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 b i r t h t i m e and d e a t h t i m e of the p e r s i s t e n t f e a t u r e s of a real-valued function on the surface that evolves with a parameter. Then, we generate the corresponding p e r s i s t e n t f e a t u r e d i a g r a m (D g m P F ) and convert it into a vector called p e r s i s t e n c e f e a t u r e d e s c r i p t o r (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 p e r s i s t e n t g e o m e t r y − t o p o l o g y d e s c r i p t o r (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. [Display omitted] [ABSTRACT FROM AUTHOR]