## 1 Introduction
Recognizing the immense potential of applying deep learning to digital images, a collaborative venture involving Manchester Metropolitan University, Lancashire Teaching Hospitals, and the Manchester University NHS Foundation Trust has established an international repository comprising approximately 11,000 diabetic foot ulcer (DFU) images. The primary objective of this repository is to facilitate the development of more advanced methods for DFU analysis. In our research, we utilize this dataset to train our algorithm and validate our model. The DFU challenge2021 organizers agreed to give access to this dataset [16]. Additionally, we incorporated datasets obtained from [PERSON] [17; 18; 19] to further enhance our training process. This research aims at evaluating the progress of the disease using images. When comparing two-element vectors, there exist various alternative similarity techniques that can be employed, such as the Euclidean distance, the Pearson correlation coefficient [20], Spearman's rank correlation coefficient, and others [21]. The choice of technique for comparison depends on the specific objective we want to achieve. However, traditional similarity measurements may not be effective when dealing with complex datasets that exhibit diverse dimensions and characteristics and potentially require compression prior to processing. In such cases, Siamese Neural Networks (SNN) emerge as a promising solution. The architecture of Siamese Neural Networks was initially introduced in the early 1990s to address the challenge of signature verification as an image matching problem [22]. Figure 2 provides an initial overview of the operation of Siamese Neural Networks (SNN). The structure of a Siamese Neural Network (SNN) consists of two identical artificial neural networks, A and A', as depicted in Figure 2. These networks are designed to learn the underlying representations of input vectors. Operating as feedforward perceptrons, they utilize error back-propagation during the training process to optimize their performance. Working in parallel, the two networks generate outputs that are compared at the end using metrics such as cosine distance or Euclidean distance. The output of an SNN operation can be interpreted as the semantic similarity between the projected representations of the two input vectors. Figure 2: Block Diagram giving an overview of components of a Siamese Neural Network (SNN). The contrastive loss [23] function is a type of distance-based loss function that updates the weights of a neural network in such a way that similar feature vectors have a minimal Euclidean distance. On the other hand, the distance is maximized between two dissimilar vectors. By employing the contrastive loss function, the neural network is encouraged to effectively separate and discriminate between different classes or categories based on their feature representations. More formally, we suppose that we have a pair of DFU images \((I_{i},I_{j})\) and a label Y that is equal to 0 if the samples are similar, and 1 otherwise. To extract a low-dimensional representation of each sample, we use a Neural Network which can be a CNN or Any ensemble model that encodes the input images \(I_{i}andI_{j}\) into an embedding space where \(x_{i}=f(I_{i})\) and \(x_{j}=f(I_{j})\). The contrastive loss is defined as:  
\[L=(1-Y)*||x_{i}-x_{j}||^{2}+Y*max(0,m-||x_{i}-x_{j}||^{2}) \tag{1}\]  
As mentioned in Section 2, our review of the existing literature reveals a noticeable scarcity of research focused on the application of deep learning specifically for assessing the progression of diabetic foot ulcers (DFUs) over time. While several classification techniques have been investigated, there is a notable gap when it comes to considering the temporal dimension of DFU evaluation. This research aims to address this critical gap by exploring the potential of Siamese Neural Networks for tracking and evaluating the development of DFUs over time.