CN113723449A - Preference information-based agent-driven multi-objective evolutionary fuzzy clustering method - Google Patents

Abstract

The invention discloses a preference information-based agent-driven multi-target evolution fuzzy clustering method, which mainly solves the problems of unsatisfactory color image segmentation performance and high calculation cost in the prior art. The scheme comprises the following steps: inputting an image to be segmented and setting an initial parameter value; constructing a fitness function fusing image region information, introducing a coarse and fine agent model and designing a multi-objective evolutionary clustering framework based on a dominance relation of a reference point and a preference angle to obtain a non-dominance solution set; constructing a clustering effectiveness index by using an information entropy of a fuzzy membership function, and selecting an optimal chromosome from a non-dominated solution set by using the index to decode the optimal chromosome to obtain an optimal clustering center; and updating the global membership matrix by using the optimal clustering center, and obtaining a classification result of the pixel points according to the maximum membership principle. Aiming at the image with a complex background and low contrast, the method can effectively improve the image segmentation effect and has short time consumption; the method can be used for identifying natural images.

Description

Preference information-based agent-driven multi-objective evolutionary fuzzy clustering method

Technical Field

The invention belongs to the field of image processing, and further relates to a fuzzy clustering image segmentation method, in particular to a preference information-based agent-driven multi-target evolution fuzzy clustering method, which can be used for identifying natural images.

Background

The image segmentation is to divide an image into a plurality of mutually disjoint areas according to characteristics such as gray scale, color, texture, geometric shape and the like, so that the characteristics show similarity in the same area and obvious difference between different areas. The image segmentation algorithm mainly comprises a threshold-based segmentation algorithm, a clustering-based segmentation algorithm, an edge detection-based segmentation algorithm, a convolutional neural network-based weak supervised learning segmentation algorithm and the like. Common clustering methods can be mainly classified into a K-means clustering algorithm, a fuzzy clustering algorithm, a density-based clustering method, a hierarchical clustering method, a spectral clustering algorithm, a kernel clustering algorithm and the like. Fuzzy clustering algorithms are one of the most widely used segmentation algorithms, and their success is mainly due to the introduction of ambiguity for each data attribution, which is more consistent with the characteristics of both things and things.

The traditional fuzzy clustering image segmentation algorithm has the following problems at present: first, the algorithm is sensitive to image noise because no spatial information of the image is considered; secondly, the initial clustering center of the traditional fuzzy clustering image segmentation algorithm is manually specified in advance, the algorithm is based on local search, and if the initial clustering center is not properly specified, the algorithm is easily caused to fall into the problem of local optimization. Thirdly, the algorithm only considers a single clustering criterion function, does not consider the image segmentation problem under multiple clustering criteria, and cannot meet the multi-aspect segmentation requirements of users. In order to solve the above problems, Zhao et al propose a noise Robust multi-objective Evolutionary Clustering algorithm (f.zhao, j.fan, h.liu, et.al.noise Robust multi objective Clustering Image Segmentation moved by the intuition noise information, ieee transformations on Fuzzy Systems, feb.2013879, 27(2)2: 401, doi: 10.1109/tfuzz.2018.2852289), define a novel noise Robust intuition Fuzzy set representation, and introduce the intuition Fuzzy set into an objective function, so as to improve the robustness to noise, and retain detail information of the Image. However, because the genetic algorithm is used as a bottom-layer optimization framework of the evolution strategy, the multi-objective evolutionary fuzzy clustering algorithm needs expensive fitness function evaluation, so that the time required for the algorithm to acquire the image segmentation result is too long.

Disclosure of Invention

The invention aims to provide a preference information-based agent-driven multi-target evolution fuzzy clustering method aiming at the defects of the prior art, and the preference information-based agent-driven multi-target evolution fuzzy clustering method is used for solving the technical problems of low calculation efficiency and long time consumption of the algorithm when the multi-target evolution fuzzy clustering algorithm is applied to image segmentation. Firstly, constructing a global fuzzy compactness function and a fuzzy separation function which fuse image region information, designing a multi-objective evolutionary clustering framework by introducing a coarse-and-fine agent model and a domination relation based on a reference point and a preference angle, guiding an evolutionary selection direction, improving the evolutionary efficiency and quality of a clustering center, and obtaining a non-domination solution set; then, constructing a clustering effectiveness index by using the information entropy of the fuzzy membership function, and selecting an optimal chromosome from the non-dominated solution set by using the index to decode the optimal chromosome to obtain an optimal clustering center; and updating the global membership matrix by using the optimal clustering center, and obtaining a classification result of the pixel points according to a maximum membership principle so as to obtain an image segmentation result. The invention can obtain good segmentation effect and obviously reduce the operation time of the algorithm.

The invention realizes the aim as follows:

(1) inputting an image I to be segmented, and setting initial parameter values: the population size E is 50, the fuzzy index m is 2, and the maximum iteration number TF of the fine search_max50, threshold σ 0.3, reference point (0.1, 0.9), maximum number of iterations TC of the coarse search_max20, the cross probability is 0.9, the variation probability is 0.1, the coefficient beta for controlling the dimension of the coarse search space is 0.3, the weighting factor χ for controlling the image area information is 0.5, and the number v of the reference vectors is 40;

(2) adopting Latin hypercube sampling to obtain an initial population X, and coding chromosomes in the population;

(3) decoding each encoded chromosome to obtain a column vector, and calculating a fitness function value Y corresponding to each chromosome;

(4) carrying out normalization processing on the initial population X and the fitness function value Y to obtain a normalized population and a normalized fitness function value;

(5) training a radial basis function model (RBF) by utilizing the normalized population and the normalized fitness function value to obtain a trained RBF;

