## 3 Materials and Methods
### Methodology for Skin Lesion Detection Using the Decision Fusion Classifier System
In this context, our initial step involves the selection of eight CNNs based on the specified criteria, a process informed by a comprehensive examination of the current state of the field and the demonstrated performance on the extensive ImageNet image database [83; 84] and pre-processing the images as we mentioned earlier by eliminating the hair and resizing them to fit the input of the CNNs. The chosen CNNs encompass DarkNet-53, DenseNet-201, GoogLeNet, Inception-V3, InceptionResNet-V2, ResNet-50, ResNet-101, and Xception. With the over-arching goal of maximizing system performance, we embarked on the exploration of an optimal approach for allocating decision fusion weights to each individual CNN. The resultant architecture of our proposed system is elucidated in Figure 17.**  
**Where the determination between melanoma and non-melanoma, executed by the decision fusion classifier, is effectuated through the utilization of the following Equations (1) and (2):**  
\[D_{M}=\sum_{i=1}^{8}d_{i}^{M}\cdot w_{i}^{M} \tag{1}\]  
\[D_{NM}=\sum_{i=1}^{8}d_{i}^{NM}\cdot w_{i}^{NM} \tag{2}\]  
**where** \(DM\) **is the decision in case of melanoma, where the false positive is considered as being a non-melanoma predicted as melanoma, and** \(DNM\) **is the decision in case of non-melanoma, where the false negative is considered as being a melanoma predicted as a non-melanoma,** \(i\) **represents the image, and** \(d_{i}\) **is the partial decision made by each CNNand \(w_{i}\) the weights calculated from the average mean of the F1 score obtained for ISIC and DermIS database as seen in Expressions (3) and (4). \[w_{1}^{M}=\frac{F_{1M}^{DermIS}(i)+F_{1M}^{ISIC}(i)}{2} \tag{3}\]  
\[w_{1}^{NM}=\frac{F_{1 NM}^{DermIS}(i)+F_{1 NM}^{ISIC}(i)}{2} \tag{4}\]  
The ultimate verdict is determined by comparing the values of the Expressions (1) and (2), with the higher value dictating the outcome. For example, if \(DM>DNM\), then the given result is melanoma. In the case of \(DM<DNM\), then the result is non-melanoma. In essence, through (1), we consider the objective melanoma, and through (2), we consider the objective non-melanoma. The choice between using the raw scores before the sigmoid activation function versus the binary decisions (0 or 1) for decision fusion can impact the overall performance and information content of the system. We took into consideration the advantages and disadvantages before taking the decision to use binary decisions. The advantage of raw scores is that they preserve the continuous nature of the model's output, providing more nuanced information about the model's confidence in its predictions. It also maps raw scores to probabilities between 0 and 1, allowing for a gradual transition from very confident negative predictions (close to 0) to very confident positive predictions (close to 1). The disadvantage is that raw scores require additional interpretation to determine decision thresholds, potentially adding complexity to the decision-making process. In addition, choosing appropriate thresholds for raw scores might be subjective and could vary depending on the application and dataset. The advantage of binary decisions is that they simplify the decision-making process as they provide a clear and immediate answer of whether a lesion is classified as positive (1) or negative (0). They are also straightforward to understand, making them more accessible for medical professionals and users. The downside is that binary decisions discard the nuanced information carried by the raw scores, potentially leading to a loss of subtleties in model confidence. We chose the binary decision in the proposed classifier because it yields some benefits that fit better in our end goal to integrate an automated melanoma detection module into an EHR, such as:  
Figure 17: Proposed system architecture. * **Simplicity and Interpretability:** Binary decisions provide a clear and straightforward answer, making it easier for both medical professionals and general users to understand the outcome of the classification.