## 3 Materials and Methods
### Standard CNN  
A CNN is a specialized class of DL models designed primarily for processing structured grid data, such as images. First introduced by [PERSON] in 1989, CNNs were inspired by the organization of the animal visual cortex, where neurons in the brain respond to overlapping regions of the visual field. The most well-known early CNN architecture, LeNet-5, was developed in 1998 and demonstrated its effectiveness in handwritten digit recognition. Since then, CNNs have become the foundation of modern computer vision, driving applications such as image classification, object detection, medical imaging, and facial recognition. CNNs leverage spatial hierarchies of features, extracting relevant patterns from input images through the application of convolutional filters. Instead of traditional fully connected layers, CNNs utilize local connectivity and weight sharing to drastically reduce the number of parameters, making them more efficient in handling large-scale image datasets [51; 52; 53; 54].  
Each convolutional filter scans over an input matrix, capturing small localized patterns such as edges or textures, which are then combined across layers to build more complex representations. As shown in Figure 2, a standard CNN consists of multiple essential layers that progressively transform the input data into high-level feature representations. The model consists of convolutional layers, pooling layers, a flattening stage, and fully connected layers, which ultimately produce the final output. The first stage is the convolutional layer, where each filter (kernel) slides over the input image and performs element-wise multiplications followed by summation. Mathematically, this operation can be expressed as follows.  
\[Y(i,j)=\sum_{m}\sum_{n}X(i-m,j-n)\times W(m,n) \tag{27}\]  
where \(X\) represents the input image, \(W\) denotes the kernel weights, and \(Y(i,j)\) is the resulting feature map. The extracted feature maps are then passed through an activation function, commonly the Rectified Linear Unit (ReLU), which introduces nonlinearity into the model, allowing it to learn complex patterns.  
Following the convolutional operation, CNNs employ pooling layers to reduce the spatial dimensions of feature maps while preserving key information. Max pooling is the most commonly used method, selecting the maximum value from each local region, thereby achieving translational invariance and improving computational efficiency. The first pooling operation in Figure 2 demonstrates this process, in which the number of feature maps is reduced while retaining important details. After multiple convolutional  
Figure 2: Standard CNN architecture illustrating the hierarchical feature extraction process.  
and pooling layers, the flattening layer converts the extracted high-dimensional features into a one-dimensional vector. This flattened representation is then fed into fully connected (dense) layers, which perform the final decision-making. These layers resemble traditional neural networks, where each neuron is connected to every neuron in the previous layer. The final output layer typically applies a SoftMax function for classification tasks or a sigmoid function for binary classification. CNNs have revolutionized deep learning due to their ability to automatically learn feature hierarchies from raw data, reducing the need for manual feature engineering. Their success extends beyond computer vision to areas such as natural language processing (NLP) and speech recognition, where CNNs extract spatial representations from text and audio signals. Using convolutional operations, pooling, and deep feature extraction, CNNs have become indispensable tools for modern AI applications.