Multi-threshold image segmentation method based on leap-over crossover and multi-optimal guidance

Abstract

The invention discloses a multi-threshold image segmentation method based on leap-over crossover and multi-optimal guidance. The method comprises the following steps: step 1, modeling a multi-threshold image segmentation problem into a target function of an optimization algorithm; step 2, proposing a leap-over crossover calculation method, and carrying out multi-level information crossover among individuals, dimensions, generations and the like on the population generated in the step 1 according to a certain probability at the beginning of each iteration; and step 3, proposing a multi-optimal oriented evolution acceleration method, and carrying out timely evolution state detection and processing on the population obtained in the step 2 through optimization rate orientation, optimal individual distance orientation and better declustering orientation. And step 4, if population evolution does not reach the maximum number of iterations, adding one to the current number of iterations, skipping to the step 2 to continue to execute the next iteration, otherwise, terminating evolution, and obtaining a multi-threshold image segmentation result and an optimal threshold combination for segmenting the image to the maximum total entropy.

Description

Technical Field

[0001] The invention relates to the use of leapfrogging, multi-optimal guided evolution acceleration method, intelligent optimization algorithm and multi-threshold image segmentation. Background Art

[0002] Image segmentation is a basic challenge in image processing, which helps researchers analyze and understand images more effectively. It is of great significance in fields such as digital image processing and computer vision. The key to image segmentation is to segment the original image into regions with specific attributes and extract related objects. In other words, image segmentation is to segment the input image into different regions so that the same region has the same attributes and different regions have different characteristics. The threshold-based method has been successfully implemented in various application fields due to its advantages such as simple operation, fast processing speed, high accuracy and small storage space. Based on the number of regions of interest in the image, threshold segmentation can be divided into dual-threshold image segmentation and multi-threshold image segmentation. Usually, an image consists of more than two regions of interest, so multiple thresholds are required for segmentation.

[0003] According to the information in the image, the threshold segmentation method is divided into histogram-based method, clustering-based method, entropy-based method, object attribute-based method, spatial method and local method. The histogram-based processing method is divided into one-dimensional histogram and two-dimensional histogram, but the threshold method based on one-dimensional histogram only considers the grayscale information of the image and does not use the spatial position information of the image. Therefore, when the target occupies a very small area in the image, serious mis-segmentation will occur, and the segmentation result is easily disturbed by noise. To address this problem, some researchers have proposed an image threshold segmentation method based on two-dimensional histogram, combining the original grayscale histogram with the local mean of the pixel to form a local mean two-dimensional histogram. This two-dimensional histogram maps the grayscale value of the pixel to the corresponding local mean to represent the spatial correlation between pixels. The diagonal plane contains object and background information, and the non-diagonal plane contains edge and noise information. However, when the traditional two-dimensional histogram is used for multi-threshold segmentation, the optimal threshold is found through an exhaustive method, and the computational cost is very high. To solve this problem, many metaheuristic algorithms (MAs) have been applied to this field and achieved remarkable results.

[0004] The Sand Cat Swarm Optimization (SCSO) algorithm is a metaheuristic algorithm inspired by the behavior of sand cats in nature. The two main activities of sand cats are foraging and attacking prey. The algorithm is based on the feature that sand cats can find prey by detecting low-frequency noise. The Sand Cat Swarm Optimization algorithm has the advantages of robustness to high-dimensional problems, simplicity of algorithm implementation, and flexibility in modifying the basic version. However, it still has many limitations in the optimization process, which are mainly manifested in two aspects: on the one hand, although the Sand Cat Swarm Algorithm converges quickly in the search space, due to the relatively simple position update method, its comprehensive exploration ability of the solution space is limited, making its ability to jump out of the local optimum poor, which causes the Sand Cat Swarm Algorithm to fall into the local optimal state in the early iterations and cannot continue to find a better solution. On the other hand, the Sand Cat Swarm Algorithm may face problems such as premature convergence or stagnation during the optimization process. Premature convergence refers to the decrease in population diversity when the population falls into the local optimum. Stagnation refers to the inability of the population to converge to a stable point, at which point there is no better solution even if the population diversity is maintained. In both cases, the algorithm wastes computing resources, resulting in slower convergence speed and reduced convergence accuracy.

