Modelling a Deep Network Model for Diabetic Foot Ulcer Prediction Using Learning Approaches

Diabetes, also known as Diabetes Mellitus (DM), is a chronic condition resulting from high blood sugar levels, which can lead to serious health complications if not properly managed. It causes significant complications like kidney failure, cardiovascular diseases, lower limb amputation, and blindness that are frequently associated using Diabetic Foot Ulcers (DFU) [1]. In 2014, about 422 million individuals had DM, compared to 108 million people in 1980, based on the global report on diabetes. The global prevalence has crossed from 4.7% to 8.5% from 1980 to 2014 among adults 18 years of age [2]. Global DM prevalence is projected to reach 600 million individuals by 2035, according to estimates [3]. It is important to note that about 20% of people are from developed countries. The others are considered from developing countries because of the lack of awareness and the restricted facilities in healthcare [4]. A diabetic patient has a chance of about 15% to 25% developing DFU eventually, and the lower limb amputation may occur if the proper care is not taken [5]. More than 1 million patients have DM lose their leg part every year because they fail to identify it and treat the DFU properly [6]. A ‘high risk’ foot requires a periodic check-up with the doctors for the diabetic patient with continuous medication, which is costly, and hygienic personal care is needed to protect from additional problems mentioned before. Hereafter, an extensive burden will be caused, burdening the patient's family and the patient, particularly in developing countries. Here, the expense of treatment for the disease is costly and equal to 5.7 years of annual income [7].

The determination of DFU consists of different vital works in the present clinical practices and early diagnosis, which keep track of enhancement, and the count of lengthy tasks is considered in the management and treatment of DFU in every specific case [8]. They are (i) the evaluation of the patient's medical history needs to be considered, (ii) a specialist of the diabetic foot and the wound is examined the DFU thoroughly, (iii) the extra tests such as MRI, CT scans, and X-ray are required for helping to help plan the treatment [9]. Based on every scenario, the DFU patients have swollen legs, even though it is painful and itchy. The DFU appearance visually and the skin around the wound is based on the different phases, like callus formation, redness, numerous types of tissues such as slough, granulation, scaly skin, bleeding, and blisters [10-12]. Generally, uncertain outer boundaries and irregular structures are there in DFU. Evaluating ulcers with computer vision algorithms depends on correctly assessing the visually considered signs as texture features and colour descriptors. However, all these methods fail to provide a substantial outcome for predicting cancer in the earlier stage. Thus, some complexities are not addressed by the existing works. They are: (i) collection requires more time and the DFU images are labelled by experts, (ii) the high inter-class similarity among the abnormal classes as DFU and regular classes as healthy skin, and the intra-class variations that are based on the DFU classification [13], the ethnicity of the patient, and the lighting conditions. Research in foot ulcer prediction using deep learning has made significant strides, particularly for diabetic patients, yet several critical gaps and limitations remain. Addressing these issues is essential to improving model performance, generalizability, and clinical relevance. One major limitation is the scarcity and imbalance in existing datasets. Most available datasets for foot ulcer prediction are small, with a disproportionate number of images representing advanced-stage ulcers compared to early-stage cases. This imbalance hinders a model's ability to generalize and accurately detect the early signs of foot ulcers. To enhance generalizability, there is a need for larger, well-annotated, and diverse datasets that include various stages of foot ulcers across different demographics, including skin tones and patient age groups. Another challenge is the interpretability of DL techniques, specifically CNNs, which are often perceived as "black boxes." Clinicians and medical experts require models that provide transparent and interpretable predictions to confidently integrate them into clinical workflows. Without interpretability, there may be hesitation to trust or adopt these AI systems in real-world settings. Early detection of foot ulcers remains an ongoing challenge. While current models perform well in predicting advanced-stage ulcers, they often struggle to identify early-stage ulcers where signs may be more subtle. Models trained on small, imbalanced datasets are prone to overfitting, reducing their effectiveness when applied to new, unseen data. Therefore, improving model robustness and preventing overfitting are key areas where progress is needed, particularly when training data is limited. Addressing these gaps can give rise to more accurate, interpretable, and clinically viable models for foot ulcer prediction. Techniques like multimodal learning, real-time monitoring, and explainable AI have the potential to enhance the applicability and effectiveness of these models in healthcare settings. Additionally, comparing the proposed model with existing methods such as LBP, LeNet, AlexNet, GoogleNet, HOG+LBP, and color descriptors is important for benchmarking performance. Improving the model's ability to detect early-stage ulcers would enable more effective preventive interventions, which is crucial for patient outcomes. Nonetheless, the proposed model shows promising results in terms of accuracy, recall, F1-score, and precision, offering a groundwork for future enhancements in this area.

