## 4 Experimental Methods
### Texture Information Extraction  
After extracting the color parameters of the wildlife image, we can determine that different areas of the same texture are susceptible to color changes in the image. Here, the texture information is obtained to ensure the integrity of the extraction of the foreground area. In this study, the texture information of the images is extracted by Hermite transform, and the texture information is used as a vital parameter component of the mean-shift algorithm. The continuous Hermite function is defined as follows [31; 32]:  
\[H_{n}(x)=(-1)^{n}e^{x^{2}/2}\frac{d^{n}}{dx^{n}}e^{-x^{2}/2},n=0,1,2,\ldots \tag{4}\]  
Hermite transform of a signal is defined as  
\[f_{n}(t_{0})=\int f(t)H_{n}(t_{0}-t)V_{n}^{2}(t_{0}-t)dt \tag{5}\]  
Figure 4: Flow-process diagram of the proposed method.  
where \(V(t)\) is a Gaussian window function defined as follows:  
\[V(t)=\frac{1}{\sqrt{\sigma\sqrt{2\pi}}}e^{-\frac{(t-p)^{2}}{2\omega^{2}}} \tag{6}\]  
\(f_{n}(t_{0})\) is obtained by convolution with the Hermite analytic function \(d_{n}(t)\) by the input signal \(f(t)\). This is described in terms of the window and the Hermite polynomials as:  
\[d_{n}(t)=\frac{1}{\sigma\sqrt{2\pi}}H_{n}(t)e^{-\frac{(t-p)^{2}}{2\omega^{2}}} \tag{7}\]  
Because the function is rotational symmetry and separable, the one-dimensional Hermite space can be transformed into a two-dimensional space. The formula is as follows:  
\[d_{n-m,m}(x,y)=d_{n-m}(x)d_{m}(y) \tag{8}\]  
where\(n-m\) and \(m\) denote the order in \(x\) and \(y\) directions, respectively [33]. The filter of \(d_{n-m,m}(x,y)\) has the characteristics of continuous attenuation, and is not as steep and discontinuous as the ideal filter, which can effectively preserve the edge information of the image. The perspective of the Hermite analytic function is shown in Figure 5.  
Finally, the input image \(I(x,y)\) can be transformed into \(d_{n-m,m}(x,y)\) as [34]  
\[I_{n-m,m}(x_{0},y_{0})=\iint I(x,y)d_{n-m,m}(x-x_{0},y-y_{0})dxdy \tag{9}\]  
Since all the Hermite analytic functions were obtained by multiplication of the Gaussian window function and Hermite polynomial, in order to reduce the computational complexity of the method, several polynomials were chosen as some of the polynomials were not capable of extracting valuable texture parameters. The steps were as follows:  
1. In order to reduce the amount of data calculated, we set the value relationship between \(m\) and \(n\) as \(m+n\leq 5\);
2. Since \(H_{mm}\) and \(H_{mm}\) are mutually converted matrices, one is arbitrarily selected as the convolution kernel;
3. The polynomial H\({}_{11}\) was not chosen due to the fact it did not extract any texture information.  
Figure 5: Perspective of Hermite analytic function \(\mathbf{H_{12}}\).  
Taking the input image of Figure 4 as an example, the image was convolved with different polynomials to obtain different texture parameters, as shown in Figure 6.  
As shown in Figure 6, when these polynomials were convolved with the input image, the polynomials H\({}_{12}\), H\({}_{22}\), H\({}_{23}\), H\({}_{31}\), and H\({}_{41}\) were determined to extract useful texture parameters in different directions, in which the texture parameters directed by H\({}_{12}\), H\({}_{22}\), and H\({}_{31}\) in Figure 6 were particularly conspicuous; however, H\({}_{11}\) did not extract any texture information. Instead, a parameter image, which is similar to the grayscale image of the input image, was generated. Thus, we next constructed the filter to extract the texture parameter. The architecture of the proposed method for extracting the Hermite texture parameter is demonstrated in Figure 7.  
The extracted texture parameter was saved for further processing to obtain a texture image, as shown in Figure 8.  
Figure 6: Polynomial convolution texture information; (**a**) H\({}_{11}\); (**b**) H\({}_{12}\); (**c**) H\({}_{31}\); (**d**) H\({}_{23}\); (**e**) H\({}_{41}\); and (**f**) H\({}_{22}\).  
Figure 7: Flow-process diagram of texture extraction.