Robust surface-correlation-function evaluation from experimental discrete digital images

Correlation functions (CFs) are universal structural descriptors; surface-surface Fss and surface-void Fsv CFs are a subset containing additional information about the interface between the phases. The description of the interface between pores and solids in porous media is of particular importance and recently Ma and Torquato [Phys. Rev. E 98, 013307 (2018)] proposed an elegant way to compute these functions for a wide variety of cases. However, their continuous approach is not always applicable to digital experimental 2D and 3D images of porous media as obtained using x-ray tomography or scanning electron microscopy due to nonsingularities in chemical composition or local solid material's density and partial volume effects. In this paper we propose to use edge-detecting filters to compute surface CFs in the digital fashion directly in the images. Computed this way, surface correlation functions are the same as analytically known for Poisson disks in case the resolution of the image is adequate. Based on the multiscale image analysis we developed a C0.5 criterion that can predict if the imaging resolution is enough to make an accurate evaluation of the surface CFs. We also showed that in cases when the input image contains all major features, but do not pass the C0.5 criterion, it is possible with the help of image magnification to sample CFs almost similar to those obtained for high-resolution image of the same structure with high C0.5. The computational framework as developed here is open source and available within the CorrelationFunctions.jl package developed by our group. Our digital approach was applied to a wide variety of real porous media images of different quality. We discuss critical aspects of surface correlation functions computations as related to different applications. The developed methodology allows applying surface CFs to describe the structure of porous materials based on their experimental images and enhance stochastic reconstructions or super-resolution procedures, or serve as an efficient metrics in machine learning applications due to computationally effective GPU implementation.

Automated summary

Correlation functions (CFs) are structural descriptors and surface-surface (Fss) CFs and surface-void (Fsv) CFs provide additional information about the interface between phases. A method to compute these functions using edge-detecting filters in digital images is proposed. The developed digital approach allows for the analysis and enhancement of porous materials based on experimental images.