A multi-threshold segmentation method for OTSU images based on Hippocampal optimization algorithm

Abstract

A multi-threshold segmentation method for OTSU images based on a hippocampus optimization algorithm. The present invention first expands the traditional Otsu threshold segmentation method, introduces the concept of multi-threshold, and implements the Otsu multi-threshold segmentation method. Next, the core mechanism of the hippocampus optimization algorithm and its specific execution process are elaborated in detail. Finally, the inter-class variance is selected as the optimization objective function of the hippocampus optimization algorithm, and the optimal solution of the multi-threshold is sought through algorithm iteration. The present invention demonstrates that the Otsu multi-threshold segmentation based on the hippocampus optimization algorithm has powerful global search and local optimization capabilities, can improve segmentation accuracy and efficiency, and has significant advantages in solving complex image segmentation problems.

Description

Technical Field

[0001] The invention belongs to the field of image processing, and in particular relates to an OTSU image multi-threshold segmentation method based on a hippocampal optimization algorithm. Background Art

[0002] The OTSU algorithm is a classic image segmentation method that determines the optimal threshold of an image by maximizing the inter-class variance. However, the traditional OTSU algorithm has a large amount of computation and high time complexity when dealing with multi-threshold segmentation. The Hippocampus optimization algorithm is an emerging swarm intelligence optimization algorithm with the advantages of fast convergence speed and strong global search capability. Therefore, applying the Hippocampus optimization algorithm to the OTSU multi-threshold segmentation can improve the efficiency and accuracy of segmentation. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide an OTSU image multi-threshold segmentation method based on the hippocampus optimization algorithm to solve the problems of low segmentation accuracy and high computational complexity in the prior art.

[0004] To achieve the above object, the present invention provides an OTSU image multi-threshold segmentation method based on a hippocampal optimization algorithm, comprising the following method steps:

[0005] Step 1: Read the image to be processed, calculate its grayscale histogram, and set the initial threshold number K;

[0006] Step 2: Initialize the parameters of the Hippocampal optimization algorithm, including population size, maximum number of iterations, etc. Randomly generate the initial population so that it is evenly distributed in the search space;

[0007] Step 3: Calculate the fitness value of each individual, using the inter-class variance of the OTSU algorithm as the fitness function;

[0008] Step 4: Update the position of the hippocampus population according to the fitness value. This includes the following actions:

[0009] Escape from predation: When an individual falls into a local optimum, random disturbances are introduced to help it escape from the local optimum;

[0010] Foraging behavior: adjust individual positions according to fitness values ​​to make them tend toward the global optimal solution;

[0011] Reproduction behavior: select excellent individuals according to fitness values ​​for crossover and mutation to produce new individuals;

[0012] Step 5: Determine whether the termination condition is met. If the maximum number of iterations is reached or the fitness no longer changes significantly, the iteration is terminated and the optimal threshold combination is output; otherwise, return to step 3 to continue iterating;

[0013] Step 6: Perform multi-threshold segmentation on the image based on the optimal threshold combination.

[0014] As a further improvement of the present invention, the parameters of the hippocampus optimization algorithm described in step 2 are initialized as follows;

[0015] Assuming that each seahorse represents a candidate solution in the search space of the problem, the entire seahorse population is represented as:

[0016]

[0017] Where Dim represents the dimension of the variable, and pop is the population size;

[0018] Each solution is randomly generated between the lower and upper bounds of a specified problem, denoted by LB and UB respectively. th Single X i In the search space [LB, UB] it is:

[0019]

[0020] Among them, rand represents a random value in [0,1]. Indicates j th in i th The dimension is a single positive integer from 1 to pop, j is a positive integer in the range [1, Dim], UB j and UB j Hints at J th The lower and upper bounds of the optimization problem are variables. Taking the minimum optimization problem as an example, the individual with the smallest fitness is the elite individual, and X elite Indicates that X elite Calculated by the following formula:

[0021] X elite =argmin(f(X i ))

[0022] Among them, f(X i ) represents the objective function value of a given problem.

