Robustness-Based Simplification of 2D Steady and Unsteady Vector Fields
Robustness-Based Simplification of 2D Steady and Unsteady Vector Fields
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DOI：
10.1109/tvcg.2015.2440250
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发表时间：
2015-08
影响因子：
5.2
通讯作者：
P. Skraba;Bei Wang;Guoning Chen;P. Rosen
中科院分区：
文献类型：
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作者：
P. Skraba;Bei Wang;Guoning Chen;P. Rosen
向量场简化的目的是通过按照特征的相关性和重要性去除特征来降低流的复杂性，以揭示突出的行为并获得用于解释的紧凑表示。大多数现有的基于拓扑骨架的简化技术使用基于距离或面积的相关性度量来连续地移除由分隔线连接的临界点对。这些方法依赖于拓扑骨架的稳定提取，但由于数值积分的不稳定性，这可能会很困难，特别是在处理高度旋转的流动时。在本文中，我们提出了一种新的简化方案，该方案源于最近引入的稳健性拓扑概念，该方案能够根据临界点集的稳定性的量化度量来剪枝临界点集，即删除它们所需的最小向量场扰动。这导致了分层简化方案，该方案以其扰动度量对流量大小进行编码。新的简化算法基于度理论，具有最小的边界约束。最后，我们给出了一个在分段线性设置下的实现，并将其应用于合成数据集和真实数据集。我们展示了定常矢量场和非定常矢量场的局部和完全层次化简。
Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification techniques based on the topological skeleton successively remove pairs of critical points connected by separatrices, using distance or area-based relevance measures. These methods rely on the stable extraction of the topological skeleton, which can be difficult due to instability in numerical integration, especially when processing highly rotational flows. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness which enables the pruning of sets of critical points according to a quantitative measure of their stability, that is, the minimum amount of vector field perturbation required to remove them. This leads to a hierarchical simplification scheme that encodes flow magnitude in its perturbation metric. Our novel simplification algorithm is based on degree theory and has minimal boundary restrictions. Finally, we provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets. We show local and complete hierarchical simplifications for steady as well as unsteady vector fields.