ideas related to scale-space are based upon iteratively smoothing the data to extract features at progressively larger scale, making it difficult to extract overlapping features. Instead, we consider spatial regions of influence in vector fields as scale, and introduce a new approach for the multiscale analysis of vector fields. Rather than smoothing the flow, we use the natural Helmholtz-Hodge decomposition to split it into small-scale and large-scale components using progressively larger neighborhoods. Our approach creates a natural separation of features by extracting local flow behavior, for example, a small vortex, from large-scale effects, for example, a background flow. We demonstrate our technique on large-scale, turbulent flows, and show multiscale features that cannot be extracted using state-of-the-art techniques.