[0023] As a further improvement of the present invention, the OTSU algorithm described in step 3 is specifically as follows:

[0024] When processing complex images or multi-target image segmentation, it is assumed that the image is multi-threshold (t 1 ,t 2 ,...t j-1 ) is divided into j categories (C 1 ,C 2 ,...,C j), the OTSU algorithm is extended to the multi-threshold Otsu threshold method, in which the maximum inter-class variance is defined as:

[0025]

[0026] in,

[0027]

[0028]

[0029] As a further improvement of the present invention, the escaping predation behavior described in step 4 is specifically as follows;

[0030] When an individual falls into a local optimum, random disturbance is introduced to help it jump out of the local optimum. The movement pattern of the hippocampus approximately conforms to the normal distribution with a mean of 0 and a standard deviation of 1. When balancing the efficiency of exploration and development, r is set. 1 = 0 is the dividing point, where half of the movement is used for in-depth exploration of the local area, and the other half is dedicated to global exploration of the space.

[0031] As a further improvement of the present invention, the movement pattern of the hippocampus is divided into the following two situations.

[0032] Case 1:

[0033] Surrounded by whirlpools in the sea, the seahorse exhibits a unique spiral motion. This motion pattern significantly serves the local refinement exploration of the seahorse optimization algorithm. 1 In the case of being on the right side of a defined point, the hippocampus can accurately move toward the elite individual X by simulating a spiral trajectory. elite In this case, the new position of the hippocampus is expressed mathematically as follows:

[0034]

[0035] Among them, x = ρ × cos(θ), y = ρ × sin(θ), and z = ρ × θ represent the three-dimensional components of the coordinates (x, y, z) under the spiral motion, which helps to update the position of the search agent. denotes the length of the stem defined by the logarithmic spiral constants u and v, set to u = 0.05 and v = 0.05, θ is a random value between [0, 2π], and Levy(z) is the Levy flight distribution function calculated by the following formula:

[0036]

[0037] Where λ is a random number between [0,2], let λ = 1.5, s is a fixed constant of 0.01, and w and k are random numbers between [0,1]. σ is calculated using the following formula:

[0038]

[0039] Case 2:

[0040] The Brownian motion of the seahorse under the action of drift is explored for the seahorse optimization algorithm, r 1 Located to the left of the cutoff point, at this point, the local extreme value problem of the hippocampus optimization algorithm can be effectively avoided through the search operation, and Brownian motion is used to simulate another moving distance of the hippocampus, thereby ensuring that it can search better. In this case, its mathematical expression is as follows:

[0041]

[0042] Where l is a constant coefficient (set to l = 0.05). t is the random walk coefficient of Brownian motion, which is actually a random value that obeys the standard normal distribution. And it can be calculated using the following formula:

[0043]

[0044] In these two cases, the new position of the hippocampus at iteration t can be obtained as follows:

[0045]

[0046] Where r1=randn() is a normal random number.

[0047] As a further improvement of the present invention, the foraging behavior described in step 4 is specifically as follows:

[0048] Foraging behavior will adjust the individual position according to the fitness value, so that it tends to the global optimal solution. Given that the seahorse has a success rate of more than 90% in the predation process, a random number r is designed. 2 To clearly distinguish these two different results, 0.1 is set as the critical value to define these two situations. 2 >0.1, which means that the seahorse's predation is successful, that is, the seahorse sneaks up on the prey and is faster than the prey to finally catch it. Otherwise, when the predation fails, the reaction speed of both is opposite to the previous one, which means that the seahorse's tendency is to explore the search space. The mathematical expression of this predation behavior is as follows:

[0049]

[0050] in Represents the new position after iteration t of movement. 2 is a random number between [0,1]. α decreases linearly with iterations to adjust the hippocampal movement step size. The calculation formula is as follows:

[0051]

[0052] Where T represents the maximum number of iterations.

[0053] As a further improvement of the present invention, the breeding behavior described in step 4 is specifically as follows:

[0054] Excellent individuals will be selected according to the fitness value for crossover and mutation to produce new individuals. In the process of grouping for reproduction, individuals are divided into male and female groups according to the fitness value. In view of the key role of male seahorses in the reproduction process, the seahorse optimization algorithm regards the individuals with the highest fitness as potential "fathers" when selecting individuals, accounting for half of the total number, and the remaining half act as "mothers". The concise mathematical expression of the seahorse role allocation is:

[0055]

[0056] in Indicates all Arranged in ascending order of fitness value, father and mother indicate the number from males and females, respectively;

[0057] Males and females are randomly mated to produce new offspring. To make the proposed seahorse optimization algorithm easy to execute, it is assumed that each pair of seahorses only reproduces one child. th The descendant expressions are as follows:

[0058]

[0059] where r 3 is a random number between [0,1], i is an integer in the range [1,pop / 2], and Representatives randomly selected individuals from the male and female populations, respectively.

