# Dermoscopy Images Enhancement via Multi-Scale Morphological Operations
## 4 Results and Discussions
### Comparison of the Proposed Algorithm with State-of-the-Art Algorithms
#### 4.2.1 Numerical Results  
In Figure 7, it can be observed that as \(n\) grows and starting from \(n=4\), MGRTH obtains higher image entropy with respect to the compared algorithms. This gives an indication that the proposed algorithm is good at improving image detail. In Figure 7, the entropy value of the original image I is also added.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Algorithms**} & **Initial Structuring Element (Disk)** & \
\begin{tabular}{c} **Number of** \\ **Iterations** \\ \end{tabular} &
\begin{tabular}{c} **Contrast Setting** \\ **Weight** \\ \end{tabular} \\ \cline{2-4}  & **H** & **H\({}^{\prime}\)** & \(n\) & \(\omega\) \\ \hline MGRTH & 1 & - & [2–20] & 0.25 \\ GRMMCE [23] & 1 & - & [2–20] & 1 \\ MMALCER [39] & 1 & - & [2–20] & 0.5 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of the algorithms based on multi-scale MM.  
Figure 6: Visual results obtained by MGRTH in the different iterations.  
Table 3 shows the average results obtained by the compared algorithms. For the algorithms based on the multiscale top-hat transform the value of \(n=4\) was considered. The best average results are highlighted in bold.  
The average results in Table 3 show that:  
* MGRTH has better average performance according to the E metric, indicating that the approach enhances the details of melanoma images;
* Among the algorithms based on the multiscale top-hat transform, MGRTH is the second best performer for PSNR. This means that it introduces low distortion to the images;
* According to the REC metric, all compared algorithms enhance images on average.  
In the [PERSON] signed rank test, the differences of the \(q\)-pairs of observations are calculated, and based on these differences in absolute value, order ranks are assigned. In Table 4 the number of positive ranks observed is presented, i.e., the number of times that the proposal has obtained higher values of the metric than the compared algorithm,  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithms** & **E** & **REC** & **PSNR** \\ \hline I & 6.581 & - & - \\ MGRTH & **6.838** & 1.049 & 28.018 \\ GRMMCE & 6.782 & 1.054 & 28.109 \\ MMALCER & 6.797 & 1.044 & 29.032 \\ HE & 6.408 & **1.249** & 12.420 \\ BBHE & 6.444 & 1.241 & 17.191 \\ MMBEBHE & 6.411 & 1.186 & 20.223 \\ QHELC & 6.554 & 1.024 & **38.342** \\ \hline \hline \end{tabular}
\end{table}
Table 3: Average results obtained by the compared algorithms.  
Figure 7: Comparison with respect to metric E.  
in the same way the number of negative ranks is observed, i.e., the number of times that the proposal has obtained lower values of the metric than the compared algorithm. The Wilcoxon statistic constitutes the sum of ranks (positive or negative) and for the number of pairs \(q\geq 20\) can be considered to be approximately normally distributed [40]. In Table 4, the Z statistic of the standard normal distribution and the significance associated with the observed Wilcoxon statistic are presented.  
After analyzing the results (level of statistical significance \(\alpha\)=0.01), the following can be observed:  
* The proposed algorithm has obtained higher values in the E metric than the other evaluated algorithms;
* For the REC metric, the proposed algorithm has obtained lower values than the HE, BBHE and MMBEBHE algorithms, and higher values than those obtained by QHELC and MMALCER;
* For the PSNR metric, the proposed algorithm has obtained lower values than the GR-MMCE, MMALCER, and QHELC algorithms, and higher values than those obtained by HE, BBHE, and MMBEBHE.