[0005] In summary, in order to solve the above two challenges and better perform multi-threshold image segmentation, we proposed a multi-threshold image segmentation method based on leapfrogging and multi-optimal guidance. First, we proposed a leapfrogging calculation method to exchange information between individuals, dimensions, generations, etc., which improved the early search efficiency and the ability to jump out of the local optimum of the sand cat swarm algorithm; second, we proposed a multi-optimal guided evolution acceleration method based on historical optimization information, which timely detected and processed the evolutionary state of the population through optimization rate guidance, optimal individual distance guidance, and better solution clustering guidance, further improving the ability of the algorithm to jump out of the local optimum, and using the saved computing resources for further development, which increased the possibility of finding the global optimal solution; finally, the non-local mean two-dimensional histogram was generated using grayscale images and non-local mean images, and Renyi entropy was used as the objective function. The efficiency of the improved sand cat swarm optimization algorithm was used to find the optimal threshold, and multi-threshold image segmentation was performed, which greatly reduced the computational complexity. Summary of the invention

[0006] In order to better perform multi-threshold image segmentation and solve the limitations of the sand cat swarm optimization algorithm that it is easy to fall into local optimality in the early stages of iteration and the problem of insufficient convergence accuracy caused by premature convergence or stagnation during algorithm optimization, this paper invented a multi-threshold segmentation method based on leapfrogging and multi-optimal guidance. The invention mainly includes: a leapfrogging calculation method to improve the early search efficiency of the sand cat swarm algorithm and the ability to jump out of local optimality, a multi-optimal guided evolution acceleration method for timely detection and processing of evolutionary states, and multi-threshold image segmentation using an improved sand cat swarm optimization algorithm based on non-local mean two-dimensional histogram and Renyi entropy.

[0007] A multi-threshold segmentation method based on leapfrogging and multi-optimal guidance, the main steps of which are as follows:

[0008] Step 1: Model the multi-threshold image segmentation problem as the objective function of the optimization algorithm. First, grayscale the input image to obtain the corresponding grayscale image, and use non-local mean filtering to obtain the non-local mean image. Calculate the local grayscale mean of pixels p and q within the local image range, then calculate the Gaussian weights of pixels p and q based on the obtained local grayscale mean, and then calculate the non-local mean filter value of pixel p based on the obtained Gaussian weight and the grayscale value of pixel q to obtain the non-local mean image. Then, the grayscale image and the non-local mean image are combined to form a non-local mean two-dimensional histogram. The probability of the occurrence of the vector (i, j) is calculated based on its frequency in the non-local mean two-dimensional histogram, thereby calculating the normalized non-local mean two-dimensional histogram. Since the main diagonal of the non-local mean two-dimensional histogram contains enough image information, in order to simplify the calculation, we only calculate the Renyi entropy of the sub-area on the main diagonal. Therefore, taking the Renyi entropy based on the non-local mean two-dimensional histogram as the objective function, the population P0 and the stage transition control parameter R are initialized in the search space to complete the subsequent population evolution.

[0009] Step 2: Propose a leapfrog crossover calculation method, and perform information crossover based on multiple levels such as individuals, dimensions, and generations at a certain probability on the population P0 generated in step 1 at the beginning of each iteration. First, based on the two parent individuals, cross their position information on a certain dimension in this iteration and the previous iteration to obtain the new position information of the two cross-individual and cross-generation crossovers. and Then cross the position information of the same individual in different dimensions to obtain the new position of the individual after cross-dimensional cross-border After combining the information exchanged between individuals, dimensions, and generations, each individual will select the best new position from the old position after the cross search, and execute the evolutionary process of the sand cat colony optimization algorithm itself to obtain the new population P1.

[0010] Step 3. Propose a multi-optimal guided evolution acceleration method based on historical optimization information. Through the optimization rate guidance, optimal individual distance guidance and better solution clustering guidance, the population P1 obtained in step 2 is timely detected and processed in the evolution state. First, the population evolution state is detected based on the optimization rate guidance. According to the position change of the optimal individual before and after the current iteration, the decline rate of the optimal fitness value is selectively calculated and added to the rate set of this evolution cycle. Each time the decline rate is newly calculated, the standard deviation of the new rate set is calculated. And judge the value of evolution acceleration E through its changes, so as to judge whether the current state is normal or bad. Second, the bad state of the population is subdivided based on the optimal individual distance orientation. The degree of aggregation of the population is judged by calculating the weighted distance WDB of each individual in the population to the current optimal individual in each dimension and a dynamic threshold Z associated with the optimization process. If the weighted distance is less than the dynamic threshold, it means that the individuals in the population are closely gathered around the current optimal individual at this time, and the population may converge too early and fall into the local optimum and cannot escape. Otherwise, it means that the weighted distance of the individuals in the population from the current optimal individual is large, and the population may not converge to a stable point. At this time, we will take intervention operations based on the clustering orientation of the better solution to alleviate the dilemma we face, that is, if the degree of population aggregation is high, the population will be dispersed through discrete operations. If the degree of population aggregation is low, the population will be gathered to three better solutions through aggregation operations, thereby expanding the search space and escaping from the local optimum or stagnation. Finally, the new population P after multi-optimal guided evolution acceleration is obtained, which is the initial population P0 in the next iteration.

