## 3 Results
Figure 5a shows a first Hurst exponent multi-channel distribution, calculated for image \(a\) in the original, not-improved state captured directly by AFM (cf. Figure 1a). In addition to a large area in which most values are located, there are also some outliers visible at smaller Hurst exponent values. The outliers as well as the dominating values are better visible in the exemplary distributions depicted for channel 20 and channel 21 in Figure 5b,c, respectively. Figure 4: Example of the random walks evaluation on AFM gray-scale-resolved images: (**a**) linear relation between In (\(\langle\Delta r^{2}\rangle\) and ln(n)); (**b**) Hurst exponent distribution. Figure 3: Gray-scale distribution (excerpt) of Figure 2a: (**a**) channels 32–39; (**b**) channels 104–111; (**c**) channels 112–119; (**d**) channels 208–215. Comparing with Figure 2a, one can conclude that (**a**) is connected with deepest features that are darkest, while (**d**) is correlated with the top features that are brightest; hence, the gray scale reflects the 3D structure of the image. In other words, smaller distances are represented by smaller values of Hurst exponents and vice-versa. It also worth mentioning that for several cases we met with nonlinear dependencies being a source of uncertainties in fitting our model, especially for smaller values of H (smaller distances). This problem will be investigated in future from the perspective of information loss during an image splitting procedure. To investigate the influence of the aforementioned post-treatments of the AFM images, Figure 6 depicts the Hurst exponent distributions of the original sample \(a\) as well as of the post-treated images of this sample. In comparison with the original image (Figure 6a), the polynomial background subtraction increases the range of channels which contain a minimum of 10 counts (positions with less than 10 counts are not colored) for some Hurst exponents values. Generally, the false-color map is stretched vertically by this post-treatment. Both the next post-processing steps, i.e., aligning rows and deleting horizontal errors (Figure 6c,d), do not lead to significant modifications of the false-color maps. While this behavior was expected, as discussed above, the impact of sharpening (Figure 6e) is unexpectedly small. Interestingly, after the second sharpening step--which is usually not performed since it lets the image look artificial--the false-color map is compressed again vertically so that Figure 6f looks similar to Figure 6a, with an additional large amount of signal in the range of small Hurst exponents values and low channel numbers. Figure 7 depicts the same calculations for sample \(b\) (cf. Figure 2b), optically looking quite similar to sample \(a\). Opposite to sample \(a\), here the original image has a broader brightness distribution and thus, the area with a signal is vertically larger. After polynomial background subtraction, however, now the signal area is vertically compressed, while again the lower left area, showing signals of small Hurst exponents values for low channel numbers (i.e., images with many small dark areas), becomes more prominent. The next two post-processing steps again leave the false-color distribution nearly unchanged (Figure 7c,d), while sharpening once or twice shifts the whole distributions to smaller Hurst exponents values, as could be expected. Similar to Figure 6f, sharpening twice again compresses the false-color map vertically (Figure 7f). Next, Figure 8 shows the results calculated for sample \(c\). As expected, the false-color maps here look quite different from the previous ones. Comparing Figure 8a with the previous false color maps of the original images, Figure 8a shows signals at much higher Hurst exponents values, especially for low channel numbers, which could be expected due to the large open (i.e., dark) areas between the fibers in the original AFM image of sample \(c\)  
The polynomial background subtraction again increases the range of channels showing a scenery, similar to sample \(a\).