Multiscale persistent topological descriptor for porous structure retrieval

Abstract Porous structures play an important role in applications such as materials science and chemistry. The development of synthesized porous materials requires novel descriptors to quantify the geometric and topological features of pore surfaces. Persistent homology provides a stable tool to capture the changes in topological invariants from a manifold filtered by a real-valued function. In this study, a framework is proposed on the basis of a real-valued function evolving with a parameter on a surface to generate a multiscale persistent topological descriptor. It is obtained by approximating the Betti number curves that are produced from a collection of persistence barcodes through a B-spline surface. A vectorizing descriptor is constructed by reshaping the control points of the B-spline surface. In our experiments, scale invariant heat kernel signature (SI-HKS) is employed as a real-valued function defined on a surface to compute the descriptor. Retrieval tasks on a synthetic porous data set and a zeolite data set show the competitiveness of the proposed method compared with the descriptors based on SI-HKS and advanced topological descriptors.