[0060] Compared with the prior art, the present invention has the following advantages:

[0061] 1) Significantly improve the accuracy of image multi-threshold segmentation:

[0062] The traditional OTSU algorithm has limited segmentation accuracy due to its large amount of calculation and the possibility of falling into the local optimal solution when processing multi-threshold segmentation. The Hippocampus optimization algorithm adopted in the present invention, with its strong global search ability and fast convergence speed, can more effectively find the global optimal threshold combination, thereby significantly improving the accuracy of image segmentation.

[0063] The predation escape, foraging and reproduction behaviors in the seahorse optimization algorithm together ensure that the algorithm can cover a wider solution space during the search process, effectively avoiding falling into the local optimal situation and further improving the segmentation accuracy.

[0064] 2) Significantly improve the efficiency of image multi-threshold segmentation:

[0065] The traditional OTSU multi-threshold segmentation method has a large amount of calculation and high time complexity when processing large images or needing to be segmented into multiple regions. The method of the present invention utilizes the rapid convergence of the Hippocampal optimization algorithm to quickly find the optimal threshold combination, thereby significantly improving the efficiency of image segmentation.

[0066] The foraging behavior in the hippocampus optimization algorithm adjusts the individual positions according to the fitness value to make it tend to the global optimal solution, which further accelerates the convergence speed of the algorithm and improves the segmentation efficiency.

[0067] 3) Strong adaptability, can be applied to image segmentation tasks with various complex backgrounds:

[0068] The method of the present invention does not rely on specific image features or backgrounds, and can be applied to image segmentation tasks with various complex backgrounds. Whether it is natural images, medical images or industrial images, as long as multi-threshold segmentation is required, the method of the present invention can be used for efficient and accurate segmentation.

[0069] Through the global search capability and flexible and diverse search strategies of the Hippocampal optimization algorithm, the method of the present invention can automatically adapt to the characteristics and requirements of different images and achieve personalized image segmentation.

[0070] 4) Strong scalability and broad application prospects:

[0071] The method of the present invention is not limited to the combination of the OTSU algorithm and the Hippocampal optimization algorithm, but can also be combined with other image processing algorithms or optimization algorithms to form a more diverse and efficient image segmentation method.

[0072] With the continuous development of image processing technology and the continuous expansion of its application fields, the method of the present invention will be applied in more fields, such as medical image processing, industrial automation, intelligent transportation, etc., providing more powerful and efficient tools and methods for image analysis and processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 is a flow chart of the method of the present invention;

[0074] Figure 2 This is a comparison chart of image segmentation effects with different numbers of thresholds. DETAILED DESCRIPTION

[0075] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. It should be noted that the words "front", "rear", "left", "right", "upper" and "lower" used in the following description refer to directions in the accompanying drawings, and the words "inner" and "outer" refer to directions toward or away from the geometric center of a specific component, respectively.

[0076] The present invention provides a flow chart such as Figure 1 The OTSU image multi-threshold segmentation method based on the Hippocampus optimization algorithm is shown in the figure, and the specific steps are as follows;

[0077] Step 1: Read the image to be processed, calculate its grayscale histogram, and set the initial threshold number K.

[0078] Step 2: Initialize the parameters of the Hippocampus optimization algorithm, including population size, maximum number of iterations, etc. Randomly generate the initial population so that it is evenly distributed in the search space.

[0079] Like other existing metaheuristic methods, the seahorse optimization algorithm also starts with overall initialization. Assuming that each seahorse represents a candidate solution in the search space of the problem, the entire seahorse population can be expressed as:

[0080]

[0081] Where Dim represents the dimension of the variable and pop is the population size.