(6) setting the current iteration frequency TF of the fine search to be 0, and generating an initial population P of the fine search by adopting Latin hypercube sampling_TFTo P_TFCarrying out iterative updating;

(6.1) obtaining the final generation population after the iteration updating of the coarse search by using a coarse search algorithm, which comprises the following specific steps:

(6.1.1) calculating the dimensionality of the coarse search space

Wherein D is the dimension of the original space; randomly selecting DC dimension population from initial population X, and recording index of selected dimension as D_indObtaining a training population XC ═ X (: D) of the coarse search space_ind)；

(6.1.2) training a polynomial regression model PR by taking (XC, Y) as a training data set to obtain a trained PR model;

(6.1.3) obtaining an initial coarse search population P by adopting Latin hypercube sampling₀And each individual is ensured to have a DC dimension, the current iteration time TC of the rough search is made equal to 0, and the current population P of the rough search is made_TC＝P₀；

(6.1.4) estimating P Using PR model_TCFitness function value in an individual, and then applying a binary tournament selection strategy from P based on the value_TCIn the formation of a parent population P_C(ii) a And to the parent population P_CPerforming crossover and mutation operations to generate a progeny population Q_C(ii) a Then, merging the parent population and the offspring population to obtain a rough search merged population R_C＝P_C∪Q_C；

(61.5) utilizing the PR model obtained by training to obtain the sub-generation population Q_CCarrying out fitness function value estimation on the individuals in the group;

(6.1.6) using an Ra dominance relation based on the reference point and the preference angle from R according to the estimated fitness function value_CSelecting individuals to form a next generation population P_TC+1The method is concretely realized as follows:

(6.1.6-1) setting a non-empty population P for storing the selected individuals each time_null；

(6.1.6-2) finding rough search merged population R according to Pareto domination relation_CAll non-dominant individuals in the Pareto dominant relationship were met, and the number was recorded as N_nrStore these individuals in P_nullPerforming the following steps; the number of remaining individuals is 2E-N_nrIf the Pareto dominance relation is not satisfied, continuing to execute the step (6.1.6-3);

(6.1.6-3) calculating the preference angle α:

(6.1.6-4) calculating a weighted Euclidean distance from the remaining individuals in the population to the reference point g:

wherein ,λ_sDenotes the weight, λ, occupied by the value of the s-th fitness function_s0.5; z represents the number of fitness function values;

(6.1.6-5) finding out the individual corresponding to the weighted Euclidean distance minimum value, and marking the individual as p_near(ii) a Calculating the preference radius r ═ dist (g, p)_near) Tan α, reference direction v vextor (g, p)_near)；

(6.1.6-6) allowing b to be 1; q-1, 2, …,2E-N_nrAnd b ≠ q;

(6.1.6-7) calculating the difference D in vertical distance_V(p,q,v)：

D_V(p_b,p_q,v)＝D_V(p_b,v)-D_V(p_q,v)，

wherein ,D_V(p_bV) represents an individual p_bPerpendicular distance to reference direction, D_V(p_qV) represents an individual p_qA vertical distance to a reference direction; if D is_V(p, q, v) < -R, then the individual p_bStore to P_null；

(6.1.6-8) allowing b to be b +1 if b < 2E-N_nrReturning to the step (6.1.6-7), otherwise, continuing to execute the step (6.1.6-9);

(6.1.6-9) selection of P_nullThe first E individuals in the group constitute the next generation population P_TC+1；

(6.1.7) determining whether the iteration is terminated, if TC < TC_maxIf yes, returning to the step (6.1.3) by making TC + TC, otherwise, terminating the iteration and continuing to execute the step (6.1.8);

(6.1.8) outputting the final generation population P after the coarse search_TCfinalAnd a dimension index D_ind；

(6.2) the last generation population P obtained by the coarse search_TCfinalMigrating to a fine search to obtain a migrated population P_T；

(6.3) executing a fine search algorithm to obtain an optimal clustering center, and specifically comprising the following steps:

(6.3.1) transferring the population P_T and P_TFCombining to obtain: p_F＝P_T∪P_TFRandom scrambling of P_F；

(6.3.2) on the population P_FPerforming crossover and mutation operations to generate a progeny population Q_F；

(6.3.3) merging contemporary population P_TFAnd progeny population Q_FObtaining a population R after fine search and combination_F＝P_TF∪Q_F；

(6.3.4) estimating a population R after fine search and combination by using the RBF model trained in the step (5)_FThe fitness function value of the medium individual is estimated, and then the Ra domination relation based on the reference point and the preference angle is adopted to carry out R_FSelecting individuals to formA next generation population; adding the population formed each time into a database DB, and outputting the database DB;

(7) judging whether the iteration is terminated, if TF is less than TF_maxIf yes, setting TF to TF +1, returning to the step (6), otherwise, ending the iteration, and continuing to execute the step (8);

(8) according to the database DB obtained in the step (6.3.4), a non-dominated solution set is obtained by utilizing a final solution set generation strategy based on the angle penalty distance APD;

(9) decoding each chromosome in the non-dominated solution set, and constructing an optimal solution selection index I by using the information entropy of the fuzzy membership function_E(X)：

(10) Selecting index I according to the optimal solution_E(X) selecting the smallest I from the non-dominated solution set_E(X) the individual corresponding to the value is used as an optimal solution and decoded to obtain an optimal clustering center;

(11) and calculating a corresponding membership matrix according to the optimal clustering center, and segmenting the image according to the maximum membership correspondence principle to obtain a final image segmentation result.

