Pore-network extraction using discrete Morse theory: Preserving the topology of the pore space

Evaluation of three-point correlation functions from structural images on CPU and GPU architectures: Accounting for anisotropy effects

Structures, or spatial arrangements of matter and energy, including some fields (e.g., velocity or pressure) are ubiquitous in research applications and frequently require description for subsequent analysis, or stochastic reconstruction from limited data. The classical descriptors are two-point correlation functions (CFs), but the computation of three-point statistics is known to be advantageous in some cases as they can probe non-Gaussian signatures, not captured by their two-point counterparts. Moreover, n-point CFs with n≥3 are believed to possess larger information content and provide more information about studied structures. In this paper, we have developed algorithms and code to compute S_{3},C_{3},F_{sss},F_{ssv}, and F_{svv} with a right-angle and arbitrary triangle pattern. The former was believed to be faster to compute, but with the help of precomputed regular positions we achieved the same speed for arbitrary pattern. In this work we also implement and demonstrate computations of directional three-point CFs-for this purpose right-triangular pattern seems to be superior due to explicit orientation and high coverage. Moreover, we assess the errors in CFs' evaluation due to image or pattern rotations and show that they have minor effect on accuracy of computations. The execution times of our algorithms for the same number of samples are orders of magnitude lower than in existing published counterparts. We show that the volume of data produced gets unwieldy very easily, especially if computations are performed in frequency domain. For these reasons until information content of different sets of correlation functions with different "n-pointness" is known, advantages of CFs with n>3 are not clear. Nonetheless, developed algorithms and code are universal enough to be easily extendable to any n with increasing computational and random access memory (RAM) burden. All results are available as part of open-source package correlationfunctions.jl [V. Postnicov et al., Comput. Phys. Commun. 299, 109134 (2024)10.1016/j.cpc.2024.109134.]. As described in this paper, three-point CFs computations can be immediately applied in a great number of research applications, for example: (1) flow and transport velocity fields analysis or any data with non-Gaussian signatures, (2) deep learning for structural and physical properties, and (3) structure taxonomy and categorization. In all these and numerous other potential cases the ability to compute directional three-point functions may be crucial. Notably, the organization of the code functions allows computation of cross correlation, i.e., one can compute three-point CFs for multiphase images (while binary structures were used in this paper for simplicity of explanations).

Measuring structural nonstationarity: The use of imaging information to quantify homogeneity and inhomogeneity

Heterogeneity is the concept we encounter in numerous research areas and everyday life. While "not mixing apples and oranges" is easy to grasp, a more quantitative approach to such segregation is not always readily available. Consider the problem from a different angle: To what extent does one have to make apples more orange and oranges more "apple-shaped" to put them into the same basket (according to their appearance alone)? This question highlights the central problem of the blurred interface between heterogeneous and homogeneous, which also depends on the metrics used for its identification. This work uncovers the physics of structural stationarity quantification, based on correlation functions (CFs) and clustering based on CFs different between image subregions. By applying the methodology to a wide variety of synthetic and real images of binary porous media, we confirmed computationally that only periodically unit-celled structures and images produced by stationary processes with resolutions close to infinity are strictly stationary. Natural structures without recurring unit cells are only weakly stationary. We established a physically meaningful definition for these stationarity types and their distinction from nonstationarity. In addition, the importance of information content of the chosen metrics is highlighted and discussed. We believe the methodology as proposed in this contribution will find its way into numerous research areas dealing with materials, structures, and measurements and modeling based on structural imaging information.

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

Correlation functions (CFs) are universal structural descriptors; surface-surface F_{ss} and surface-void F_{sv} 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)2470-004510.1103/PhysRevE.98.013307] 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 C_{0.5} 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 C_{0.5} 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 C_{0.5}. 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.