## 4 Experimental Results
### Objective Evaluation
#### Information Entropy  
Information entropy is an important indicator of the richness of image information. For images, the wider the grey-scale distribution, the richer the details, and the greater the information entropy. The calculation is shown in Formulas (7) and (8), where \(f(i,j)\) is \begin{table}
\begin{tabular}{l l l} \hline \hline
**Operating System** & **Processing Software** & **CPU** & **Running Memory** \\ \hline Windows 10 & MATLAB R2021a & Intel(R) Core(TM) i5-6300 HQ & 12 GB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The computer configuration used for the experiments in this paper. Figure 13: Experimental processing results: (**a**) Original drawing, (**b**) Algorithm in this study, (**c**) HE algorithm, (**d**) CLAHE algorithm, (**e**) Wavelet, (**f**) Adaptive \(\gamma\) in this study. the frequency of occurrence of feature binary \((i,j)\), \(N\) is the scale of the image, and \(P_{(i,j)}\) denotes the proportion of the image whose feature binary is \((i,j)\). \[P_{ij}=\frac{f(i,j)}{N^{2}} \tag{7}\]  
\[H=-\sum_{i=0}^{255}p_{ij}\log p_{ij} \tag{8}\]  
2. _MSE_ The root mean square represents the square of the difference between the true and predicted values. The, the sum of the squares is found in the average. The smaller the value of \(MSE\), the more similar the images. The calculation formula is shown in Equation (9), where \(f^{\prime}(i,j)\) and \(f(i,j)\) denote the image to be evaluated and the original image, respectively, and \(M,N\) denote the length and width of the image, respectively. \[MSE=\frac{1}{M\times N}\sum_{i=1}^{M}\sum_{j=1}^{N}\left(f^{\prime}(i,j)-f(i, j)\right)^{2}\] (9)
3. _PSNR_ The peak signal-to-noise ratio (\(PSRN\)) is used to evaluate the parameters of image quality and can reflect the size of the impact of noise on the image. A larger peak in the signal-to-noise ratio of the image indicates better image quality. Its expression is shown in Formula (10), where \(Max_{1}\) is the maximum possible pixel value in the image, \(MSE\) is the root mean square and \(\log_{10}\) performs the logarithmic operation. \[PSNR=10\cdot\log_{10}\left(\frac{Max_{1}^{2}}{MSE}\right)\] (10)
4. _SSIM_ Structural similarity (\(SSIM\)) is derived from the structural similarity theory and is used to measure the magnitude of structural similarity between two images, with a maximum value of 1, where larger values represent greater similarity. It especially reflects the similarity of the contours, details, etc. of the images. The formula is shown in Equations (11) and (12), where \(l(f,g)\) denotes the luminance change, \(c(f,g)\) denotes the variance change, and \(s(f,g)\) is the structural change. In addition, \(f\) and \(g\) denote the two images, \(\mu_{f}\) and \(u_{g}\) denote the mean of the images, \(\sigma_{f}\) and \(\sigma_{g}\) denote their variance, and \(\sigma_{fg}\) denotes their covariance. \(C_{1}\), \(C_{2}\) and \(C_{3}\) are relatively small constants used to ensure that the denominator is not equal to zero. \[SSIM(f,g)=l(f,g)\cdot c(f,g)\cdot s(f,g)\] (11)  
\[l(f,g)=\frac{2\mu_{f}\mu_{g}+C_{1}}{\mu_{f}{}^{2}+\mu_{g}{}^{2}+C1},c(f,g)= \frac{2\sigma_{f}\sigma_{g}+C2}{\sigma_{f}{}^{2}+\sigma_{g}{}^{2}+C2},s(f,g)= \frac{\sigma_{fg}+C3}{\sigma_{f}\sigma_{g}+C3} \tag{12}\]
5. Processing time The processing time reflects the timeliness of the algorithm and also shows the consumption of resources to a certain extent; the shorter the time, the better the processing results, providing further proof of the algorithm's advantages. According to the data in Table 2, the adaptive value formula designed in this study combined with this study's algorithm used in image processing has obvious advantages in objective indexes and obviously surpasses the fixed value processing method, achieving excellent processing results. According to Table 3, compared with the histogram equalisation algorithm, the algorithm in this study achieves a greater improvement in image richness, detail enhancement and other aspects.