To enhance the diversity and distribution uniformity of initial population, as well as to avoid local extrema in the Chimp Optimization Algorithm (CHOA), this paper improves the CHOA based on chaos initialization and Cauchy mutation. First, Sin chaos is introduced to improve the random population initialization scheme of the CHOA, which not only guarantees the diversity of the population, but also enhances the distribution uniformity of the initial population. Next, Cauchy mutation is added to optimize the global search ability of the CHOA in the process of position (threshold) updating to avoid the CHOA falling into local optima. Finally, an improved CHOA was formed through the combination of chaos initialization and Cauchy mutation (CICMCHOA), then taking fuzzy Kapur as the objective function, this paper applied CICMCHOA to natural and medical image segmentation, and compared it with four algorithms, including the improved Satin Bowerbird optimizer (ISBO), Cuckoo Search (ICS), etc. The experimental results deriving from visual and specific indicators demonstrate that CICMCHOA delivers superior segmentation effects in image segmentation.

With the widespread application of various medical images in auxiliary medicine, computer-aided diagnosis has attracted increasing attention [

Image thresholding divides an image into two or more non-overlapping regions according to a vector of thresholds and the image’s gray level. While the length of the thresholds’ vector is 1, image thresholding can only divide the image into two regions: foreground and background. When its length exceeds 2, the image is divided into more and better-defined regions. However, as the number of thresholds increases, the corresponding calculations also rise exponentially, so swarm IOA is an effective solution [

In the objective function selection, Li et al. [

On the application of swarm IOA in multilevel image segmentation, Yan et al. [

The various ideas for improving the global search ability of swarm IOA and avoiding local optima in its iterations can be summarized into two respects: (1) Improving the initialization mode of its population. At the beginning of the swarm IOA, the initial population with higher dispersion and stronger randomness is provided, to improve the optimal search ability and accelerate the convergence speed. (2) Optimizing the renewal strategy of the individual population. A mechanism to update the population of IOA is the most important means to avoid it falling into local optima. Theoretically, with the continuous iteration of the IOA, the final optimal solution is closer to the ideal one. However, if the IOA cannot continuously produce better solutions in its iteration, it easily falls into local optima. Therefore, this paper seeks to improve CHOA based on the above two key improvement directions, and to verify its segmentation effect in natural and medical images.

The CHOA is a swarm IOA proposed by Khishe et al. [

In order to improve the initial population diversity and convergence performance of the CHOA, the random initialization mode of CHOA was improved by Sin chaotic initialization in CICMCHOA.

The population update strategy of CHOA has been improved by utilizing Cauchy mutation. this not only avoids the CHOA falling into local optima but also enhances its global search ability and image segmentation performance.

By combining fuzzy logic and fuzzy membership functions through fuzzy Kapur, this work explored the global optimization ability of CICMCHOA and improved the quality of image segmentation.

The effectiveness of CICMCHOA in natural and medical image segmentation has been validated through extensive visual and data analysis, the experimental results were compared with those of the ISBO [

The rest of this paper is organized as follows.

In the CHOA [

The basic steps of CHOA are as follows: assume there are

where

In

In the exploration stage, CHOA simulates the predation process of chimps in nature. The attacker chimps representing the optimal solution complete the last attack on the prey, and the barrier, chaser and driver chimps occasionally participate in the attack behavior while completing their respective tasks. To improve the convergence speed, the CHOA model assumes that the barrier, chaser and driver chimps can also determine the location of the prey. Therefore, other chimps need to complete the iterative updating of their locations according to the location of the first four types of chimps, as shown in

where

The selection of parameter

The results of swarm IOA are to an extent controlled by the initial value of the initial population. The original CHOA initializes the population in a random way, which will lead to poorer initial solution quality, less population diversity and stronger distribution randomness in some cases. These problems will directly affect the global optimization ability of the CHOA in the subsequent optimization steps. Chaotic variables are used to improve the initial solution of the IOA because of their ergodicity, randomness and uniform distribution, and improve the quality of the initial population [

