Multifractal Analyses of Grayscale and Binary Soil Thin Section Images

Multifractal analyses of binary images of soil thin sections (STS) are widely used to characterize pore structure. However, no geometrical model is known to exist for a binary multifractal. Thus, the multifractality of binary images, and the accuracy of multifractal parameters estimated from them, need to be carefully evaluated. We captured 8-bit depth resolution digital grayscale images of three STS images with dimensions of 1024× 1024 pixels and a pixel length of 1.9μm. Random grayscale geometrical multifractal fields (GMF) with similar dimensions and known multifractal parameters were constructed using generators extracted from the STS images. The STS and GMF grayscale images were objectively thresholded to give six binary images. The method of moments was used to compute the log-transformed partition function, log(χ(q, δ)) versus log(δ) where δ is box size, for each grayscale image and its binary counterpart. §Corresponding author.