[0082] Each solution is randomly generated between a lower bound and an upper bound of a specified problem, denoted by LB and UB respectively. th Single X i In the search space [LB, UB] it is:

[0083]

[0084] Among them, rand represents a random value in [0,1]. Indicates j th in i th The dimension of LB is a single positive integer from 1 to pop, and j is a positive integer in the range [1, Dim]. j and UB j Hints at J th The lower and upper bounds of the optimization problem variables. Taking the minimum optimization problem as an example, the individual with the smallest fitness is the elite individual, and X elite Indicates. elite It can be calculated by the following formula:

[0085] X elite=argmin(f(X i ))

[0086] Among them, f(X i ) represents the objective function value of a given problem.

[0087] Step 3: Calculate the fitness value of each individual, and use the inter-class variance of the OTSU algorithm as the fitness function. The calculation formula for the inter-class variance when the single threshold is as follows:

[0088] Calculation of the total average gray value of the image:

[0089] u=w 0 *u 0 +w 1 *u 1

[0090] Calculation of between-class variance:

[0091] σ=w 0 *(u 0 -u) 2 +w 1 *(u 1 -u) 2

[0092] Among them, the proportion of target points to the total image is w 0 , the average gray value is u 0 , the background points account for the proportion of the image is w 1 , the average gray value is u 1 , the total average gray value of the image is u, and the between-class variance is σ.

[0093] When processing complex images or multi-target image segmentation, it is assumed that the image is multi-threshold (t 1 ,t 2 ,...t j-1 ) is divided into j categories (C 1 ,C 2 ,...,C j ). The OTSU algorithm is then extended to the multi-threshold Otsu threshold method. At this time, the maximum inter-class variance is defined as:

[0094]

[0095] in,

[0096]

[0097]

[0098] Step 4: Update the position of the hippocampus population according to the fitness value. This includes the following actions:

[0099] Escape from predation: When an individual falls into a local optimum, random disturbances are introduced to help it escape from the local optimum.

[0100] The movement pattern of the hippocampus is approximately in accordance with the normal distribution with a mean of 0 and a standard deviation of 1. When balancing the efficiency of exploration and development, setting r 1 = 0 is the dividing point, half of which is used for in-depth exploration of the local area, while the other half is dedicated to global exploration of the space. Based on this setting, the movement of the hippocampus can be divided into the following two situations.

[0101] Case 1: Surrounded by whirlpools in the sea, the seahorse exhibits a unique spiral motion. This motion pattern significantly serves the local refinement exploration of the seahorse optimization algorithm, especially when the random value r 1 In the case of being on the right side of a defined point, the hippocampus can accurately move toward the elite individual X by simulating a spiral trajectory. elite In this case, the new position of the generated seahorse can be expressed mathematically as follows:

[0102]

[0103] Among them, x = ρ × cos (θ), y = ρ × sin (θ) and z = ρ × θ represent the three-dimensional components of the coordinates (x, y, z) under the spiral motion, which helps to update the position of the search agent. represents the length of the stem defined by the logarithmic spiral constants u and v (set to u = 0.05 and v = 0.05). θ is a random value between [0, 2π]. Levy(z) is the Levy flight distribution function, calculated by the following formula:

[0104]

[0105] Where λ is a random number between [0,2] (assuming λ=1.5). s is a fixed constant of 0.01, and w and k are random numbers between [0,1]. σ is calculated using the following formula:

[0106]

[0107] Case 2: Brownian motion of the seahorse under the action of drift, the seahorse optimization algorithm is explored, r 1 Located to the left of the cutoff point. At this point, the local extremum problem of the hippocampus optimization algorithm can be effectively avoided by searching. Using Brownian motion to simulate another moving distance of the hippocampus ensures that it can search better. In this case, its mathematical expression is as follows:

[0108]

[0109] Where l is a constant coefficient (set to l = 0.05). t is the random walk coefficient of Brownian motion, which is actually a random value that obeys the standard normal distribution. And it can be calculated using the following formula:

[0110]

[0111] In these two cases, the new position of the hippocampus at iteration t can be obtained as follows:

[0112]

[0113] Where r1=randn() is a normal random number.

[0114] Foraging behavior: adjust the individual position according to the fitness value to make it tend to the global optimal solution.