In commonly used methods of chaos initialization, Tent and Logistic chaotic models display limited map iterations. The distribution of Tent map is too uniform, which reduces the diversity of initial population. The distribution of logistic map also tends to be uniform and can only produce a small number of singular solutions, contributing less to population diversity. Sin chaotic model by comparison, is a framework with infinite-collapse, with more even distribution while ensuring the differentiation of the initial population. Therefore, this paper uses Sin chaotic map to initialize the population. The Sin chaotic map can be expressed as:

In

After the initial population generated by Sin chaotic map, several

As can be seen from

From the probability density distribution of Cauchy function, it can be seen that the function obtains the maximum at the coordinate origin, and the absolute value of the maximum is relatively small (only between 0.30 and 0.35), to ensure that the mutated chimp individuals will not spend much time exploring the surrounding area, and to improve the global search performance of the CHOA without increasing its complexity. Therefore, making full use of the disturbance ability of Cauchy strategy can improve the diversity of the population, escape of local optima, and improve the global search ability of the CICMCHOA. The improved optimal solution is obtained by

Although Cauchy Mutation can effectively increase the diversity of the population, it can conversely reduce the convergence speed of the CHOA. To balance conflicts between convergence speed and population diversity, a probability variable

In order to verify the practicality of the CICMCHOA in the field of image segmentation, this paper selects four benchmark test images to analyze and compare the segmentation effects of the CICMCHOA and CHOA, and then selects six distinct kinds of medical images to investigate the effectiveness of CICMCHOA in medical image segmentation. In addition to comparison with the CHOA, it is also fully compared and analyzed with the DE [

Parameter | SAN | m | NTT | Iteration | |
---|---|---|---|---|---|

Value | 50 | 0.05 | Iterative | 2, 3, 4, 5 | 1000 |

In

SAN | 30 | 40 | 50 | 60 | 70 |
---|---|---|---|---|---|

PSNR | 25.6884 | 25.9482 | 26.2161 | 25.6923 | 25.4043 |

FSIM | 0.8843 | 0.8918 | 0.8974 | 0.8884 | 0.8743 |

Strategies | Chebyshev | Circle | Gauss/mouse | Iterative | Logistic |
---|---|---|---|---|---|

PSNR | 25.4742 | 26.1347 | 25.4191 | 26.4559 | 25.7350 |

FSIM | 0.8741 | 0.8936 | 0.8696 | 0.8958 | 0.8883 |

Strategies | Piecewise | Sine | Singer | Sinusoidal | Tent |
---|---|---|---|---|---|

PSNR | 26.2108 | 25.6456 | 26.1236 | 25.4126 | 25.9001 |

FSIM | 0.8964 | 0.8877 | 0.9016 | 0.8736 | 0.8950 |

Iteration | 500 | 800 | 1000 | 1500 | 5000 | 10,000 |
---|---|---|---|---|---|---|

PSNR | 25.3633 | 25.4541 | 26.4762 | 25.5896 | 25.5594 | 25.4707 |

FSIM | 0.8676 | 0.8878 | 0.8969 | 0.8792 | 0.8761 | 0.8769 |

In

This paper selects four different benchmark test images to analyze and compare the segmentation effects of CHOA and CICMCHOA. In

From

Line of image | NTT | PSNR/FSIM | |||
---|---|---|---|---|---|

CHOA | CICMCHOA | ||||

Line1 | 2 | 16.6325 | 0.5927 | 18.2777 | 0.5929 |

3 | 22.8013 | 0.6206 | 22.9048 | 0.6218 | |

4 | 23.0232 | 0.6227 | 24.1159 | 0.7145 | |

5 | 25.4728 | 0.7355 | 25.8534 | 0.7640 | |

Line2 | 2 | 18.6404 | 0.6477 | 18.6674 | 0.6473 |

3 | 19.3210 | 0.7060 | 19.6164 | 0.7896 | |

4 | 19.9355 | 0.7545 | 20.2547 | 0.7982 | |

5 | 20.1264 | 0.7879 | 21.2241 | 0.8047 | |

Line3 | 2 | 17.0308 | 0.6974 | 17.0302 | 0.6974 |

3 | 20.1111 | 0.7073 | 20.2844 | 0.7235 | |

4 | 20.1589 | 0.7226 | 21.3638 | 0.7245 | |

5 | 21.5246 | 0.7440 | 22.3725 | 0.7621 | |

Line4 | 2 | 17.4571 | 0.5098 | 17.4140 | 0.5099 |

3 | 19.4479 | 0.5671 | 20.3477 | 0.5886 | |

4 | 21.2640 | 0.6592 | 22.7391 | 0.7124 | |

5 | 22.5665 | 0.7041 | 23.2952 | 0.7251 |

Based on PSNR, it can be seen from

Based on six distinct kinds of medical images, this paper uses CICMCHOA to optimize fuzzy Kapur to obtain the optimal thresholds, and then completes the thresholding segmentation.

