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

Abstract

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 persistentfeatures of a real-valued function on the surface that evolves with a parameter. Then, we generate the corresponding persistentfeaturediagram (DgmPF) 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.

Keywords

• Heat kernel signature
• Porous structure retrieval
• Shape retrieval
• Persistent homology
• Computational topology