[0115] Given that seahorses have a success rate of more than 90% in predation, a random number r is designed. 2 To clearly distinguish these two different results, 0.1 is set as the critical value to define these two situations. 2 >0.1, which means that the seahorse's predation is successful, that is, the seahorse sneaks up on the prey and is faster than the prey to finally catch it. Otherwise, when predation fails, the reaction speeds of both are opposite to the previous ones, which means that the seahorse's tendency is to explore the search space. The mathematical expression of this predation behavior is as follows:

[0116]

[0117] in Represents the new position after iteration t of movement. 2 is a random number between [0,1]. α decreases linearly with iterations to adjust the hippocampal movement step size. The calculation formula is as follows:

[0118]

[0119] Where T represents the maximum number of iterations.

[0120] Reproduction behavior: Select excellent individuals according to fitness values ​​for crossover and mutation to produce new individuals.

[0121] In the reproduction grouping process, we divide individuals into male and female groups based on fitness values. It is particularly noteworthy that, given the key role of male seahorses in the reproduction process, the seahorse optimization algorithm considers the individuals with the highest fitness as potential "fathers" when selecting individuals, accounting for half of the total, while the remaining half act as "mothers". The concise mathematical expression of seahorse role allocation is:

[0122]

[0123]

[0124] in Indicates all Arranged in ascending order of fitness value. Father and Mother indicate the number from male and female, respectively.

[0125] Males and females are randomly mated to produce new offspring. In order to make the proposed seahorse optimization algorithm easy to execute, it is assumed that each pair of seahorses only produces one offspring. th The descendant expressions are as follows:

[0126]

[0127] where r 3 is a random number between [0,1]. i is an integer in the range [1,pop / 2]. and Representatives randomly selected individuals from the male and female populations, respectively.

[0128] Step 5: Determine whether the termination condition is met. If the maximum number of iterations is reached or the fitness no longer changes significantly, the iteration is terminated and the optimal threshold combination is output; otherwise, return to step 3 to continue the iteration.

[0129] Step 6: Perform multi-threshold segmentation on the image based on the optimal threshold combination.

[0130] The conclusion is as follows. The eagle image is selected as the image to be segmented. Figure 2 , an OTSU image multi-threshold segmentation method based on the hippocampus optimization algorithm proposed in the present invention is used to perform single threshold, double threshold and triple threshold segmentation. The experimental results show that the present invention can effectively perform multi-threshold image segmentation.

[0131] It should be noted that the above content only illustrates the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. For ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications all fall within the protection scope of the claims of the present invention.