From the visual segmentation results illustrated in

Image | NTT | Thresholds | PSNR | FSIM |
---|---|---|---|---|

Brain | 2 | 54.5 160.5 | 18.0098 | 0.6269 |

3 | 33 96 188.5 | 22.6342 | 0.7824 | |

4 | 37.5 97 140 208.5 | 24.1835 | 0.8511 | |

5 | 8.5 28.5 70 109 193 | 26.4762 | 0.8969 | |

Skin | 2 | 79.5 184.5 | 18.1418 | 0.7396 |

3 | 71 131.5 183 | 19.1666 | 0.7564 | |

4 | 43 119 147 84 | 19.4107 | 0.7867 | |

5 | 39 90 117.5 164 223.5 | 19.5638 | 0.8062 | |

Lung | 2 | 56.5 187 | 17.6378 | 0.7611 |

3 | 53 104.5 198.5 | 22.9036 | 0.7786 | |

4 | 54 131.5 166.5 220.5 | 26.1315 | 0.7904 | |

5 | 49.5 110 157 202.5 247 | 28.5490 | 0.8073 | |

Bone | 2 | 30 198 | 16.1760 | 0.6341 |

3 | 51 120 194 | 20.0797 | 0.6760 | |

4 | 47 113.5 147.5 212.5 | 21.2199 | 0.7274 | |

5 | 33 80.5 117 171 227.5 | 22.8263 | 0.7606 | |

Liver | 2 | 90 204.5 | 15.4078 | 0.6415 |

3 | 54 123.5 212 | 20.1877 | 0.6502 | |

4 | 23 81 124 210 | 24.4217 | 0.8087 | |

5 | 23.5 83.5 123 160 214 | 25.7501 | 0.8263 | |

Stomach | 2 | 89.5 146 | 15.8611 | 0.7787 |

3 | 13 54.5 146 | 21.2631 | 0.8233 | |

4 | 11.5 48.5 79 154.5 | 22.2832 | 0.8234 | |

5 | 3.5 25.5 72 112 186 | 25.5278 | 0.8648 |

To more specifically and definitively compare the performance of the CICMCHOA, this paper takes PSNR as the evaluation standard and compares the segmentation effectiveness of CICMCHOA, CHOA, DE, ISBO, ABCSCA and ICS in medical images through the measured data, as shown in