Compared with the prior art, the invention has the following advantages:

firstly, because the invention introduces the thickness agent model to design the multi-objective evolutionary clustering framework and guides the evolutionary selection direction, the evolutionary efficiency of the clustering center is improved, thereby effectively reducing the time cost required by the algorithm;

secondly, a domination relation based on a reference point and a preference angle is introduced to a frame of a multi-objective evolutionary clustering algorithm guided by a rough and fine agent model, so that a population is guided to correctly evolve towards the Pareto frontier direction on the basis of the reference point, and the evolution quality of a clustering center is improved;

thirdly, the invention designs a global fuzzy compactness function and a fuzzy separation function which are fused with the image area information, can retain the detail information of the image and enables the segmentation effect to be better.

Drawings

FIG. 1 is a flow chart of an implementation of the method of the present invention;

FIG. 2 is a comparison graph of the results of simulation segmentation of images numbered 124084 in a Berkeley image database using the present invention and existing methods;

fig. 3 is a comparison graph of the results of simulation segmentation of an image numbered 300091 in a Berkeley image database using the present invention and a prior art method.

FIG. 4 is a comparison of results of simulation segmentation of an image numbered pict2272 in a Weizmann image database using the present invention and a prior art method.

FIG. 5 is a comparison of the results of a simulation segmentation of an image with the number img-1965 in a Weizmann image database using the present invention and a prior art method.

Detailed Description

The invention is further described below with reference to the accompanying drawings.

The first embodiment is as follows:

referring to the attached figure 1, the agent-driven multi-objective evolutionary fuzzy clustering method based on preference information provided by the invention integrally comprises the following steps:

step A, inputting an image to be segmented and setting an initial parameter value.

Inputting an image I to be segmented;

setting initial parameter values: the population size E is 50, the fuzzy index m is 2, and the maximum iteration number TF of the fine search_max50, threshold σ 0.3, reference point (0.1, 0.9), maximum number of iterations TC of the coarse search_max20, the cross probability is 0.9, the variation probability is 0.1, the coefficient beta for controlling the dimension of the coarse search space is 0.3, the weighting factor χ for controlling the image area information is 0.5, and the number v of the reference vectors is 40;

and B: applying a multi-objective evolutionary fuzzy clustering method based on reference points and preference angles guided by a coarse and fine proxy model to the two objective functions to obtain a group of non-dominated solution sets S;

2.1) population initialization: coding each chromosome into K clustering centers by utilizing a latin hypercube sampling method, and randomly generating 50 parent chromosomes to form an initial population;

2.2) calculating the fitness function value Y of each chromosome in the population, namely two objective function values: global fuzzy compactness function C_RIAnd a fuzzy separation function Sep;

2.3) carrying out normalization processing on the initial population X and the fitness function value Y to obtain a normalized population and a normalized fitness function value, and training a radial basis function model RBF by using the normalized population and the normalized fitness function value to obtain a trained radial basis function model RBF;

2.4) setting the iteration frequency TF of the fine search to be 0, and performing population iteration updating;

2.4.1) executing a coarse search algorithm to quickly find some better individuals.

2.4.2) transferring some better individuals obtained in the coarse search step into the fine search by using a knowledge transfer strategy;

2.4.3) executing a fine search algorithm to obtain an ideal clustering center;

2.5) judging whether the iteration is terminated, if TF is less than TF_maxIf yes, setting TF to TF +1, returning to step 2.4), otherwise, terminating the iteration, and continuing to execute step 2.6);

2.6) executing a final solution set generation strategy based on the angle penalty distance to obtain a final non-dominated solution set S of the algorithm.

And C: the optimal chromosome is selected.

3.1) constructing a clustering effectiveness index I according to the information entropy of the fuzzy membership function_E(X)：

wherein ,u_kiIs a global membership function.

3.2) selecting an optimal chromosome from the interval value non-dominated solution set S obtained in the step B according to the index, and taking the clustering center coded on the chromosome as the optimal clustering center.

Step D: and outputting the result of the image segmentation.

And D, updating a global membership matrix U ═ U by using the optimal clustering center obtained in the step C_ki]_K×nAnd classifying the pixel points according to the maximum membership principle to obtain the segmentation result of the color image.

Example two:

referring to fig. 1, the method provided by the invention specifically comprises the following steps:

step 1: inputting an image I to be segmented, and setting initial parameter values: the population size E is 50, the fuzzy index m is 2, and the maximum iteration number TF of the fine search_max50, threshold σ 0.3, reference point (0.1, 0.9), maximum number of iterations TC of the coarse search_max20, the cross probability is 0.9, the variation probability is 0.1, the coefficient beta for controlling the dimension of the coarse search space is 0.3, the weighting factor χ for controlling the image area information is 0.5, and the number v of the reference vectors is 40;

step 2: adopting Latin hypercube sampling to obtain an initial population X, and coding chromosomes in the population;

and step 3: decoding each encoded chromosome to obtain a column vector, and calculating a fitness function value Y corresponding to each chromosome, specifically calculating a global fuzzy compactness function C_RIAnd a fuzzy separation function Sep comprising:

(3.1) calculating the characteristic information of the super-pixel region of the image I, which comprises the following specific steps:

(3.1.1) performing superpixel segmentation on the image I by adopting a linear iterative clustering algorithm to obtain H superpixel regions: p ═ P₁,P₂,…,P_h,…,P_H}，h＝1,2,...,H；

(3.1.2) respectively extracting the characteristics of each super-pixel region by using the color and position information in the super-pixel region, wherein the formula is as follows:

wherein ,R_hFeatures representing the h-th super-pixel region;f_arepresenting the 3-dimensional LAB color component, f, of the pixel point a in the superpixel region_medRepresenting a 3-dimensional LAB color component of a median pixel point med of the superpixel region; omega (f)_a,f_med) The weight between the pixel point a and the median pixel point med in the super pixel region is represented and obtained according to the following calculation:

ω(f_a,f_med)＝D_amed×C_amed，

wherein ,D_amedRepresents a position weight, C_amedRepresenting a color weight;

wherein (phi, eta) represents the coordinates of the pixel points in the superpixel region, N_umThe number of pixel points in the superpixel is represented, and delta represents the color characteristic variance of the superpixel region.