Claims

1. A multi-threshold segmentation method for OTSU images based on the hippocampal optimization algorithm, characterized by: The method comprises the following steps: Step 1: Read the image to be processed, calculate its grayscale histogram, and set the initial threshold number K; Step 2: Initialize the parameters of the Hippocampal optimization algorithm, including population size and maximum number of iterations, and randomly generate the initial population so that it is evenly distributed in the search space; Initialize the parameters of the hippocampus optimization algorithm as described in step 2, as follows; Assuming that each seahorse represents a candidate solution in the search space of the problem, the entire seahorse population is represented as: Where Dim represents the dimension of the variable, and pop is the population size; Each solution is randomly generated between the lower and upper bounds of a specified problem, denoted by LB and UB respectively. th Single X i In the search space [LB, UB] it is: Among them, rand represents a random value in [0,1]. Indicates j th in i th The dimension is a single positive integer from 1 to pop, j is a positive integer in the range [1, Dim], LB j and UB j Hints at J th The lower and upper bounds of the optimization problem are variables. Taking the minimum optimization problem as an example, the individual with the smallest fitness is the elite individual, and X elite Indicates that X elite Calculated by the following formula: X elite =argmin(f(X i )) Among them, f(X i ) represents the objective function value of a given problem; Step 3: Calculate the fitness value of each individual, and use the inter-class variance of the OTSU algorithm as the fitness function; The OTSU algorithm described in step 3 is as follows: When processing complex images or multi-target image segmentation, it is assumed that the image is segmented by multiple thresholds (t1, t2, ... t j-1 ) is divided into j categories (C1, C2, ..., C j ), the OTSU algorithm is extended to the multi-threshold Otsu threshold method, in which the maximum inter-class variance is defined as: in, Step 4: Update the position of the hippocampus population according to the fitness value, including the following behaviors: Escape from predation: When an individual falls into a local optimum, random disturbances are introduced to help it escape from the local optimum; Foraging behavior: adjust individual positions according to fitness values ​​to make them tend toward the global optimal solution; Reproduction behavior: select excellent individuals according to fitness values ​​for crossover and mutation to produce new individuals; The predation escape behaviors described in step 4 are as follows; When an individual falls into a local optimum, random disturbances are introduced to help it escape from the local optimum. The movement pattern of the hippocampus approximately conforms to a normal distribution with a mean of 0 and a standard deviation of 1. When balancing the efficiency of exploration and development, r1=0 is set as the dividing point, where half of the movement is used for in-depth exploration of the local area, and the other half is dedicated to global exploration of the space. The movement patterns of the hippocampus are divided into the following two situations: Case 1: Surrounded by the whirlpool in the sea, the seahorse exhibits a unique spiral motion. This motion pattern significantly serves the local refinement exploration of the seahorse optimization algorithm. When the random value r1 is located to the right of a certain defined point, the seahorse can accurately move toward the elite individual X by simulating the spiral trajectory. elite In this case, the new position of the hippocampus is expressed mathematically as follows: where x = ρ × cos(θ), y = ρ × sin(θ), and z = ρ × θ represent the three-dimensional components of the coordinates (x, y, z) under the spiral motion, which helps to update the position of the search agent, ρ = u × e θv denotes the length of the stem defined by the logarithmic spiral constants u and v, set to u = 0.05 and v = 0.05, θ is a random value between [0, 2π], and Levy(z) is the Levy flight distribution function calculated by the following formula: Where λ is a random number between [0,2], λ=1.5, s is a fixed constant of 0.01, w and k are random numbers between [0,1], and σ is calculated using the following formula: Case 2: The Brownian motion of the hippocampus, under the action of drift, explores the hippocampus optimization algorithm. r1 is located to the left of the cutoff point. At this time, the local extreme value problem of the hippocampus optimization algorithm can be effectively avoided through the search operation. The Brownian motion is used to simulate another moving distance of the hippocampus, thereby ensuring that it can search better. In this case, its mathematical expression is as follows: Among them, l is a constant coefficient, set to l = 0.05, β t is the random walk coefficient of Brownian motion, which is actually a random value that follows a standard normal distribution and is calculated using the following formula: In these two cases, the new position of the hippocampus at iteration t can be obtained as follows: Where r1 = randn() is a normal random number; The foraging behavior described in step 4 is as follows; Foraging behavior adjusts individual positions according to the fitness value to make it tend to the global optimal solution. Given that the seahorse has a success rate of more than 90% in the predation process, a random number r2 is designed to clearly distinguish these two different results. Among them, 0.1 is set as the critical value to define these two situations. If r2>0.1, it means that the seahorse's predation is successful, that is, the seahorse secretly catches the prey and is faster than the prey to finally catch it. Otherwise, when the predation fails, the reaction speed of both is opposite to the previous one, which means that the seahorse tends to explore the search space. The mathematical expression of this predation behavior is as follows: in represents the new position after iteration t movement, r2 is a random number between [0,1], and α decreases linearly with iteration to adjust the moving step of the hippocampus. The calculation formula is as follows: Where T represents the maximum number of iterations; The reproductive behavior described in step 4 is as follows; Excellent individuals will be selected according to the fitness value for crossover and mutation to produce new individuals. In the process of grouping for reproduction, individuals are divided into male and female groups according to the fitness value. In view of the key role of male seahorses in the reproduction process, the seahorse optimization algorithm regards the individuals with the highest fitness as potential "fathers" when selecting individuals, accounting for half of the total, and the remaining half act as "mothers". The concise mathematical expression of the seahorse role allocation is: in Indicates all Arranged in ascending order of fitness value, father and mother indicate the number from males and females, respectively; Males and females are randomly mated to produce new offspring. To make the proposed seahorse optimization algorithm easy to execute, it is assumed that each pair of seahorses only reproduces one child. th The descendant expressions are as follows: where r3 is a random number between [0,1], i is an integer in the range [1,pop / 2], and Representatives randomly selected individuals from male and female populations, respectively; Step 5: Determine whether the termination condition is met. If the maximum number of iterations is reached or the fitness no longer changes significantly, the iteration is terminated and the optimal threshold combination is output; otherwise, return to step 3 to continue iterating; Step 6: Perform multi-threshold segmentation on the image based on the optimal threshold combination.

Images