Image | NTT | PSNR | |||||
---|---|---|---|---|---|---|---|

CICMCHOA | CHOA | DE | ISBO | ABCSCA | ICS | ||

Brain | 2 | 17.6992 | 17.7010 | 17.2584 | 14.7724 | 17.0768 | |

3 | 21.7280 | 21.6577 | 21.7430 | 20.1213 | 22.0331 | ||

4 | 24.1835 | 23.0560 | 23.7295 | 23.4397 | 23.9289 | ||

5 | 23.6177 | 24.7445 | 24.9479 | 25.8953 | 25.7719 | ||

Skin | 2 | 18.0941 | 14.1347 | 18.0033 | 17.7937 | 18.1418 | |

3 | 18.9858 | 15.7833 | 19.0514 | 19.0418 | 19.1062 | ||

4 | 19.3633 | 19.0796 | 19.3842 | 19.3177 | 19.3530 | ||

5 | 19.5288 | 19.5036 | 19.3863 | 19.4785 | 19.4240 | ||

Lung | 2 | 17.6378 | 17.2469 | 16.5993 | 16.4747 | 21.3147 | |

3 | 19.0481 | 19.1016 | 20.4965 | 22.8380 | 22.4543 | ||

4 | 25.3602 | 21.2744 | 25.5515 | 24.9327 | 24.8792 | ||

5 | 27.7000 | 23.7303 | 26.1204 | 25.9318 | 25.6843 | ||

Bone | 2 | 14.7495 | 15.5891 | 15.9479 | 15.1600 | 15.9377 | |

3 | 18.4985 | 18.3537 | 17.4725 | 17.0787 | 18.9662 | ||

4 | 20.0755 | 20.6766 | 20.0562 | 20.2923 | 20.8143 | ||

5 | 21.6295 | 21.7537 | 21.5860 | 21.7469 | 22.0395 | ||

Liver | 2 | 15.4078 | 15.4020 | 14.9604 | 15.2818 | 15.4370 | |

3 | 20.1877 | 19.0481 | 19.6764 | 22.6678 | 19.3162 | ||

4 | 24.4217 | 24.4321 | 22.9191 | 24.3071 | 24.4157 | ||

5 | 25.3861 | 24.6356 | 25.2640 | 25.1425 | 24.7731 | ||

Stomach | 2 | 15.6761 | 14.6029 | 15.6102 | 14.6255 | 15.6102 | |

3 | 19.7095 | 21.1438 | 20.7793 | 17.4763 | 18.6252 | ||

4 | 22.2832 | 20.2801 | 21.8841 | 22.2386 | 21.7074 | ||

5 | 25.5278 | 23.5804 | 24.8018 | 23.3761 | 24.7403 |

From the comparison of the data in

Compared with DE, the segmentation effect of the CICMCHOA improves by 28% at the maximum, an average increase of 7.7%. Compared with ISBO, the CICMCHOA improves by 15% at the maximum, an average increase of 3%. Compared with ABCSCA, CICMCHOA is slightly weaker than the ABCSCA in the “Lung” when the NTT is 2, in the “Liver” when the NTT is 2,3,4. In other cases, the effects of CICMCHOA are stronger than those of ABCSCA. Overall, compared with ABCSCA, CICMCHOA increases by 4.3%. Compared with the ICS, the CICMCHOA performs slightly lower than the ICS in the “Brain” with NTT = 4, the “Lung” and “Liver” with NTT = 2. On the whole, the CICMCHOA is 2.2% higher than the ICS. Therefore, the improved strategy of CICMCHOA significantly improves the optimization effectiveness of CICMCHOA in medical image segmentation, and outperforms the other similar algorithms.

To meet the needs of natural and medical image segmentation, this paper uses the Sin chaotic to improve the random initialization strategy of CHOA. This not only improves the diversity of the initial population, but also reduces the risk of the CHOA falling into local optima. In the process of population position updating, the small disturbance ability of Cauchy mutation strategy is fully utilized to improve the probability of population mutation, further reduce the probability of CHOA falling into local optima, and balance the global search ability and local exploration ability of CICMCHOA. Finally, taking the fuzzy Kapur as the objective function, different kinds of natural and medical images are selected and compared with CHOA, DE, ISBO, ABCSCA and ICS, respectively. From the comparison results, the CICMCHOA shows better segmentation effect in medical image segmentation. In the future, we shall conduct in-depth exploration in the selection, fusion, and optimization of fuzzy objective functions, as well as integration with other IOA, to further improve the performance of CHOA in image segmentation.

Thanks for the support and help of the team when writing the paper. Thanks to the reviewers and experts of your magazine for their valuable opinions on the article revision. This has provided great inspiration when writing.

This work is supported by Natural Science Foundation of Anhui under Grant 1908085MF207, KJ2020A1215, KJ2021A1251 and 2023AH052856, the Excellent Youth Talent Support Foundation of Anhui under Grant gxyqZD2021142 and the Quality Engineering Project of Anhui under Grant 2021jyxm1117, 2021kcszsfkc307, 2022xsxx158 and 2022jcbs043.

The authors confirm contribution to the paper as follows: study conception and design: Shujing Li, Linguo Li, Zhangfei Li; data collection: Wenhui Cheng, Chenyang Qi; analysis and interpretation of results: Zhangfei Li, Shujing Li, Linguo Li, Wenhui Cheng; draft manuscript preparation: Zhangfei Li, Shujing Li. All authors reviewed the results and approved the final version of the manuscript.

The data that support the findings of this study are openly available in P. Arbelaez et al. at

The authors declare that they have no conflicts of interest to report regarding the present study.