[0011] Step 4: Compare the current number of iterations with the maximum number of iterations. If the population evolution has not reached the maximum number of iterations, the current number of iterations is increased by one, and the next iteration is skipped to step 2. Otherwise, the evolution is terminated to obtain the multi-threshold image segmentation result and the optimal threshold combination that segments the image to the maximum total entropy value. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 .Multi-threshold image segmentation method framework flow chart

[0013] Figure 2 .Flowchart of the leapfrog cross calculation method

[0014] Figure 3 .Flowchart of multi-optimal guided evolution acceleration method DETAILED DESCRIPTION

[0015] Step 1: Model the multi-threshold image segmentation problem as the objective function of the optimization algorithm.

[0016] (1) First, the input image is grayed to obtain the corresponding grayscale image, and the non-local mean image is obtained by non-local mean filtering.

[0017] Calculate the local grayscale mean μ(p) and μ(q) of pixels p and q in the local image size m×m:

[0018]

[0019]

[0020] Then, the Gaussian weights ω(p, q) of pixels p and q are calculated based on the local grayscale mean:

[0021]

[0022] Then, based on the obtained Gaussian weight and the grayscale value of pixel q, the non-local mean filter value O(p) of pixel p is calculated to obtain the non-local mean image:

[0023]

[0024] (2) The grayscale image and the non-local mean image are combined to form a non-local mean two-dimensional histogram. The probability P of the vector (i, j) appearing in the non-local mean two-dimensional histogram is calculated based on its frequency. ij , thereby calculating the normalized non-local mean two-dimensional histogram.

[0025]

[0026] Where M×N is the total number of pixels.

[0027] (3) Since the main diagonal of the non-local mean two-dimensional histogram contains sufficient image information, in order to simplify the calculation, we only calculate the Renyi entropy of the sub-region on the main diagonal, that is:

[0028]

[0029] Where {t1, t2, ...L-1} represents the threshold level of the grayscale image, and {s1, s2, ...L-1} represents the threshold level of the non-local mean image. Therefore, the Renyi total entropy value F based on the non-local mean two-dimensional histogram is the objective function to be calculated by the optimization algorithm:

[0030]

[0031] The position of the population in each dimension is represented as a threshold, and the search space of the population is represented as a search space for threshold combinations. Next, the population P0 and the stage transition control parameter R are initialized in the search space to complete the subsequent population evolution.

[0032] Step 2: Propose a leapfrog crossover calculation method, and perform multi-level information crossover based on individuals, dimensions, generations, etc. on the population P0 generated in step 1 at the beginning of each iteration with a certain probability. That is, when If yes, then leapfrog crossing is performed; otherwise, no crossing is performed.

[0033] (1) First, calculate the operator for crossover between individuals. and Take a random number α1 between 0 and 1, and random numbers β1 and η1 between -1 and 1, and use α1 and 1-α1 to weight the positions of the two parent individuals and add them together. Then add the result of multiplying the difference vector between the parent individuals by β1, and then add the result of multiplying the difference vector between the positions of the previous generation of the parent individuals by η1 to obtain a new position of individual i in the nth dimension. The combination obtains the new position of the individual across individuals and generations Similarly, take a random number α2 between 0 and 1, and a random number β2 and η2 between -1 and 1, and use α2 and 1-α2 to weight the positions of the parent individuals, add the result of multiplying the difference vector between the parent individuals by β2, and add the result of multiplying the difference vector between the positions of the parent individuals in the previous generation by η2, and calculate the new position of individual j in the nth dimension. After the combination, we can get the new position of the individual across individuals and generations.

[0034]

[0035]

[0036] (2) Calculate the cross-dimensional operator. Take a random number γ between 0 and 1 and use it and 1-γ to calculate the individual The positions of different dimensions (such as the mth dimension and the nth dimension) are weighted added to obtain the new position on the mth dimension Then the new positions of each dimension form the new position of the individual after cross-dimensional crossing.

[0037]

[0038] After the crossover calculation is completed, each individual compares the new position and The fitness value of the position before the crossover is selected, and the best one is updated. Then the evolution process of the sand cat group optimization algorithm is executed to obtain the new population P1.

