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

TL;DR

This paper analyzes how image resolution reduction affects statistical descriptors of heterogeneous media, providing theoretical insights into the preservation of statistical information during decimation.

Contribution

It introduces a theoretical framework for understanding the impact of image decimation on statistical descriptors and error estimation in heterogeneous media analysis.

Findings

Normalized correlation functions predict original data trends when decimation is minimal.

Error remains small during initial decimation stages regardless of procedure.

Beyond a threshold, statistical information loss increases error and depends on decimation method.

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 microscopy techniques. In this study, we present a theoretical analysis of the effects of the image size reduction, due to a gradual decimation of the original image. Three different decimation procedures were implemented and their consequences on the discrete correlation functions and the coarseness are reported and analyzed. 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. In contrast, when the decimated image does not represent the 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 differences 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 of 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.