(3.1.3) obtaining superpixel region characteristic information R ═ R₁,R₂,…,R_h,…,R_H}；

(3.2) set an image I ═ x₁,x₂,…,x_i,…,x_NN pixels, i is 1,2, …, N, the number of clusters is K, K is 1, 2. Calculating a pixel x_iTo class k center c_kMahalanobis distance d (c)_k,x_i)：

Where T represents the transpose of the matrix, A_kThe symmetric positive definite matrix is expressed, and the calculation formula is as follows:

wherein, -1 represents the inverse of the matrix, F_kRepresenting the covariance matrix, the formula is calculated as follows:

wherein ,u_kiRepresenting the ith pixel point x_iBelonging to class k center c_kThe calculation formula of the membership degree of (c) is as follows:

wherein d (-) represents the mahalanobis distance;

representing pixel points in the h-th super pixel region; c. C_jRepresents class j center, j ═ 1, 2.., K;

(3.3) according to the characteristic information of the super-pixel region, the pixel characteristic R in the h-th super-pixel region_hAs all pixel information in the area

Computing

To the center of the cluster c_kMahalanobis distance of

(3.4) calculating a global fuzzy compactness function C of the fused image area information_RIThe value of (c):

(3.5) calculating the fuzzy separation function Sep:

wherein ,u_pi and u_qiRespectively representing the membership degree of the ith pixel point to the p-th and the q-th clustering centers, h (x)_i) To describe the weighting coefficients for different degrees of membership, the following is defined:

and 4, step 4: carrying out normalization processing on the initial population X and the fitness function value Y to obtain a normalized population and a normalized fitness function value;

and 5: training a radial basis function model (RBF) by utilizing the normalized population and the normalized fitness function value, wherein the model is obtained by directly calling a proxy SURROGATES tool carried by MATLAB software, and the model is trained to obtain the trained RBF;

step 6: setting the current iteration frequency TF of the fine search to be 0, and generating an initial population P of the fine search by adopting Latin hypercube sampling_TFTo P_TFCarrying out iterative updating;

(6.1) obtaining the final generation population after the iteration updating of the coarse search by using a coarse search algorithm, which comprises the following specific steps:

(6.1.1) calculating the dimensionality of the coarse search space

Wherein D is the dimension of the original space; randomly selecting DC dimension population from initial population X, and recording index of selected dimension as D_indObtaining a training population XC ═ X (: D) of the coarse search space_ind)；

(6.1.2) training a polynomial regression model PR by taking (XC, Y) as a training data set, wherein the model is obtained by directly calling a proxy SURROGATES tool carried by MATLAB software, and training the model to obtain a trained PR model;

(6.1.3) obtaining an initial coarse search population P by adopting Latin hypercube sampling₀And each individual is ensured to have a DC dimension, the current iteration time TC of the rough search is made equal to 0, and the current population P of the rough search is made_TC＝P₀；

(6.1.4) estimating P Using PR model_TCFitness function value in an individual, and then applying a binary tournament selection strategy from P based on the value_TCIn the formation of a parent population P_C(ii) a And to the parent population P_CPerforming crossover and mutation operations to generate a progeny population Q_C(ii) a Then, merging the parent population and the offspring population to obtain a rough search merged population R_C＝P_C∪Q_C(ii) a In which a binary tournament selection strategy is applied from the current population P_TCIn the formation of a parent population P_CThe method comprises the following specific steps:

(6.1.4-1) from the Current population P_TCRandomly selecting 2 individuals, wherein the selected probability of each individual is the same, and selecting the individual with the largest fitness value to enter the next generation of population according to the fitness function value of each individual;

(6.1.4-2) repeating the step (6.1.4-1) until the next generation population size reaches population P_TCScale;

(6.1.4-3) obtaining population size and P_TCParent population P of the same size_C。

(6.1.5) utilizing the PR model obtained by training to obtain the sub-generation population Q_CCarrying out fitness function value estimation on the individuals in the group;

(6.1.6) based on the estimated fitnessFunction value from R using Ra-dominated relationship based on reference point and preference angle_CSelecting individuals to form a next generation population P_TC+1The method is concretely realized as follows:

(6.1.6-1) setting a non-empty population P for storing the selected individuals each time_null；

(6.1.6-2) finding rough search merged population R according to Pareto domination relation_CAll non-dominant individuals in the Pareto dominant relationship were met, and the number was recorded as N_nrStore these individuals in P_nullPerforming the following steps; the number of remaining individuals is 2E-N_nrIf the Pareto dominance relation is not satisfied, continuing to execute the step (6.1.6-3);

(6.1.6-3) calculating the preference angle α:

(6.1.6-4) calculating a weighted Euclidean distance from the remaining individuals in the population to the reference point g:

wherein ,λ_sDenotes the weight, λ, occupied by the value of the s-th fitness function_s∈[0,1](ii) a z represents the number of fitness function values;

(6.1.6-5) finding out the individual corresponding to the weighted Euclidean distance minimum value, and marking the individual as p_near(ii) a Calculating the preference radius r ═ dist (g, p)_near) Tan α, reference direction v vextor (g, p)_near)；

(6.1.6-6) allowing b to be 1; q-1, 2, …,2E-N_nrAnd b ≠ q;