Thus, the proposed model intends to address these issues with the proper clinical findings in the earlier stage. The computer vision approaches are proposed to differentiate the DFU with deep learning and conventional machine learning techniques from healthy skin [14, 15]. The proposed system shows some major contributions as listed below:

1) Here, a novel computerized telemedicine system is presented to address the issues in DFU. The input dataset consists of 397-foot image samples, where 292 samples show DFU and 105 images of a healthy foot.

2) Subsequently, a novel learning approach is employed to learn and extract the features from the patches of healthy skin and the DFU. With the boom of DL, CNNs are used to develop the fully automated technique for classifying the DFU skin over the regular skin.

3) The proposed CNN-DFUNet is developed with fine-tuned input data and works more effectively than the modern CNN. It requires the actual data to generate the exact outcomes, yet in the convolutional blocks parallel with the larger filter size of CNN-DFUNet, which can create better results on the dataset.

The work is structured as follows: Section 2 offers a comprehensive evaluation of existing techniques and discusses the benefits and drawbacks related to the model. Section 3 provides an elaborate discussion on the proposed CNN-DFCNet model. The numerical results are provided in Section 4, followed by the research summary in Section 5.

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Figure 1. Flow of the anticipated model

Figure 1 illustrates the workflow of the proposed model. The medical professionals outline the ground truth labels in infected skin patches and normal skin patches from the area of the ROI. The ground truth of the abnormality type is labelled and exported for every delineated abnormal area to the Extensible Markup Language (XML) file. The experts gathered both the patch classes from the region of ROI in the group of ground truth patches, which helps have a more meaningful categorization of the patches than involving the complete foot as the area. There are about 292 ROI, such as only for ulcers; foot images for the annotation of 397-foot images having both the non-ulcer and ulcer with 1679 skin patches, have the 1038 abnormal class and the 641 normal classes from these annotations. Lastly, the dataset is divided into 84 patches for validation, 1423 for the training, and 172 for testing.

3.3 Data augmentation

The deep networks need more training image data due to the many parameters. The learning algorithms assign the weights with the convolutional layers, which can be tuned. Moreover, data augmentation enhances deep learning techniques. Different image processing approaches, such as flipping, rotation, and enhancement of contrast, are combined with the help of random scaling and the various colour spaces for data augmentation. Angles of 90° and 180° rotate the image, and 270° is used for further rotation. Thus, the three flipping methods, vertical flip, horizontal flip, and horizontal and vertical flip, are needed to serve on the original patches. Four colour spaces are required to augment data like NTSC, HSV, $L * a * b$, and YCbCr. There are three functions in contrast enhancement. The two cropped patches having the random orientation and the random offset are produced in the proposed system from the skin patches in the original dataset. The amount of training and validation patches is increased by fifteen times, that is, 1260 patches for validation and 21,345 patches for training with these approaches.

3.4 Pre-processing

There is a necessity for pre-processing on these patches since many training data augments are obtained. The zero-centre approach is utilized to pre-process these attained patches, and then the normalization is done for each pixel.