[0039] Step 3: Propose a multi-optimal guided evolution acceleration method based on historical optimization information, and timely detect and process the evolutionary state of the population P1 obtained in step 2 by optimizing rate guidance, optimal individual distance guidance and better solution clustering guidance.

[0040] (1) First, the population evolutionary state is detected based on the optimization rate guidance.

[0041] Selectively calculate the rate of decrease of the optimal fitness value based on the position change of the optimal individual before and after the current iteration If the current best individual obtained in this iteration has the same position in each dimension as the current best individual obtained in the previous iteration, the best fitness value must not change, and it is meaningless to calculate the rate of decline. Therefore, only when the positions of the best individuals before and after this iteration are not exactly the same, the average decline of their fitness values ​​in each fitness evaluation, that is, the rate of decline, will be calculated:

[0042]

[0043] in, and is the fitness value of the best individual at the beginning and end of the current evolutionary stage, ΔFEs is the number of fitness evaluations consumed in the current evolutionary stage, and δ is a parameter set to 1 to control the rate of decline.

[0044] When a new evolution cycle executes more than two iterations, the decline rate is calculated each time For the new rate set Find the standard deviation of the rate of decline in and determine the evolutionary acceleration E by its change:

[0045]

[0046] If the standard deviation of the set G after adding the new decline rate The standard deviation before adding Compared with the original value, the evolution acceleration E = 1, indicating that the optimal fitness value still maintains the original rate of decline, the algorithm is in a normal state, and the next iteration can be directly continued. Otherwise, the evolution acceleration E = 0, indicating that the optimal fitness value may remain unchanged, the algorithm may converge too early, fall into a local optimum, or the population may enter a stagnant state.

[0047] (2) At this time, the undesirable state of the population is subdivided based on the optimal individual distance guidance. The degree of aggregation of the population is determined by calculating the weighted distance WDB from each individual in the population to the current optimal individual in each dimension and a dynamic threshold Z associated with the optimization process.

[0048] Calculate the value of x for each individual in the populationi,j In each dimension, the current optimal individual The weighted distance of:

[0049]

[0050] Based on the initial threshold Z0 and a parameter c associated with the optimization process p Calculate the dynamic threshold Z:

[0051] Z=Z0·c p

[0052] Compare the weighted distance WDB with the dynamic threshold Z. If WDB is less than Z, it means that the individuals in the population are closely gathered around the current optimal individual, the population aggregation degree is high, and it may converge prematurely and fall into the local optimum and cannot escape. Otherwise, it means that the population aggregation degree is low, the weighted distance between the individuals and the current optimal individual is large, and the population may not converge to a stable point.

[0053] (3) Take intervention operations based on the clustering guidance of the better solution to alleviate the dilemma faced by the algorithm. That is, if the population aggregation degree is high, the population is dispersed through the discrete operation. If the population aggregation degree is low, the population is gathered to the three better solutions through the aggregation operation, thereby expanding the search space and escaping the local optimum or stagnation. Finally, the new population P after the multi-optimal guided evolution acceleration is obtained, which is the initial population P0 in the next iteration.

[0054] When performing discrete operations, first calculate the probability DP of an individual moving to the upper bound in a given dimension i :

[0055]

[0056] The global optimal solution x gbest The closer to the upper bound, the population will disperse towards the lower bound with a larger step size, and vice versa. Then perform discrete operations to update the population position:

[0057]

[0058] Here, r is a random number between 0 and 1.

[0059] When performing the aggregation operation, the fitness state ST of individuals in the population is first calculated using the global worst fitness value and the global best fitness value. i :

[0060]

[0061] Then calculate the aggregation threshold RP according to the obtained fitness state i :

[0062] RP i =(ST i +c p )·WDB

[0063] Compare the position x of the i-th individual in the population in the j-th dimension i,j To the current optimal individual position The weighted distance and the polymerization degree threshold RP i The size of Less than RP i , indicating that the population aggregation degree is high enough and no further aggregation is needed. Otherwise, the aggregation operator is calculated to move the population to the three solutions with better current fitness values. Gather together, thereby expanding the search space and escaping from local optimality or stagnation:

[0064]

[0065] Among them, r1, r2, and r3 are all random numbers between 0 and 1.

[0066] Step 4: Compare the current number of iterations with the maximum number of iterations. If the population evolution has not reached the maximum number of iterations, the current number of iterations is increased by one, and the next iteration is skipped to step 2. Otherwise, the evolution is terminated to obtain the multi-threshold image segmentation result and the optimal threshold combination that segments the image to the maximum total entropy value.

