Persistent geometry-topology descriptor for porous structure retrieval based on Heat Kernel Signature

Porous structures are essential in a variety of fields such as materials science and chemistry. To retrieve porous materials efficiently, novel descriptors are required to quantify the geometric and topological features. In this paper, we present a novel framework to create a descriptor that incorporates both topological and geometric information of a porous structure. To capture geometric information, we keep track of the $birthtime$ and $deathtime$ of the $persistentfeature$s of a real-valued function on the surface that evolves with a parameter. Then, we generate the corresponding $persistentfeaturediagram$ ($Dg{m}_{PF}$) and convert it into a vector called $persistencefeaturedescriptor$ (PFD). To extract topological information, we sample points from the pore surface and compute the corresponding persistence diagram, which is then transformed into the Persistence B-Spline Grids (PBSG). Our proposed descriptor, namely $persistentgeometry-topologydescriptor$ (PGTD), is obtained by concatenating PFD with PBSG. In our experiments, we use the heat kernel signature (HKS) as the real-valued function to compute the descriptor. We test the method on a synthetic porous dataset and a zeolite dataset and find that it is competitive compared to other descriptors based on HKS and advanced topological descriptors.