## 3 Methods
### Feature Extraction Module (FEM)  
The image's edges and contrast should be improved for greater accuracy and clarity, and this can be achieved by using the image's colormap. After obtaining the set of boundary pixels, the updated threshold was calculated by taking the average of the boundary pixels from the contrasted image. The transformation was accomplished through a series of steps depicted in Figure 4.  
The transformation process can be described as:  
Convert the RGB (Red, Green, and Blue) color space to the HSV (Hue, Saturation, and Value) color space; the following formulas were used [15; 16]. \[H=\mathit{Cos}^{-1}\quad\frac{0.5[(R-G)+(R-B)]}{\sqrt{(R-G)\ ^{2}+(R-G)(R-B)}} \tag{1}\]  
\[S=1-\frac{3}{R+G+B}\ [\min(R,G,B)] \tag{2}\]  
\[V=\frac{1}{3}(R+G+B) \tag{3}\]  
A color histogram, in general, is based on a specific color space, such as RGB or HSV. The correlogram is obtained when the pixels in an image that contains different colors are calculated. A correlogram can be represented as a table indexed by pairs of colors (i,j), with the \(\mathrm{dth}\) entry indicating the probability of finding a pixel (j) from pixel (i) at distance d. On the other hand, an auto-correlogram has been stored as a table indexed by color (i), where the \(\mathrm{dth}\) entry shows the probability of finding pixel (i) from the same pixel at a distance of (d). As a result, the auto-correlogram shows only the spatial correlation between identical colors. Experimental results showed that correlograms and auto-correlograms are both computationally expensive. As a result, a correlogram with a small number of colors and a small distance value will produce very good results without raising the computational cost. Let [D] denote a set of D fixed distances {\(d_{1},\ldots,d_{\mathrm{D}}\)}. Then the correlogram of the image (_l_) has been defined for color pair (\(c_{i}\), \(c_{j}\)) at a distance \(d\)[16]. \[\gamma_{c_{i}c_{j}}^{d}(I)=\mathit{Pr}_{p_{1}\in I_{c_{i}},p_{2}\in I}\big{[} p_{2}\in Ic_{j}\big{|}|p_{1}-p_{2}|=d\big{]} \tag{4}\]  
Figure 4: Series of transformation steps. The auto-correlogram of the image (I) is defined for color \(C_{i}\) at a distance d.  
\[\alpha_{c_{i}}^{d}(I)=\gamma_{c_{i}c_{i}}^{d}(I) \tag{5}\]  
The color moments were used to differentiate images based on their color characteristics. These moments provide a measure of color similarity between images. These similarity values can be compared with the values of images stored in a database for image retrieval tasks. Color moments are based on the assumption that the color distribution in an image is interpreted as a probability distribution; the number of distinct moments are characterized by the probability distributions. As a result, if the color in an image follows a specific probability distribution, the moments of that distribution can be used as features to identify that image based on color [17]. \[E_{i}=\sum_{N}^{j=1}\frac{1}{N}\ P_{ij} \tag{6}\]  
In general, the image has three central moments of color distribution. They can be expressed as the mean, the standard deviation, and the skewness. A color is defined by three or more values; in the proposed methodology, it can be expressed as the HSV scheme of hue, saturation, and brightness. Therefore, the image is defined by nine moments, three moments for each of the three color channels. The \(i\)th color channel at the \(j\)th image pixel is denoted as \(p_{ij}\). The average color value in the image is represented by the mean (\(E\)), the standard deviation (\(\sigma\)) which is the square root of the distribution's variance, and skewness (\(S\)) which is a metric for deciding the level of asymmetry in distribution [17,18]. \[\sigma_{i}=\sqrt{(\frac{1}{N}\sum_{N}^{j=1}(P_{ij}-E_{i})^{2})} \tag{7}\]  
\[S_{i}=\sqrt[3]{\left(\frac{1}{N}\sum_{N}^{j=1}(P_{ij}-E_{i})^{3}\right)} \tag{8}\]  
The channels were represented by a bank of two-dimensional Gabor filters.