[0067] When the multi-threshold image segmentation method based on leapfrogging and multi-optimal guidance in this paper is applied to the multi-threshold image segmentation problem, not only the efficiency of image segmentation can be improved, but also the accuracy of segmentation can be improved. The obtained image segmentation results perform well in terms of detail retention and overall segmentation effectiveness.

Claims

1. A multi-threshold image segmentation method based on leapfrogging and multi-optimal guidance, characterized in that: At least the following steps are included: Step 1. Model the multi-threshold image segmentation problem as the objective function of the optimization algorithm. First, grayscale the input image to obtain the corresponding grayscale image, and use non-local mean filtering to obtain the non-local mean image. The final non-local mean two-dimensional histogram is formed by combining and normalizing the grayscale image and the non-local mean image. Since the main diagonal of the non-local mean two-dimensional histogram contains enough image information, in order to simplify the calculation, we only calculate the Renyi entropy of the sub-area on the main diagonal. Therefore, the Renyi entropy based on the non-local mean two-dimensional histogram is used as the objective function, and the individual position of the population is the threshold combination. Next, the population and related parameters are initialized in the search space; Step 2: Propose a leapfrog crossover calculation method. First, exchange information between the two parent individuals to obtain the new position after the crossover between individuals and generations. Then exchange information between different dimensions within the individual to obtain the new position of the individual after the crossover across dimensions. After the leapfrog crossover search, each individual will greedily select the new position obtained from the position before the crossover to update the population; Step 3: Propose a multi-optimal guided evolution acceleration method. First, the population evolution state is detected based on the optimization rate guidance. Each time the rate of decline of the optimal fitness value is newly calculated, the standard deviation of the rate set is recalculated, and the value of the evolution acceleration is determined by its change, so as to determine whether the current population evolution is in a normal state or an unfavorable state. Then, the unfavorable state of the population is subdivided based on the optimal individual distance guidance. Finally, the intervention operation based on the better solution clustering guidance is used to eliminate the unfavorable state and obtain a new population. Step 4: Compare the current number of iterations with the maximum number of iterations. If the population evolution has not reached the maximum number of iterations, the current number of iterations is increased by one, and the next iteration is skipped to step 2. Otherwise, the evolution is terminated to obtain the multi-threshold image segmentation result and the optimal threshold combination that segments the image to the maximum total entropy value.

2. The multi-threshold image segmentation method based on leapfrogging and multi-optimal guidance according to claim 1 is characterized in that: In step 2, a leapfrog crossover calculation method is proposed. At the beginning of each iteration, the population generated in step 1 is cross-pollinated based on multiple levels of information such as individuals, dimensions, and generations according to a certain probability. First, in a certain dimension, the position information of the two parent individuals in this iteration and the previous iteration is crossed to obtain the new position after the cross-individual and cross-generation crossover. Then, the position information of the same individual in different dimensions is crossed to obtain the new position of the individual after the cross-dimensional crossover. The information exchanged between individuals, dimensions, and generations is combined, and each individual will greedily choose the new and old positions after the crossover calculation.

3. The multi-threshold image segmentation method based on leapfrogging and multi-optimal guidance according to claim 1 is characterized in that: In step 3, a multi-optimal guided evolution acceleration method is proposed. The population obtained in step 2 is timely detected and processed by optimizing rate guidance, optimal individual distance guidance and better solution clustering guidance, so as to achieve the purpose of accelerating evolution. First, the population evolution state is detected based on the optimization rate guidance. According to the position change of the optimal individual before and after the current iteration, the decline rate of the optimal fitness value is selectively calculated and added to the rate set of this evolution cycle. Each time the decline rate is newly calculated, the standard deviation of the new rate set is calculated, and the value of evolution acceleration is judged by its change, so as to judge whether the current state is normal or bad. Second, the bad state of the population is subdivided based on the optimal individual distance guidance. The degree of aggregation of the population is judged by judging the weighted distance of each individual in the population to the current optimal individual in each dimension. A high degree of aggregation means that the individuals of the population are closely gathered around the current optimal individual at this time, and the population may converge too early and fall into a local optimum and cannot escape. Otherwise, it means that the population may not converge to a stable point. At this time, intervention operations based on the guidance of better solution clustering are taken to alleviate the dilemma. That is, if the population aggregation degree is high, the population is dispersed through discrete operations. Otherwise, the population is gathered towards the current three better solutions through aggregation operations, thereby expanding the search space and escaping from local optimality or stagnation.

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