Effect of the image resolution on the statistical descriptors of heterogeneous media

Abstract

The characterization and reconstruction of heterogeneous materials, such as porous media and electrode materials, involve the application of image processing methods to data acquired by scanning electron microscopy or other microscopy techniques. Among them, binarization and decimation are critical in order to compute the correlation functions that characterize the microstructure of the above-mentioned materials. In this study, we present a theoretical analysis of the effects of the image-size reduction, due to the progressive and sequential decimation of the original image. Three different decimation procedures (random, bilinear, and bicubic) were implemented and their consequences on the discrete correlation functions (two-point, line-path, and pore-size distribution) and the coarseness (derived from the local volume fraction) are reported and analyzed. The chosen statistical descriptors (correlation functions and coarseness) are typically employed to characterize and reconstruct heterogeneous materials. A normalization for each of the correlation functions has been performed. When the loss of statistical information has not been significant for a decimated image, its normalized correlation function is forecast by the trend of the original image (reference function). In contrast, when the decimated image does not hold statistical evidence of the original one, the normalized correlation function diverts from the reference function. Moreover, the equally weighted sum of the average of the squared difference, between the discrete correlation functions of the decimated images and the reference functions, leads to a definition of an overall error. During the first stages of the gradual decimation, the error remains relatively small and independent of the decimation procedure. Above a threshold defined by the correlation length of the reference function, the error becomes a function of the number of decimation steps. At this stage, some statistical information is lost and the error becomes dependent on the decimation procedure. These results may help us to restrict the amount of information that one can afford to lose during a decimation process, in order to reduce the computational and memory cost, when one aims to diminish the time consumed by a characterization or reconstruction technique, yet maintaining the statistical quality of the digitized sample.

Computed Tomography 3D Super-Resolution with Generative Adversarial Neural Networks: Implications on Unsaturated and Two-Phase Fluid Flow

“…Additionally, this resolution study, even though it was only limited to one sample, has merit in research, as often, the impact of resolution is only studied, either for artificial resolution reduction [26,34,150] or for mechanically lower resolution but on different samples [20,30,151,152]. Only rarely was the effect of resolution studied on the same volume, but results and conclusions are consistent with other studies.…”

Critical Resolution and Sample Size of Digital Rock Analysis for Unconventional Reservoirs

“…Works have been done on the effect of sample size and resolution, however almost all of them are done separately [31][32][33][34][35][36][37]. The effect of sample size is well studied since Bear [38] brought up the idea of representative element volume (REV), which is the smallest volume over which the measurement result is representative of the macroscopic property.…”

Effect of An Image Resolution Change on the Effective Transport Coefficient of Heterogeneous Materials

“…Progressive and sequential decimation process is applied to obtain an image of minimal size (in pixels). In this work, random bilinear decimation is implemented [13]. Statistical characterization is obtained with the following correlation functions (descriptors): two-point correlation (Sj), line-path correlation (Lj), and pore-size distribution (Pj).…”

“…The size reduction strategy has been previously published [13]. In Figure 1, the original image (matrix A0, with size M0×N0) has a decimation step k = 0 , afterward, the image is reduced for its progressive and sequential evaluation from k = 1 to k = 4 .…”

“…However, the reconstruction of volume and computation of ETC needs vast computational resources. In previous work, a gradual decimation process was developed in order to obtain the image of minimal size without losing statistical information [13]. The method, based on normalized coarseness and the correlation length, indicates the maximum number of steps (kmax) of a gradual decimation process.…”