## 3 Proposed Approach
### Preprocessing  
In the examined datasets, a substantial portion of images display low visual quality, often being dark or monochromatic in the AWE dataset. In a previous study [23], we introduced a framework with a generative model to colorize grayscale and enhance dark ear images, yielding improved performance when subjected to a trained classifier. We employed deep convolutional generative adversarial networks (DCGANs) for colorization and enhancement. A standard U-Net paradigm was designed for the generative model to create colorized ear representations, as shown in Figure 1.  
The structural configuration of the discriminative model, illustrated in Figure 2, exhibits a comparatively simpler architecture than that of the generator. Comprising five convolutional layers, the model utilizes 4 \(\times\) 4 filters with a stride of two, concomitant with batch normalization and Leaky-ReLU activation. The ultimate layer employs a singular 4 \(\times\) 4 filter with a stride of one and is activated through the sigmoid function, yielding a scalar value indicative of the authenticity of the generated image. This binary classification model generates a probability output within the range of [0, 1], designated as \(P\) in Figure 2.  
The discriminator is presented with a 256 \(\times\) 256 \(\times\) 4 input, achieved through the concatenation of a grayscale image and either an authentic or synthesized color image. Its primary aim is to optimize the probability of accurately discerning between generated and genuine images, expressed as (\(log\ D\ (y|x)\)). In contrast, the generator endeavors to minimize the complementary expression, \(1-log\ D\ (G(\theta_{z}|x))\). The ultimate cost function, denoted as \(V\), is formally articulated through Equation (1) [11].  
\[min_{G}max_{D}V(G,D)=\mathbb{E}_{x}[\log D(y\ |\ x)]+\mathbb{E}_{z}[1-logD(G(O_{z} \ |\ x))] \tag{1}\]  
where the grayscale image is denoted as \(x\), the ground truth as \(y\), and \(G(O_{z}\ |\ x)\) represents the mapping function embodying the generator's output color image derived from the input image \(x\). Correspondingly, the discriminator is denoted by the mapping function, \(D(y\ |\ x)\), yielding a scalar within the range [0, 1], signifying the probability of the input being generated or otherwise. The symbol \(\mathbb{E}_{x}\) represents the expected value across all real color images, while \(\mathbb{E}_{z}\) signifies the expected value computed across all generated color images.  
Equation (2) delineates the objective of training the adversarial model, aiming to minimize the average Euclidean distance at the pixel level between colorized images (\(\theta\)) and ground truth images (\(y\)). In this formulation, \(x\) represents the grayscale image, \(e\) denotes the channel index, and \(i,\ j\) are indices referring to individual pixels.  
\[Distance(x,\theta)=\frac{1}{3 uv}\sum_{e=1}^{3}\sum_{i=1}^{u}\sum_{j=1}^{v} \
orm{x_{i,j}^{e}-y_{i,j}^{e}}_{2}^{2} \tag{2}\]  
Figure 3 visually represents the outcomes subsequent to the preprocessing application. The results demonstrate the successful colorization of the images and the simultaneous  
Figure 1: Design of the U-Net for the generative model.  
Figure 2: Design of the discriminative model.  
achievement of uniform brightness and intensity equalization, along with the standardization of image dimensions. These transformations were obtained through the utilization of the proposed DCGAN model.