(6.1.6-7) calculating the difference D in vertical distance_V(p,q,v)：

D_V(p_b,p_q,v)＝D_V(p_b,v)-D_V(p_q,v)，

wherein ,D_V(p_bV) represents an individual p_bRadix GinsengPerpendicular distance between directions of examination, D_V(p_qV) represents an individual p_qA vertical distance to a reference direction; if D is_V(p, q, v) < -R, then the individual p_bStore to P_null；

(6.1.6-8) allowing b to be b +1 if b < 2E-N_nrReturning to the step (6.1.6-7), otherwise, continuing to execute the step (6.1.6-9);

(6.1.6-9) selection of P_nullThe first E individuals in the group constitute the next generation population P_TC+1；

(6.1.7) determining whether the iteration is terminated, if TC < TC_maxIf yes, returning to the step (6.1.3) by making TC + TC, otherwise, terminating the iteration and continuing to execute the step (6.1.8);

(6.1.8) outputting the final generation population P after the coarse search_TCfinalAnd a dimension index D_ind；

(6.2) the last generation population P obtained by the coarse search_TCfinalMigrating to a fine search to obtain a migrated population P_T(ii) a The method comprises the following specific steps:

(6.2.1) inputting the final generation population P after the coarse search_TCfinalAnd a dimension index D_ind；

(6.2.2) performing a migration from the coarse search to the fine search, making the number of lines l in the population of the fine search 1, the population P after the current migration_T(l,D_ind)＝P_TCfinal(l,:)；

(6.2.3) judging whether the iteration is terminated, if l is less than E, setting l to l +1, returning to the step (6.2.2), otherwise, ending the iteration, and obtaining the post-migration population P_T＝P_T(l,D_ind)。

(6.3) executing a fine search algorithm to obtain an optimal clustering center, and specifically comprising the following steps:

(6.3.1) transferring the population P_T and P_TFCombining to obtain: p_F＝P_T∪P_TFRandom scrambling of P_F；

(6.3.2) on the population P_FPerforming crossover and mutation operations to generate a progeny population Q_F；

(6.3.3) merging contemporary population P_TFAnd progeny population Q_FObtaining a population R after fine search and combination_F＝P_TF∪Q_F；

(6.3.4) estimating a population R after fine search and combination by using the RBF model trained in the step (5)_FThe fitness function value of the medium individual is estimated, and then the Ra domination relation based on the reference point and the preference angle is adopted to carry out R_FSelecting individuals to form a next generation population; adding the population formed each time into a database DB, and outputting the database DB;

and 7: judging whether the iteration is terminated, if TF is less than TF_maxIf yes, setting TF to TF +1, returning to the step 6, otherwise, ending iteration, and continuing to execute the step 8;

and 8: according to the database DB obtained in the step (6.3.4), a non-dominated solution set is obtained by utilizing a final solution set generation strategy based on the angle penalty distance APD;

the method comprises the following steps of obtaining a non-dominated solution set according to a final solution set generation strategy based on an angular punishment distance APD, and specifically comprises the following steps:

(8.1) generating v reference vectors by a simplex mesh method design;

(8.2) calculating an included angle between each individual and the reference vector, and associating each solution with the reference vector according to a minimum included angle principle so as to form a sub-population;

and (8.3) calculating Angular Penalty Distances (APD) of all individuals in each sub-population, selecting the individual with the minimum APD value from each sub-population, and generating a non-dominated solution set.

The angular penalty distance APD is defined as follows:

wherein ,

representing the objective function value vector obtained after the ith individual reduction,

f_i ^sthe s-th target value of the ith individual is indicated,

represents the minimum of the s-th objective function for all individuals; theta_iDenotes the angle between the ith individual and the associated reference vector, P (θ)_i) Is a penalty function defined as follows:

where z denotes the number of fitness functions, γ_vReference vector v representing the ith individual_iThe minimum angle between any other reference vector.

And step 9: decoding each chromosome in the non-dominated solution set, and constructing an optimal solution selection index I by using the information entropy of the fuzzy membership function_E(X)：

Step 10: selecting index I according to the optimal solution_E(X) selecting the smallest I from the non-dominated solution set_E(X) the individual corresponding to the value is used as an optimal solution and decoded to obtain an optimal clustering center;

step 11: and calculating a corresponding membership matrix according to the optimal clustering center, and segmenting the image according to the maximum membership correspondence principle to obtain a final image segmentation result.

The technical effects of the invention are further explained by combining simulation experiments as follows:

1. simulation conditions are as follows:

the simulation experiment is carried out in the environment of computer Inter (R) core (TM) i5-8250CPU 1.80GHZ CPU, 8G memory and MATLAB R2018a software.

2. Simulation content:

simulation 1, selecting an image with a number of 124084 in a Berkeley image database, and segmenting the image with the Fuzzy C-mean clustering algorithm FCM (Fuzzy C-means clustering algorithm), the Kernel Fuzzy C-mean clustering algorithm KFCM (Kernel-based Fuzzy C-means clustering algorithm), the fast FCFCFCFCM (superpixel-based fast FCM clustering algorithm), the multi-objective variable length genetic Fuzzy clustering algorithm MOVGA (Multi objective variable clustering algorithm), the Keritin assisted reference vector guided evolution algorithm KRVESA (acquired reference vector guided evolution algorithm), wherein the results are shown in FIG. 2:

fig. 2 (a) is an original image of the 124084 image;

fig. 2 (b) is a standard segmentation chart of the 124084 image;

fig. 2 (c) is a result of segmenting 124084 images by the existing FCM method;

fig. 2 (d) is a result of segmentation of 124084 image by the existing KFCM method;

fig. 2 (e) shows the segmentation result of 124084 image by the existing SFFCM method;

fig. 2 (f) is a result of segmentation of 124084 images using the existing MOVGA method;

