Percolating length scales from topological persistence analysis of micro-CT images of porous materials

Topological persistence is a powerful and general technique for characterizing the geometry and topology of data. Its theoretical foundations are over 15 years old and efficient computational algorithms are now available for the analysis of large digital images. We explain here how quantities derived from topological persistence relate to other measurements on porous materials such as grain and pore-size distributions, connectivity numbers, and the critical radius of a percolating sphere. The connections between percolation and topological persistence are explored in detail using data obtained from micro-CT images of spherical bead packings, unconsolidated sand packing, a variety of sandstones, and a limestone. We demonstrate how persistence information can be used to estimate the percolating sphere radius and to characterize the connectivity of the percolating cluster.