# Region Adjacency Graph Approach for Acral Melanocytic Lesion Segmentation
## 3 Results
### Statistical Analysis  
The performance of the acral skin lesion segmentation approach based on the RAG algorithm can be assessed based on the analysis of the Sorensen index also known as the dice similarity coefficient (DSC), which is a statistic used to compare the similarity of two samples [39]. The DSC is calculated based on two binary sets, \(X\) and \(Y\), as follows:  
\[\text{DSC}=\frac{2|X\cap Y|}{|X|+|Y|}. \tag{8}\]  
The DSC is frequently used as a statistical measure which calculates the degree of overlapping between the experimental segmentation and the manual segmentation. Using the definition of true positive (TP), false positive (FP), and false negative (FN), it can be re-written as:  
\[\text{DSC}=\frac{2\text{TP}}{2\text{TP}+\text{FP}+\text{FN}}. \tag{9}\]  
In our case, TP denotes acral lesion pixels, FP--omitted acral lesion pixels, and FP--healthy skin pixels classified as an acral lesion.  
Furthermore, precision (PRC), accuracy (ACC), sensitivity (SE), and specificity (SP) are calculated using the following equations:  
\[\text{ACC}=\frac{\text{TP}+\text{TN}}{\text{TP}+\text{TN}+\text{FP}+\text{ FN}}. \tag{10}\]  
Precision describes random errors while accuracy is more commonly systematic errors (statistical bias):  
\[\text{PRC}=\frac{\text{TP}}{\text{TP}+\text{FP}}, \tag{11}\]  
\[\text{SE}=\frac{\text{TP}}{\text{TP}+\text{FN}}, \tag{12}\]  
\[\text{SP}=\frac{\text{TN}}{\text{TN}+\text{FP}}. \tag{13}\]  
Table 1 compares segmentation results obtained with the implemented algorithm (RAG) and other common segmentation approaches including region growing (RG), Otsu's method (Otsu), and active contour model (ACM). Our proposed method is able to correctly detect the acral lesions while most of the other methods tend to oversegment the area. The proposed algorithm achieved an average DSC of 0.85, accuracy 0.91, precision 0.89, sensitivity 0.87, and specificity 0.88. Only 12 images were scored less than 0.7 with the proposed algorithm.  
Figure 8 illustrates the obtained results of the proposed segmentation algorithm based on the region adjacency graphs when applied to the test images. At the beginning, the medical image undergoes the pre-processing step. The first step of the segmentation process includes the SLIC oversegmentation with superpixels' detection; results of these step are presented in the third column of Figure 8. Afterwards, the RAG construction algorithm which connects the oversegmented regions with calculated weights has been applied (the 4 th column). The merging process is necessary to achieve the balance between over- and undersegmentation (the 5 th column). Considering the obtained results presented in the last  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **DSC** & **ACC** & **PRC** & **SE** & **SP** \\ \hline RAG & 0.85 & 0.91 & 0.89 & 0.93 & 0.89 \\ \hline RG & 0.81 & 0.83 & 0.85 & 0.87 & 0.88 \\ Otsu & 0.69 & 0.72 & 0.79 & 0.81 & 0.76 \\ ACM & 0.76 & 0.79 & 0.72 & 0.67 & 0.81 \\ \hline \hline \end{tabular}
\end{table}
Table 1: A comparison between implemented RAG algorithm and various segmentation methods.  
column of Figure 8, it can be reported that the implemented algorithm is very effective in detecting the acral melanomas on the dermoscopic image datasets. Furthermore, unlike many previously published dermatoscopic segmentation algorithms, it can handle multiple lesions (Figure 8d).