fig. 2 (g) shows the result of segmenting 124084 image by the conventional KRVEA method;

fig. 2 (h) is the segmentation result of 124084 image with the present invention;

as can be seen from fig. 2, the standard segmentation maps are the images divided into three categories: flower leaves, flowers and pistils. Since the #124084 image looks complicated and the background and object are unclear, resulting in poor segmentation results of FCM, KFCM and MOVGA methods, a certain part of the flower leaves is mistaken for the false division of the pistil. The SFFCM and KRVEA methods have few phenomena of wrong division, and basically, the flower leaves and the flowers can be clearly divided. However, the best visual effect is that the invention has few wrong division phenomena, and the characteristics and the outlines of flowers, flower leaves and flower pistils are clearly divided. Therefore, the segmentation effect of the color image is better than that of the traditional FCM method, KFCM method, SFFCM method, MOVGA method and KRVEA method.

Simulation 2, selecting an image with the number of 300091 in a Berkeley image database, and segmenting the image by using the method, the conventional FCM method, the KFCM method, the SFFCM method, the MOVGA method and the KRVEA method respectively, wherein the result is shown in FIG. 3, wherein:

fig. 3 (a) is an original image of the 300091 image;

fig. 3 (b) is a standard segmentation map of the 300091 image;

fig. 3 (c) shows the result of segmentation of 300091 images by the existing FCM method;

fig. 3 (d) is a result of segmentation of 300091 images by the existing KFCM method;

fig. 3 (e) shows the result of segmentation of 300091 images by the existing SFFCM method;

fig. 3 (f) is a result of segmenting 300091 an image by the existing MOVGA method;

fig. 3 (g) shows the result of 300091 image segmentation using the conventional KRVEA method;

fig. 3 (h) shows the result of the segmentation of 300091 images by the present invention;

as can be seen from fig. 3, the standard segmentation map divides the map into two categories: human and sea water. Since the pictures are complex and the color contrast is not high, the FCM method, KFCM method, SFFCM method, MOVGA method and KRVEA method all use human and seawater as background and splash spray as target, which obviously does not meet our segmentation requirements. The invention does not completely divide people, but the division of the background is correct. This is because the present invention employs a preference point and a plurality of objective functions to satisfy the variously different segmentation needs of the user.

Simulation 3, selecting an image with the number pict2272 in a Weizmann image database, and segmenting the image by using the method, the conventional FCM method, KFCM method, SFFCM method, MOVGA method and KRVEA method respectively, wherein the result is shown in FIG. 4, wherein:

fig. 4 (a) shows an original image of a pict2272 image;

fig. 4 (b) is a standard segmentation map of the pict2272 image;

fig. 4 (c) shows the result of segmenting a pict2272 image by the conventional FCM method;

fig. 4 (d) is a result of segmentation of a pict2272 image by the existing KFCM method;

fig. 4 (e) shows the result of segmenting a pict2272 image by the conventional SFFCM method;

fig. 4 (f) shows the result of segmenting a pict2272 image by the conventional MOVGA method;

fig. 4 (g) shows the result of segmenting a pict2272 image by using the conventional KRVEA method;

fig. 4 (h) shows the result of segmenting a pict2272 image by the present invention;

as can be seen from fig. 4, the FCM method, the KFCM method, the MOVGA method, and the KRVEA method are more serious in the phenomenon of wrong division of the background region, and the segmentation effect of the SFFCM algorithm with the addition of the region information is significantly improved, but the segmentation result of the present invention is very close to the standard segmentation map. Therefore, the segmentation effect of the color image is better than that of the traditional FCM method, KFCM method, SFFCM method, MOVGA method and KRVEA method.

Simulation 4, selecting an image with the number img _1965 in a Weizmann image database, and segmenting the image by using the method, the conventional FCM method, the KFCM method, the SFFCM method, the MOVGA method and the KRVEA method respectively, wherein the result is shown in FIG. 5, wherein:

fig. 5 (a) shows an original image of the img _1965 image;

fig. 5 (b) is a standard segmentation map of the img _1965 image;

fig. 5 (c) is a segmentation result of the img _1965 image by the existing FCM method;

fig. 5 (d) is a segmentation result of the img _1965 image by the existing KFCM method;

fig. 5 (e) is a segmentation result of the img _1965 image by the existing SFFCM method;

fig. 5 (f) is the result of image segmentation for img _1965 using the existing MOVGA method;

fig. 5 (g) shows the result of segmenting img _1965 image by the conventional KRVEA method;

fig. 5 (h) is a result of segmentation of the img _1965 image by the present invention;

as can be seen from FIG. 5, the building segmentation of the present invention is more consistent with the visual perception of people, and other methods have serious misclassification phenomena. Therefore, the segmentation effect of the color image is better than that of the traditional FCM method, KFCM method, SFFCM method, MOVGA method and KRVEA method.

The simulation analysis proves the correctness and the effectiveness of the method provided by the invention.

The invention has not been described in detail in part of the common general knowledge of those skilled in the art.

While the invention has been particularly shown and described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention.