3.5 Classifier model

The proposed CNN-DFU model is a lightweight model that reduces complexity and enhances processing speed. The model intends to reduce the computational complexity and processing speed. The novelty of the work relies on the layer description and the changes done between the standard feature extraction layer of CNN and the fully connected layer. The features are analyzed, and the approximation with the extracted linear features is derived.

3.6 Model description

Assume $\chi$ is the set of $N$ images where the feature maps are obtained from the $i^{\text {th }}$ image with the feature extraction block. There is no constraint with the architectural model adopted for the feature extraction procedure. Consider $L$ as the number of layers (lightweight) where the features are extracted. Here, $X_{i j} \in \mathbb{R}^{N_f}$ is adopted for the extracted feature vector for the $i^{t h}$ image of $\chi$, and $N_f$ is the convolutional layers' channel (features extracted). The length of the feature maps describes several feature vectors, which are available across the intermediate layers. The feature vector count defines the feature map size and is available over the extracted feature. For instance, when the $20 * 20$ feature maps are extracted, the vectors are provided for different quantization processes. The factor $N_i$ extracts several feature vectors from the available $i^{\text {th }}$ mage. The image is specified with the set of $N_i$ feature vectors $x_{i j} \in \mathbb{R}^{N_F}\left(j=1, \ldots, N_i\right)$ extracted with the trained convolutional feature extractor. The intermediate layers are compiled using the histogram generated for every image after feature vector quantization. The prevailing global pooling approaches are fused with the feature vectors or used for pooling the spatial information for feature representation. The proposed model decouples the extracted feature representation size based on dimensionality and feature vectors. It facilitates independently controlling the feature representation size and allows the reduction of layer parameters required by the fully connected layers.

Input layer: It also helps in handling images of various sizes. Similarly, two diverse layers are utilized to examine the extracted features: 1) one layer measures the input feature vector similarity and measures the input vectors, and 2) accumulation layers execute the histogram representation by integrating the feature vectors (quantized). Thus, the layers form the pooling structure used for extracting the representation, which is fed as an input to the successive classifier. The differential similarity function is adopted to measure the feature vectors' similarity issues. The feature formulation of the anticipated model relies on the kernel-based radial basis function, which is used as a similarity metric. Thus, the RBF neurons are included in the preliminary layers, and the output of $k^{\text {th }}$ neuron $[\emptyset(x)]_k$ is expressed in Eq. (1):

$[\emptyset(x)]_k=\exp \left(-\left.\left\|x-v_k\right\|\right|_2 / \sigma_k\right) \in \mathbb{R}$    (1)

Here, $v_k$ refers to the number of features and feature representation size. Where $x$ specifies the feature vector, $v_k$ is the output of the k -th neuron, and $\sigma_k$ is the scaling factor used to adjust the Gaussian function in RBF neurons over the intermediate layers. Then, $l^1$ scaling is used for feature formulation and normalization is applied over the neurons. The output from the RBF neuron is represented in Eq. (2):

$[\emptyset(x)]_k=\frac{\exp \left(-\left|\left|x-v_k\right|\right|_2 / \sigma_k\right)}{\sum_{m=1}^{N_k} \exp \left(-\left|\left|x-v_m\right|\right|_2 / \sigma_m\right)}$       (2)

It can be efficiently understood by the feature vector quantization and normalizing of the higher similarity feature vectors. The normalization process is adapted to the layers of the anticipated model to ensure the distribution shift and enhance the scale invariance. The enhanced scale invariance of the expected model is shown in Figure 1. The final image representation is extracted based on the RBF neuron response of every vector, and it is fed to the intermediate layers, and it is expressed in Eq. (3):

$s_i=\frac{1}{N_i} \sum_{j=1}^{N_i} \emptyset\left(x_{i j}\right) \in \mathbb{R}^{N_k}$       (3)

