## 3 Results and Discussion
### Tuning of the Binarisarion Algorithm Using PST  
To understand how the PST find the optimal parameters, a deeper analysis of the binarisation algorithm is done. The analysis of the graphic in Figure 7 makes it possible to see the evolution of the sensitivity and coverage similarity indicators for the image A in Figure 1. It must be noted that very similar successive segmented images can also be found when certain parameters take very low or very high values, i.e., values outside the useful range of a parameter. For example, when an image is thresholded by hand, it is easy to see that if the threshold is too low or too high, the resulting images will be almost completely white or black, and the changes between two successive binarised images will be very low. Therefore, the scanning of extreme values should be avoided, which will also speed up the process of searching for the best parameters values. In any case, if the ranges of useful values are unknown, the problem is easily solved by excluding the maximum and minimum similarity values found at the ends of each parameter range, as shown in Figure 7.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Images** & \multicolumn{2}{c}{**PST Parameters**} & \multicolumn{2}{c}{**Duration**} & \multicolumn{2}{c}{**Manual Parameters**} & \multicolumn{2}{c}{**Duration**} \\ \hline
**Original** & \(\mathbf{h_{min}}\) & \(\mathbf{h_{max}}\) & \(\mathbf{\sigma}\) & **Time [s]** & \(\mathbf{h_{min}}\) & \(\mathbf{h_{min}}\) & \(\mathbf{\sigma}\) & **Time [min]** \\ \hline A1 & 0.095 & 0.7 & 0.8 & 24 & 0.15 & 0.7 & 0.2 & 16 \\ A2 & 0.015 & 0.7 & 0.8 & 35 & 0.05 & 0.7 & 0.6 & 23 \\ A3 & 0.015 & 0.5 & 0.8 & 25 & 0.05 & 0.5 & 0.4 & 21 \\ A4 & 0.095 & 0.7 & 0.9 & 34 & 0.05 & 1.0 & 0.4 & 22 \\ A5 & 0.095 & 0.7 & 0.9 & 45 & 0.05 & 0.6 & 0.7 & 24 \\ A6 & 0.015 & 0.3 & 0.8 & 57 & 0.05 & 0.3 & 0.9 & 20 \\ A7 & 0.095 & 0.7 & 0.6 & 55 & 0.09 & 0.8 & 0.9 & 35 \\ A8 & 0.095 & 0.3 & 0.9 & 47 & 0.17 & 0.3 & 0.7 & 28 \\ A9 & 0.095 & 0.4 & 0.4 & 59 & 0.09 & 0.4 & 0.3 & 40 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Segmentation results.  
Figure 6: Optimal Canny segmentation; (**A**) Original images; (**B**) PST results; (**C**) Manual results obtained by an expert.  
Figure 7: Coverage and sensitivity indexes. At can be observed, these similarity functions have three local minima. The local minima located at the ends of the range of values are not useful and are ignored. The local minimum located close to 105 provides the best threshold value.  
Figure 8 shows the graphics of the four indexes for the image A5 in Figure 9. As it can be observed, the shape of the sensitivity and the total coverage indexes are very similar and the best threshold is \(t=170\). Indexes of minimum distance analysis (Figure 8B) and co-linearity (Figure 8C) vary in a similar way, and the first local maximum, employed as optimal threshold, is also located close to \(t=170\).  
Figure 8: Similarity indexes from Image A5 in Figure 9: (**A**) sensitivity and coverage index; (**B**) minimum distance index; (**C**) co-linearity index. The best threshold is given by the local minimum or maxima located around \(t=170\).  
Figure 9: The thresholding results by using the PST and Otsu techniques: (**A**) original images; (**B**) segmented images using the TSP approach (_t_); (**C**) segmented images using the Otsu technique (_t_o).  
Figure 9 and Table 2 compare the threshold outcomes obtained by PST technique with the results obtained by means of the Otsu algorithm. It can be seen that the results are similar, showing the quality of the PST in finding an optimum threshold.