Viscous and gravitational flow instabilities cause a displacement front to break up into finger-like fluids. The detection and evolutionary analysis of these fingering instabilities are critical in multiple scientific disciplines such as fluid mechanics and hydrogeology. However, previous detection methods of the viscous and gravitational fingers are based on density thresholding, which provides limited geometric information of the fingers. The geometric structures of fingers and their evolution are important yet little studied in the literature. In this work, we explore the geometric detection and evolution of the fingers in detail to elucidate the dynamics of the instability. We propose a ridge voxel detection method to guide the extraction of finger cores from three-dimensional (3D) scalar fields. After skeletonizing finger cores into skeletons, we design a spanning tree based approach to capture how fingers branch spatially from the finger skeletons. Finally, we devise a novel geometric-glyph augmented tracking graph to study how the fingers and their branches grow, merge, and split over time. Feedback from earth scientists demonstrates the usefulness of our approach to performing spatio-temporal geometric analyses of fingers.

中文翻译：

---

粘性手指和重力手指的几何驱动检测、跟踪和视觉分析

粘性和重力流动的不稳定性导致位移前沿分裂成手指状流体。这些指法不稳定性的检测和演化分析在流体力学和水文地质学等多个科学学科中至关重要。然而，以往粘性手指和重力手指的检测方法是基于密度阈值的，这提供了有限的手指几何信息。手指的几何结构及其演变很重要，但在文献中却鲜有研究。在这项工作中，我们详细探索了手指的几何检测和演化，以阐明不稳定性的动力学。我们提出了一种脊体素检测方法来指导从三维（3D）标量场中提取手指核心。在将手指核心骨架化为骨架后，我们设计了一种基于生成树的方法来捕捉手指如何从手指骨架在空间上分支。最后，我们设计了一个新颖的几何字形增强跟踪图来研究手指及其分支如何随着时间的推移生长、合并和分裂。来自地球科学家的反馈证明了我们的方法对手指进行时空几何分析的有用性。