Here, $\emptyset(x)=\left([\emptyset(x)]_1, \ldots,[\emptyset(x)]_{N_k}\right)^T \in R^{N_k}$ specifies the RGF vector output, and $s_i$ specifies the histogram, which is expressed based on the distribution of RBF neurons and determines the visual content of every sample image. The $s_i$ vectors possess an $l^1$ normalization unit. It is provided to the fully connected layers-the extracted features from the histogram and projects the feature vector distribution with the elimination of spatial information. The spatial information is provided to the extracted feature representation, which is like of matching technique. The images are segmented to the number of regions, and individual histograms are acquired from one another. The histograms are integrated to produce the resultant representation. The representation is provided as $N_K N_S$, where $N_S$ specifies the total spatial regions. The classifier model needs to infer the image class after hauling out the histogram representation and the model with loss function (differential) is utilized for analysis.

Hidden layer: The multi-layer perceptron with the hidden layer is specific to the anticipated model. The quantity of hidden neurons is specified as $N_H$, while the output neuron is utilized for every class that leads to output layer $N_c$ (classification problem for various courses). Nc specifies the total hidden neurons, the regression is performed, and the neuron's output is set as $N_c=1$.

Activation layer: The ReLU activation function with hyper-parameters (default) is utilized for hidden layers. With the ReLU, the obtained histograms enhance the network convergence velocity over the various activation functions. The softmax layer is employed for the classification of output layer, while regression does not employ any activation function. The classification process used cross-entropy loss function for network training, whereas regression used squared loss function. The dropout is set as $p=0.5$ is utilized for the hidden layer, and gradient descent is used for learning the attributes, and it is shown in Eq. (4):

$\begin{aligned} & \Delta\left(W_{M L P}, V, \sigma, W_{c o n v}\right) \\ & =-\left(\eta_{M L P} \frac{\partial L}{\partial W_{M L P}}, \eta v \frac{\partial L}{\partial V}, \eta_\sigma \frac{\partial L}{\partial \sigma}, \eta_{c o n v} \frac{\partial L}{\partial W_{c o n v}}\right)\end{aligned}$     (4)

Here, the symbol $L$ is utilized to specify the loss function, $\sigma$ sets the scaling factors $\left(\sigma=\left(\sigma_1, \ldots, \sigma_{N_K}\right)\right)$, and $V=$ ( $v_1, \ldots, v_{N_K}$ ) identifies the RBF neurons (centroid). The classifier and feature parameters are expressed as $W_{M L P}$ and $W_{\text {conv }}$, respectively. The learning rate of the parameters is specified as $\eta_{M L P}, \eta v, \eta_{\text {sigma }}$, and $\eta_{\text {conv }}$. The adam optimizer is used to perform optimization, and the derivations from the intermediate layers are derived analytically using supplementary materials. The convolutional feature extraction is initialized randomly or pre-trained. In MLP, $k$ - means is initialized, and the vectors $S=\left\{x_{i j} \mid i=1, \ldots, N, j=\right.$ $\left.1, \ldots, N_i\right\}$ are clustered to $N_K$ clusters and centroids $V K \in$ $\mathbb{R}^{N_F}\left(k=1, \ldots, N_K\right)$ are utilized for initializing the neurons centroid. The process is adopted for learning purposes, applied for centre initialization and optimized to fulfil the objective. The scaling factor is set as 0.1. At last, the random initialization process is utilized for MLP parameter initialization.

The critical concept that relies on linear feature pooling is to substitute the higher non-linear similarity evaluation that performs computation with pairwise distance and transforms the RBF kernel similarity, i.e., linear operator. The non-linear exponential operator and scaling factor adopted in Eq. (1) are eliminated and attain the similarity function.

$[\emptyset(x)]_k=-\left.\left\|x-v_k\right\|\right|_2 \in \mathbb{R}$  (5)

The above Eq. (5) can also be developed with the squared distance among the feature vectors.

