Statistical Analysis of Nanofiber Mat AFM Images by Gray-Scale-Resolved Hurst Exponent Distributions

Abstract

Two-dimensional structures, either periodic or random, can be classified by diverse mathematical methods. Quantitative descriptions of such surfaces, however, are scarce since bijective definitions must be found to measure unique dependency between described structures and the chosen quantitative parameters. To solve this problem, we use statistical analysis of periodic fibrous structures by Hurst exponent distributions. Although such a Hurst exponent approach was suggested some years ago, the quantitative analysis of atomic force microscopy (AFM) images of nanofiber mats in such a way was described only recently. In this paper, we discuss the influence of typical AFM image post-processing steps on the gray-scale-resolved Hurst exponent distribution. Examples of these steps are polynomial background subtraction, aligning rows, deleting horizontal errors and sharpening. Our results show that while characteristic features of these false-color images may be shifted in terms of gray-channel and Hurst exponent, they can still be used to identify AFM images and, in the next step, to quantitatively describe AFM images of nanofibrous surfaces. Such a gray-channel approach can be regarded as a simple way to include some information about the 3D structure of the image.

Electrospun Nanofiber Mats for Filtering Applications—Technology, Structure and Materials

“…This is why research groups use it. Especially, many researchers are interested in environmentally friendly electrospinning, in which low-toxic solvents and biopolymers are used to produce nanofibers [ 51 , 52 ].…”

Effect of Ion and Binding Site on the Conformation of Chosen Glycosaminoglycans at the Albumin Surface

“…Hence, further analysis concerning pattern recognition machine learning techniques like SVM (Support Vector Machine) [ 47 ] and its modification for colored image processing [ 48 ] can be performed to extend the research. Another approach to this problem may be the colored image segmentation by a random walk [ 49 ], Sub-Markov random walk [ 50 ] or the Hurst Exponent image processing in [ 51 , 52 ]. Alternatively, one can analyze angles as multivariate series and process them with dedicated tools such as higher-order multivariate cumulants, see [ 53 ].…”

Multidimensional Fractal Scaling Analysis Using Higher Order Moving Average Polynomials and Its Fast Algorithm

“…To date, the Hurst exponent was used to quantify the diversity of 3D landscape, and, thus may be extended to quantitatively describe the atomic-force-microscope (AFM) images of electrospun nanofiber mats [32,33] . In this section, we show an application of the proposed method that can be used as a tool to quantitatively describe the density of the actin filament network behind the cell cortex.…”