## 4 Materials and Methods
### Design of the Introduced CAD
#### 4.2.3 Handcrafted Descriptors Mining  
Several textural descriptors were mined from pap smear photos from the spatial and time-frequency domains. Spatial domain features include GLCM, whereas time-frequency features involve DWT as well as GW. Additionally, numerous statistical features were obtained from the spatial domain. This section will describe the methods of feature extraction. A technique for extracting statistical features from a signal or image is known as statistical explanatory feature extraction. Nine statistical features, including variance, Root Mean Square (RMS), kurtosis, entropy, mean, skewness, Inverse Difference Moment (IDM) [56], smoothness, and standard deviation (std), were among the statistical variables. Moreover, four texture features were calculated from the spatial domain involving contrast, energy, correlation, and homogeneity. Equations used to extract these features from the pap smear slides are shown below (1)-(17). \[Mean\ (\mu)=\frac{1}{NM}\sum_{i,j=1}^{NM}A(i,j) \tag{1}\]  
\[Variance=\frac{1}{(N-1)(M-1)}\sum_{i,j=1}^{MN}(A(i,j)-\mu)^{2} \tag{2}\]  
\[Std(\sigma)\ =\ \surd(Variance) \tag{3}\]  
\[Skewness=\frac{1}{MN}\sum_{i,j=1}^{MN}\left[\frac{A(i,j)-\mu}{\sigma}\right]^{3} \tag{4}\]  
\[Entropy=-\sum_{g=0}^{G-1}pr_{g}\ \times\log pr_{g} \tag{5}\]\[IDM=\sum_{i}^{M}\sum_{j}^{N}\frac{1}{1+\left(i,j\right)^{2}}A(i,j) \tag{6}\] \[Kurtosis(A_{1}\ldots\ldots\.\ A_{N})=\left\{\frac{1}{MN}\sum_{i,j =1}^{MN}\left[\frac{A(i,j)-\mu}{\sigma}\right]^{4}\right\}-3\] (7) \[RMS=\sum_{i}^{M}\sum_{j}^{N}P(i,j)\left(\frac{\sqrt{\sum_{i,j =1}^{MN}\left|\mu_{ij}\right|^{2}}}{G^{2}}\ \right)\] (8) \[Smoothness=1-\frac{1}{1+\sum_{i}^{M}\sum_{j}^{N}A(i,j)}\] (9) \[Contrast=\sum_{g\ =\ 0}^{G-1}n^{2}\left\{\sum_{i}^{M}\sum_{j}^{N} pr_{g}\left(i,j\right)\right\}\] (10) \[Variance=\frac{1}{(N-1)(M-1)}\sum_{i,j=1}^{MN}(A(i,j)-\mu)^{2} \tag{2}\]0 (11) \[Variance=\frac{1}{(N-1)(M-1)}\sum_{i,j=1}^{MN}(A(i,j)-\mu)^{2} \tag{2}\]1 (12) \[Variance=\frac{1}{(N-1)(M-1)}\sum_{i,j=1}^{MN}(A(i,j)-\mu)^{2} \tag{2}\]2  
where \(A(i,j)\) is the pixel value at location \(i\) and \(j\) in an image, \(\mu\) is the mean, \(G\) is the number of grey levels. \(pr_{i}\) is the probability of a pixel having gray level \(g\), \(N\) and \(M\) are the length and width of the image. Grey Level Co-Occurrence Matrix Texture Features  
The GLCM strategy is a 2 nd order statistical method that calculates the intensity of adjacent pixels in an image that has identical grey-levels and applies extra information acquired from spatial pixel relations [57]. A co-occurrence matrix was used to retrieve textural details about grey-level transfers among two pixels. This co-occurrence matrix illustrated the common distribution of gray-level pairs of adjacent pixels given a spatial association described between pixels in a texture. As a result, changing the spatial correlation yields matrices with various data (different directions or distances between pixels). Such matrices were used to extract descriptors. The dimension of the co-occurrence matrix was determined solely by the texture's grey levels and not by the image size [58]. The four orientations used in this study were 0, 45, 90, and 135, and the number of grey levels was 8. Four GLCM texture features were determined involving contrast, correlation, energy, and homogeneity; the same statistical features were also calculated from the co-occurrence matrix of GLCM. \[Variance=\frac{1}{(N-1)(M-1)}\sum_{i,j=1}^{MN}(A(i,j)-\mu)^{2} \tag{2}\]3 \[Variance=\frac{1}{(N-1)(M-1)}\sum_{i,j=1}^{MN}(A(i,j)-\mu)^{2} \tag{2}\]4 (15) \[Variance=\frac{1}{(N-1)(M-1)}\sum_{i,j=1}^{MN}(A(i,j)-\mu)^{2} \tag{2}\]5\[Variance=\frac{1}{(N-1)(M-1)}\sum_{i,j=1}^{MN}(A(i,j)-\mu)^{2} \tag{2}\]6  
where _P_(_i_,_j_) is a marginal joint probability gray-level co-occurrence matrix. \(x\) and \(y\) are two adjacent pixels. Discrete Wavelet Transform Textural Features  
The discrete wavelet transforms (DWT) a popular image processing technique, analyses images in both time-frequency domains.