## 5 Results  
There are 100 HistAENNs trained using the same single labeling for every image with random starting weights. Both training phases use the SGD (Stochastic Gradient Descent) algorithm [70; 71] and 10,000 training steps. The labeling process is controlled by a human using additional training steps before the Monte Carlo test and iteratively corrected if the segmentation results are insufficient. It is expected from the user's perspective that similar results should be achieved if single segmentation is visually checked.  
Example results for box-counting and lacunarity are shown in Figures 6 and 7 respectively. All Monte Carlo results (Richardson's and lacunarity plots) are shown, for illustrative purposes for a single image as a set of 100 overlapping curves. Raw discrete distributions derived from these distributions are shown as vertical lines with grayscale coding. Direct analysis of such raw distributions is possible, but it leads to a very large set of parameters. The reductive approach is possible by simplification, so only mean and standard deviation are used. Mean values and standard deviations are depicted for particular \(r\) values as a continuous line (red) and vertical lines (black), respectively. More precise visualization with median and range is possible, with the use of box and whisker plot. Furthermore, local FDs are shown for box-counting.  
NVIDIA Titan X (Maxwell) GPU card was used for training of HistAENNs. Calculations of local histograms (SWLH) were on the CPU. It is possible to process SWLH on GPU, but it will be considered in further versions of HistAENNseg software, because the integration with dlib is necessary.  
Figure 6: Exemplary results for box-counting analysis for single image (standard deviations are shown as a vertical line in left figures; raw distributions are shown in right figures).  
Figure 7: Exemplary results for lacunarity analysis for single image (standard deviations are shown as a vertical line in left figures; raw distributions are shown in right figures).  
Multi-parameter box-counting and lacunarity are selected for the analysis of method-induced errors. There are about 19 and 20 results for both algorithms, respectively, so the analysis in this high-dimensional space is difficult and unnecessary. Smooth curves are obtained for every image to avoid sampling problems. A few parameters are sufficient for the analysis. The problem depends on their selection and their equidistant selection is the direct solution, so three values out of four are tested.  
Four cases of multi-parameter box-counting and lacunarity are calculated for the configurations and are shown in Table 1.  
Overlapping table is shown graphically in Figure 8.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Type** & **Scales List** & \(\mathbf{Q_{\%}}\) \\ \hline
1 & box-counting & \(-2.5649,-1.9459,0\) & 7.24 \\
2 & box-counting & \(-2.9444,-2.5649,-1.9459\) & 14.10 \\
3 & lacunarity & \(0.8451,1.1361,1.3010\) & 67.72 \\
4 & lacunarity & \(0,0.8451,1.1461\) & 73.30 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Configuration of multi-parameter methods and obtained results.  
Figure 8: Examples of overlapping: (**a**) box-counting (Case 1), (**b**) box-counting (Case 2), (**c**) lacunarity case (Case 3), (**d**) lacunarity (Case 4). Black is for overlapping.