# [PERSON]'s Entropy Based Multilevel Thresholding Using a Novel Meta-Heuristics Algorithm
## 4 Simulation Results and Discussion  
We implement the proposed approach by the language of matlab2015 on a personal computer with 8.00 G RAM, a CPU of Intel (R) Core (TM) i5-3470 @3.20 GHz, under Windows10 system. In order to show the advantages of this method, half of our test images are natural images of standard images and the other half are SEM images of cement. The cement image used in the experiment was taken from po42.5 cement produced by Hubei Huaxin Cement Plant, and the water cement ratio was 0.35, which was prepared according to the standard of GB / t17671-1999. Standard images are named \"baboon\", \"cameraman\", \"house\", \"pepper\", and we have named SEM images of cement \"image1\", \"image2\", \"image3\", \"image4\". The images are shown in Figure 3.  
The paper also mentions some commonly used evolutionary algorithms or swarm intelligence algorithms to seek the best multiple thresholds. In order to make a purposeful and effective comparison, the selected threshold segmentation method is [PERSON]'s entropy, which is optimized by evolutionary algorithm or swarm intelligence optimization algorithm. The paper uses HRO-based [PERSON]'s entropy (HRO-Renyi). The threshold segmentation methods for comparison experiments are: GA-based [PERSON]'s entropy (GA-Renyi), PSO-based [PERSON]'s entropy (PSO-Renyi), DE-based [PERSON]'s entropy (DE-Renyi), ALO-based [PERSON]'s entropy (ALO-Renyi), WOA-based [PERSON]'s entropy (WOA-Renyi), SSA-based [PERSON]'s entropy (SSA-Renyi). GA, PSO, DE, ALO, WOA, and SSA all use their standard algorithms, parameters of algorithm are shown in Table 1. The number of iterations of all algorithms is 100 and the number of populations is 60. To test the stability of the algorithm, all algorithms are run 50 times. In this section, we provide some comparative experimental results, including some segmentation examples, performance evaluation tables, and function convergence graphs, which  
Figure 3: The eight images used in the experiment. clearly demonstrate the advantages of the proposed method. Here we present 2-level, 4-level, 6-level, and 8-level thresholding for visual evaluation of natural images. Because the number of thresholds is too large, the exhaustive method is not applicable, our main interest is the optimization ability, which is mainly demonstrated through the fitness value of the objective function and stability analysis. For a further comparison, a multi-threshold segmentation method based on inter-class variance is also implemented in the paper, which is optimized using HRO (HRO-OTSU). The HRO-OTSU method is compared with the HRO-Renyi method, the accuracy of target segmentation is evaluated by peak signal to noise ratio (PSNR) and structural similarity index (SSIM). PSNR is a widely used method of image quality evaluation index, which is based on the gray value of image pixels for statistics and average calculation. Although there may be a large deviation between the quality of some images or video quality evaluation and the quality of subjective perception, PSNR is still effective for most image quality evaluation. Given an image \(I\) with a size of \(m\)\(*\)\(n\) and an image \(K\) after threshold segmentation, MSE is defined as Equation (18):  
\[\text{MSE}=\frac{1}{\text{mn}}\sum_{i=0}^{m-1}\sum_{j=0}^{n-1}[\text{I}(i,j)- \text{K}(i,j)]^{2} \tag{18}\]  
PSNR is defined as Equation (19):  
\[\text{PSRN}=10\log_{10}\left(\frac{\text{MAX}_{1}^{2}}{\text{MSE}}\right) \tag{19}\]  
_MAX\({}_{I}^{2}\)_ is the maximum possible pixel value of the image. If each pixel is represented by 8-bit binary, it is 255. Generally, if the pixel value is represented by B-bit binary, then \(MAX_{I}=2^{B}-1\). Generally, for uint8 data, the maximum pixel value is 255, and for floating-point data, the maximum pixel value is 1. SSIM is an index to measure the similarity of two images. It measures the similarity of images from three aspects of luminance, contrast and structure.