## 3 Results
Comparing with sample \(b\), this may mean that the polynomial background subtractions levels out the original differences between the highest channels to a certain amount. While the next presented modifications again do not change the false-color maps much, sharpening again increases the noise-like patterns in the area of small Hurst exponent values. Sharpening twice again compresses the false-color map vertically, as was already found for the other two samples. Figure 6: Gray-scale-resolved Hurst exponent distribution of sample \(a\): (**a**) original (identical to Figure 5a); (**b**) after polynomial background subtraction; (**c**) after aligning rows; (**d**) after deleting horizontal errors; (**e**) after sharpening; (**f**) after sharpening twice. Finally, Figure 9 shows the results of the calculations for sample \(d\). The original image, mostly consisting of a dark background area, shows correspondingly high signals at relatively large Hurst exponent values for the lower (darker) channels (close to a value of 0.5). Figure 7: Gray-scale-resolved Hurst exponent distribution of sample \(b\): (**a**) original; (**b**) after polynomial background subtraction; (**c**) after aligning rows; (**d**) after deleting horizontal errors; (**e**) after sharpening; (**f**) after sharpening twice. Figure 8: Gray-scale-resolved Hurst exponent distribution of sample \(c\): (**a**) original; (**b**) after polynomial background subtraction; (**c**) after aligning rows; (**d**) after deleting horizontal errors; (**e**) after sharpening; (**f**) after sharpening twice. Again, after polynomial background subtraction, the false-color map is vertically stretched (Figure 9b) and remains similar after aligning rows and deleting horizontal errors (Figure 9c,d). Polynomial background subtraction this time also leads to a horizontal stretching towards smaller Hurst exponent values which can be attributed to the fine fibers in the background which became visible due to this operation. Sharpening once this time does not change the false-color map significantly (Figure 9e), while the second sharpening step modifies the map without a significant vertical compression (Figure 9f). Figure 9: Gray-scale-resolved Hurst exponent distribution of sample \(c\): (**a**) original; (**b**) after polynomial background subtraction; (**c**) after aligning rows; (**d**) after deleting horizontal errors; (**e**) after sharpening; (**f**) after sharpening twice. Comparing the gray-scale-resolved Hurst exponent distributions calculated for different AFM images with different post-processing steps, the following general statements can be concluded:  
* False-color maps of gray-scale-resolved Hurst exponent distributions enable distinguishing between different fiber distributions, especially between images with many and with only few fibers. * Polynomial background subtraction levels out the upper channel numbers for which a signal occurs and should thus be performed, especially in order to avoid ignoring hidden features (cf. Figure 9a,b). * Aligning rows and deleting horizontal errors leaves the images and thus, the false-color maps nearly unaltered. * The effect of sharpening once differs from sample to sample and must be investigated further in the next study. * Sharpening twice modifies not only the image in an unnaturally looking way, but also the false-color maps of the gray-scale-resolved Hurst exponent distributions and should thus be avoided. * What could not be performed yet, but has to be tested in the near future, is a comparison with a highly accurate AFM with increased quality of the original images, as reported in [36]. * Generally, the meaning of the \"noise\" in the range of Hurst exponents values below approx. 0.25 needs further investigation to find out whether this range should be ignored since it is mostly based on errors in the images, or whether it can oppositely be used as part of the \"fingerprint\" of such AFM images. To explain the threshold value of 0.25, we can refer to the composition of two random processes in analogy to [37].