  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.
