## 3 Multiple Features
### Tamura Feature  
One of the most prevalent merits of different image types' analysis is texture. Texture has properties like regularity and scale, and it can be characterized by different orientations, coarseness, contrast, and other factors [18]. Texture plays a big role in human eyesight. Even though everyone can identify texture, defining it might be difficult. As a result, image texture-based classification [4] has recently been utilized to classify malware.  
Tamura is one of the most popular texture features. [PERSON] and colleagues devised texture features that correlate to human visual perception [18]. They evaluated psychological assessments for human volunteers to six textural features (coarseness, contrast, directionality, line-likeness, regularity, and roughness). The first three achieved excellent results and included coarseness, contrast, and directionality.  
An image will have textures at various scales; coarseness seeks to find the biggest size from which a texture occurs, even when a tiny micro-texture is present. In terms of computation, one calculates averages at each point across neighborhoods with linear sizes that are powers of two. At the point \((x,y)\), the mean over the neighborhood of size \(2^{k}\times 2^{k}\) equals:  
\[A_{k}(x,y)=\sum_{i=x-2^{k-1}-1}^{x+2^{k-1}-1}\sum_{j=y-2^{k-1}}^{y+2^{k-1}-1} \frac{f(i,j)}{2^{2k}} \tag{1}\]  
where, \(2^{k}\times 2^{k}\) size is the average of neighborhood.  
\[E_{k,h}\left(x,y\right)=\left|A_{k}\left(x+2^{k-1},y\right)-A_{k}\Big{(}x-2^{ k-1},\ y\Big{)}\right| \tag{2}\]  
The difference between these two means that they belong to non-overlapping neighborhoods is calculated using Equation (2).  
Contrast is a metric that determines how the distribution of gray levels fluctuates in an image and how skewed it is toward black or white. The standard deviation of grey levels is first calculated. The kurtosis \(\alpha_{4}\) is then used in the second step. As a result, the contrast measure is defined as:  
\[Contrast=\sigma/(\alpha_{4}) \tag{3}\]  
\[\alpha_{4}=\mu_{4}/\sigma^{4} \tag{4}\]  
when the variance is \(\alpha_{2}\) and the fourth moment around the mean is \(\mu_{4}\). The closest value, according per [PERSON], is \(n=\frac{1}{4}\).  
Directionality is a texture characteristic that affects the entire image. The presented feature does not attempt to distinguish between various orientations or patterns but rather the overall degree of directionality. A scale of 0 to 1 was employed to determine the degree of directionality. As a result, two patterns with the same degree of directionality but different orientations are deemed the same. Equation (5) was used to calculate the directionality.  
\[Directionality=1-rn_{peals}\ \sum\
olimits_{p=1}^{n_{peals}}\sum\
olimits_{a \in\mathit{vp}}\bigl{(}a-a_{p}\bigr{)}^{2}H\ directionality\ (a) \tag{5}\]  
where \(r\) signifies a normalizing factor associated to quantizing levels of the angle \(a\), an indicates quantization direction angle, \(\mathit{np}\) represents the number of peaks, \(\mathit{ap}\) indicates the location of the peaks, \(\mathit{wp}\) indicates the range of the angles assigned to the Pth peak, and the histogram of quantization direction value known as _HDirectionality_ is created by calculating the number of edge pixels that have associated directional angles.