$[\emptyset(x)]_k=-\left|\left|x-v_k\right|\right|_2^2=2 x^T v_k-||x||_2^2-\left|\left|v_k\right|\right|_2^2$       (6)

Thus, the similarities among the feature vectors are specified as the inner product among the vectors after subtracting $l^2$ normalization. After the training, the normalization factor is set constant, i.e. $\left\|v_k\right\|_2^2=c_k$. Consider that the feature vector normalization is constant, and $\left|\left|v_k\right|\right|_2^2=$ $c_f$ is reduced to $[\emptyset(x)]_k=2 x^T v_k-c$, where $c=c_k+c_f$ is a constant (fixed). Thus, with the elimination of additive factor " $c$ ", the similarity function is given by Eq. (7):

$[\emptyset(x)]_k=C^{S T} v_k$       (7)

The above Eq. (7) represents the cosine similarity $\left(\left(x^T v_k /||x||_2| | v_k| |_2\right)\right)$ with unit length representation. Moreover, the unit length ranges from $-\infty$ to $\infty$ while cosine similarity ranges between -1 and 1. To avoid normalization during network deployment, the absolute operator fulfills the similarity metrics and leads to similarity metrics for linear feature analysis.

$[\bar{\bar{\phi}}(x)]_k=\left|x^T v_k\right| \in \mathbb{R}$        (8)

where, |$.$| specifies the absolute value operator. The similarity value specifies a higher correlation degree with (+ $ve$ and - $v e)$ vectors, while values nearer to 0 specify the no correlation factor. The anticipated similarity metrics eliminate the correlation sign. It may not harm the model accuracy, as the degree of correlation among the vectors, i.e., essential information. Moreover, the feature vectors are provided to the similarity metrics, and the gradients are back-propagated to the related layers with the elimination of the correlation sign. The quantization used over the regular pooling operations is evaluated with Eq. (9):

$[\bar{\bar{\emptyset}}(x)]_k=\frac{\left|x^T v_k\right|}{\sum_{m=1}^{N_k}\left|x^T v_m\right|}$      (9)

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Figure 2. Internal representation of the network model

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Figure 3. CNN-DFUNet model

Convolutional layers: The similarity evaluation is executed as the absolute value operator in the convolutional layer. Thus, $N_K$ is the filter size $\left(1 * 1 * N_F\right)$, and $N_f$ specifies the filter count. Moreover, with the experimentation, it is noted that the skipping normalization does not affect the performance of the pooling. At last, average pooling with stride and window length equal to the extracted feature length maps are utilized to extract the input sample representation as a feature size map $1 * 1 * N_k$. As the independent histogram is hauled out, the spatial segmentation needs to alter the window length, i.e. diminishing the window length is equal to the spatial segmentation (i.e., level=1). The segmentation process provides the spatial regions. However, it does not diminish the model's learning ability and reduces the overfitting risk. The architecture adopted for executing the linear variants is similar to the network, i.e., $1 * 1$ convolutions to diminish the extracted features. The network model provides a primitive way of removing the feature representation and gives successive insights (Figure 3).

The feature extraction model is competent in decoupling the feature representation from the extracted feature count and its dimensionality, allowing the network model. The CNN model needs $O\left(N_i N_F N_H+C_L\right)$ parameters for the fully connected layers, the pooling layer needs $O\left(N_F N_H+C_L\right)$, and the linear features require $O\left(N_S N_K N_F+N_S N_K N_H+C_L\right)$. The parameters are diminished to $O\left(N_K N_F+N_S N_K N_H+C_L\right)$. The cost of evaluating the network process is $O\left(N_i N_F N_H+\right.$ $\left.C_L\right), O\left(N_i N_F+N_F N_H+C_L\right)$ for global mapping and $O\left(N_i N_K N_F+N_S N_K N_H+C_L\right)$ for feature mapping. The cost to assess the similarity among the feature vectors is the same for the linear feature. The distance among the vectors is evaluated with the product evaluation, i.e., $\|x-y\|_2^2=x^T x+y^T y-$ $2 x^T y$ for two diverse features vectors $x$. The obtained feature count is based on the input image dimension. Therefore, the complexity is handled by the global mapping and linear feature analysis with the suitable input image.