Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion
Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion
复制标题
3D 矢量场中的临界点消除：鲁棒性和讨论
DOI：
10.1109/tvcg.2016.2534538
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发表时间：
2016
影响因子：
5.2
通讯作者：
Valerio Pascucci
中科院分区：
文献类型：
--
作者：
P. Skraba;P. Rosen;Bei Wang;Guoning Chen;H. Bhatia;Valerio Pascucci
矢量场拓扑已被成功地应用于表示稳定矢量场的结构。临界点是向量场拓扑的重要组成部分，在描述抽取结构的复杂性方面起着重要的作用。通过临界点消去简化矢量场对于解释复杂矢量场如湍流的行为具有实际价值。然而，没有有效的技术允许直接取消3D中的临界点。这项工作填补了这一空白，并引入了第一个框架，以分层方式直接取消3D临界点对或组，并根据其鲁棒性（其稳定性的定量测量）保证最小的扰动量。此外，我们的框架不需要提取整个3D拓扑结构，其中包含非平凡的分离结构，因此在计算上是有效的。此外，我们的算法可以删除临界点的域的任何子区域的度为零，并处理复杂的边界配置，使其能够解决具有挑战性的情况下，可能无法解决，否则。我们将我们的方法应用于合成和模拟数据集，以证明其有效性。
Vector field topology has been successfully applied to represent the structure of steady vector fields. Critical points, one of the essential components of vector field topology, play an important role in describing the complexity of the extracted structure. Simplifying vector fields via critical point cancellation has practical merit for interpreting the behaviors of complex vector fields such as turbulence. However, there is no effective technique that allows direct cancellation of critical points in 3D. This work fills this gap and introduces the first framework to directly cancel pairs or groups of 3D critical points in a hierarchical manner with a guaranteed minimum amount of perturbation based on their robustness, a quantitative measure of their stability. In addition, our framework does not require the extraction of the entire 3D topology, which contains non-trivial separation structures, and thus is computationally effective. Furthermore, our algorithm can remove critical points in any subregion of the domain whose degree is zero and handle complex boundary configurations, making it capable of addressing challenging scenarios that may not be resolved otherwise. We apply our method to synthetic and simulation datasets to demonstrate its effectiveness.
DOI：
10.1109/tvcg.2015.2440250
发表时间：
2015-08
影响因子：
5.2
作者：
P. Skraba;Bei Wang;Guoning Chen;P. Rosen
通讯作者：
P. Skraba;Bei Wang;Guoning Chen;P. Rosen