Claims (8)

1. A preference information-based agent-driven multi-objective evolution fuzzy clustering method is characterized by comprising the following steps:

(1) inputting an image I to be segmented, and setting initial parameter values: the population size E is 50, the fuzzy index m is 2, and the maximum iteration number TF of the fine search_max50, threshold σ 0.3, reference point (0.1, 0.9), maximum number of iterations TC of the coarse search_max20, the cross probability is 0.9, the variation probability is 0.1, the coefficient beta for controlling the dimension of the coarse search space is 0.3, the weighting factor χ for controlling the image area information is 0.5, and the number v of the reference vectors is 40;

(2) adopting Latin hypercube sampling to obtain an initial population X, and coding chromosomes in the population;

(3) decoding each encoded chromosome to obtain a column vector, and calculating a fitness function value Y corresponding to each chromosome;

(4) carrying out normalization processing on the initial population X and the fitness function value Y to obtain a normalized population and a normalized fitness function value;

(5) training a radial basis function model (RBF) by utilizing the normalized population and the normalized fitness function value to obtain a trained RBF;

(6) setting the current iteration frequency TF of the fine search to be 0, and generating an initial population P of the fine search by adopting Latin hypercube sampling_TFTo P_TFCarrying out iterative updating;

(6.1) obtaining the final generation population after the iteration updating of the coarse search by using a coarse search algorithm, which comprises the following specific steps:

(6.1.1) calculating the dimensionality of the coarse search space

Wherein D is the dimension of the original space; randomly selecting DC dimension population from initial population X, and recording index of selected dimension as D_indObtaining a training population XC ═ X (: D) of the coarse search space_ind)；

(6.1.2) training a polynomial regression model PR by taking (XC, Y) as a training data set to obtain a trained PR model;

(6.1.3) obtaining an initial coarse search population P by adopting Latin hypercube sampling₀And each individual is ensured to have a DC dimension, the current iteration time TC of the rough search is made equal to 0, and the current population P of the rough search is made_TC＝P₀；

(6.1.4) estimating P Using PR model_TCFitness function value in an individual, and then applying a binary tournament selection strategy from P based on the value_TCIn the formation of a parent population P_C(ii) a And to the parent population P_CPerforming crossover and mutation operations to generate a progeny population Q_C(ii) a Then, merging the parent population and the offspring population to obtain a rough search merged population R_C＝P_C∪Q_C；

(6.1.5) utilizing the PR model obtained by training to obtain the sub-generation population Q_CCarrying out fitness function value estimation on the individuals in the group;

(6.1.6) using an Ra dominance relation based on the reference point and the preference angle from R according to the estimated fitness function value_CSelecting individual body shapeInto next generation population P_TC+1The method is concretely realized as follows:

(6.1.6-1) setting a non-empty population P for storing the selected individuals each time_null；

(6.1.6-2) finding rough search merged population R according to Pareto domination relation_CAll non-dominant individuals in the Pareto dominant relationship were met, and the number was recorded as N_nrStore these individuals in P_nullPerforming the following steps; the number of remaining individuals is 2E-N_nrIf the Pareto dominance relation is not satisfied, continuing to execute the step (6.1.6-3);

(6.1.6-3) calculating the preference angle α:

(6.1.6-4) calculating a weighted Euclidean distance from the remaining individuals in the population to the reference point g:

wherein ,λ_sDenotes the weight, λ, occupied by the value of the s-th fitness function_s0.5; z represents the number of fitness function values;

(6.1.6-5) finding out the individual corresponding to the weighted Euclidean distance minimum value, and marking the individual as p_near(ii) a Calculating the preference radius r ═ dist (g, p)_near) Tan α, reference direction v vextor (g, p)_near)；

(6.1.6-6) allowing b to be 1; q-1, 2, …,2E-N_nrAnd b ≠ q;

(6.1.6-7) calculating the difference D in vertical distance_V(p,q,v)：

D_V(p_b,p_q,v)＝D_V(p_b,v)-D_V(p_q,v)，

wherein ,D_V(p_bV) represents an individual p_bPerpendicular distance to reference direction, D_V(p_qV) represents an individual p_qA vertical distance to a reference direction; if D is_V(p, q, v) < -R, then the individual p_bStore to P_null；

(6.1.6-8) allowing b to be b +1 if b < 2E-N_nrReturning to the step (6.1.6-7), otherwise, continuing to execute the step (6.1.6-9);

(6.1.6-9) selection of P_nullThe first E individuals in the group constitute the next generation population P_TC+1；

(6.1.7) determining whether the iteration is terminated, if TC < TC_maxIf yes, returning to the step (6.1.3) by making TC + TC, otherwise, terminating the iteration and continuing to execute the step (6.1.8);

(6.1.8) outputting the final generation population P after the coarse search_TCfinalAnd a dimension index D_ind；

(6.2) the last generation population P obtained by the coarse search_TCfinalMigrating to a fine search to obtain a migrated population P_T；

(6.3) executing a fine search algorithm to obtain an optimal clustering center, and specifically comprising the following steps:

(6.3.1) transferring the population P_T and P_TFCombining to obtain: p_F＝P_T∪P_TFRandom scrambling of P_F；

(6.3.2) on the population P_FPerforming crossover and mutation operations to generate a progeny population Q_F；

(6.3.3) merging contemporary population P_TFAnd progeny population Q_FObtaining a population R after fine search and combination_F＝P_TF∪Q_F；

(6.3.4) estimating a population R after fine search and combination by using the RBF model trained in the step (5)_FThe fitness function value of the medium individual is estimated, and then the Ra domination relation based on the reference point and the preference angle is adopted to carry out R_FSelecting individuals to form a next generation population; adding the population formed each time into a database DB, and outputting the database DB;

(7) judging whether the iteration is terminated, if TF is less than TF_maxIf yes, setting TF to TF +1, returning to the step (6), otherwise, ending the iteration, and continuing to execute the step (8);

(8) according to the database DB obtained in the step (6.3.4), a non-dominated solution set is obtained by utilizing a final solution set generation strategy based on the angle penalty distance APD;

(9) decoding each chromosome in the non-dominated solution set, and constructing an optimal solution selection index I by using the information entropy of the fuzzy membership function_E(X)：

(10) Selecting index I according to the optimal solution_E(X) selecting the smallest I from the non-dominated solution set_E(X) the individual corresponding to the value is used as an optimal solution and decoded to obtain an optimal clustering center;

(11) and calculating a corresponding membership matrix according to the optimal clustering center, and segmenting the image according to the maximum membership correspondence principle to obtain a final image segmentation result.

2. The method of claim 1, further comprising: calculating a fitness function value Y corresponding to each chromosome in the step (3), specifically calculating a global fuzzy compactness function C_RIAnd a fuzzy separation function Sep comprising:

(3.1) calculating the characteristic information of the super-pixel region of the image I, which comprises the following specific steps:

(3.1.1) performing superpixel segmentation on the image I by adopting a linear iterative clustering algorithm to obtain H superpixel regions: p ═ P₁,P₂,…,P_h,…,P_H}，h＝1,2,...,H；

(3.1.2) respectively extracting the characteristics of each super-pixel region by using the color and position information in the super-pixel region, wherein the formula is as follows:

wherein ,R_hFeatures representing the h-th super-pixel region; f. of_aRepresenting the 3-dimensional LAB color component, f, of the pixel point a in the superpixel region_medRepresenting a 3-dimensional LAB color component of a median pixel point med of the superpixel region; omega (f)_a,f_med) Representing the weight between the pixel point a and the median pixel point med in the super pixel area;

(3.1.3) obtaining superpixel region characteristic information R ═ R₁,R₂,…,R_h,…,R_H}；

(3.2) set an image I ═ x₁,x₂,…,x_i,…,x_NN pixels, i is 1,2, …, N, the number of clusters is K, K is 1, 2. Calculating a pixel x_iTo class k center c_kMahalanobis distance d (c)_k,x_i)：

Where T represents the transpose of the matrix, A_kThe symmetric positive definite matrix is expressed, and the calculation formula is as follows:

wherein, -1 represents the inverse of the matrix, F_kRepresenting the covariance matrix, the formula is calculated as follows:

wherein ,u_kiRepresenting the ith pixel point x_iBelonging to class k center c_kThe calculation formula of the membership degree of (c) is as follows:

wherein d (-) represents the mahalanobis distance;

representing pixel points in the h-th super pixel region; c. C_jRepresents class j center, j ═ 1, 2.., K;

(3.3) according to the characteristic information of the super-pixel region, the pixel characteristic R in the h-th super-pixel region_hAs all pixel information in the area

Computing

To the center of the cluster c_kMahalanobis distance of

(3.4) calculating a global fuzzy compactness function C of the fused image area information_RIThe value of (c):

(3.5) calculating the fuzzy separation function Sep:

wherein ,u_pi and u_qiRespectively representing the membership degree of the ith pixel point to the p-th and the q-th clustering centers, h (x)_i) To describe the weighting coefficients for different degrees of membership, the following is defined:

3. the method of claim 2, further comprising: in the step (3.1.2), the weight between the pixel point a in the superpixel region and the median pixel point med is calculated as follows:

ω(f_a,f_med)＝D_amed×C_amed，

wherein ,D_amedRepresents a position weight, C_amedRepresenting a color weight;

wherein (phi, eta) represents the coordinates of the pixel points in the superpixel region, N_umThe number of pixel points in the superpixel is represented, and delta represents the color characteristic variance of the superpixel region.

4. The method of claim 1, further comprising: the radial basis function model RBF and the polynomial regression model PR are realized by calling an agent SURROGATES tool box of MATLAB software.

5. The method of claim 1, further comprising: step (6.1.4) uses binaryTournament selection strategy from the current population P_TCIn the formation of a parent population P_CThe method comprises the following specific steps:

(6.1.4-1) from the Current population P_TCRandomly selecting 2 individuals, wherein the selected probability of each individual is the same, and selecting the individual with the largest fitness value to enter the next generation of population according to the fitness function value of each individual;

(6.1.4-2) repeating the step (6.1.4-1) until the next generation population size reaches population P_TCScale;

(6.1.4-3) obtaining population size and P_TCParent population P of the same size_C。

6. The method of claim 1, further comprising: the last generation population P obtained by the coarse search is used in the step (6.2)_TCfinalMigrating to a fine search, and specifically comprising the following steps:

(6.2.1) inputting the final generation population P after the coarse search_TCfinalAnd a dimension index D_ind；

(6.2.2) performing a migration from the coarse search to the fine search, making the number of lines l in the population of the fine search 1, the population P after the current migration_T(l,D_ind)＝P_TCfinal(l,:)；

(6.2.3) judging whether the iteration is terminated, if l is less than E, setting l to l +1, returning to the step (6.2.2), otherwise, ending the iteration, and obtaining the post-migration population P_T＝P_T(l,D_ind)。

7. The method of claim 1, further comprising: step (8) obtaining a non-dominated solution set according to a final solution set generation strategy based on the angular punishment distance APD, and the specific steps are as follows:

(8.1) generating v reference vectors by a simplex mesh method design;

(8.2) calculating an included angle between each individual and the reference vector, and associating each solution with the reference vector according to a minimum included angle principle so as to form a sub-population;

and (8.3) calculating Angular Penalty Distances (APD) of all individuals in each sub-population, selecting the individual with the minimum APD value from each sub-population, and generating a non-dominated solution set.

8. The method of claim 7, further comprising: the angular penalty distance APD is defined as follows:

wherein ,

representing the objective function value vector obtained after the ith individual reduction,

the s-th target value of the ith individual is indicated,

represents the minimum of the s-th objective function for all individuals; theta_iDenotes the angle between the ith individual and the associated reference vector, P (θ)_i) Is a penalty function defined as follows:

where z denotes the number of fitness functions, γ_vReference vector v representing the ith individual_iThe minimum angle between any other reference vector.

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