基于灰狼算法优化最小交叉熵，如何实现图像多阈值分割？

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1+内容介绍+阈值分割方法的关键在于阈值选择。阈值决定了图像分割结果的好坏。随着阈值数量的增加，图像分割的计算过程越来越复杂。为了进行图像分割，文中提出了离群值方法。

1 内容介绍

阈值分割方法的关键在于阈值选取.阈值决定了图像分割结果的好与坏,随着阈值数量的增加,图像分割的计算过程越来越复杂.为了选取适当的阈值进行图像分割,文中提出了离散灰狼算法(Discrete Grey Wolf Optimizer,DGWO),即经过离散化处理的灰狼算法,并用该算法求解以Kapur分割函数为目标函数的全局优化问题.DGWO算法具有很好的全局收敛性与计算鲁棒性,能够避免陷入局部最优,尤其适合高维,多峰的复杂函数问题的求解,并且可以很好地融合到图像分割过程当中.大量的理论分析和仿真实验的结果表明,与遗传算法(GA),粒子群算法(PSO)的图像分割结果相比,在选取多张分割图像,多个分割阈值的情况下,该算法具有更好的分割效果,更高的分割效率,优化得到的阈值范围更加稳定,分割质量更高.

2 部分代码

%___________________________________________________________________%

% Grey Wolf Optimizer (GWO) source codes version 1.0 %

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% Developed in MATLAB R2011b(7.13) %

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% Author and programmer: Seyedali Mirjalili %

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% e-Mail: ali.mirjalili@gmail.com %

% seyedali.mirjalili@griffithuni.edu.au %

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% Homepage: www.alimirjalili.com %

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% Main paper: S. Mirjalili, S. M. Mirjalili, A. Lewis %

% Grey Wolf Optimizer, Advances in Engineering %

% Software , in press, %

% DOI: 10.1016/j.advengsoft.2013.12.007 %

% %

%___________________________________________________________________%

% Grey Wolf Optimizer

function [Alpha_score,Alpha_pos,Convergence_curve]=GWO(SearchAgents_no,Max_iter,lb,ub,dim,fobj)

% initialize alpha, beta, and delta_pos

Alpha_pos=zeros(1,dim);

Alpha_score=inf; %change this to -inf for maximization problems

Beta_pos=zeros(1,dim);

Beta_score=inf; %change this to -inf for maximization problems

Delta_pos=zeros(1,dim);

Delta_score=inf; %change this to -inf for maximization problems

%Initialize the positions of search agents

Positions=initialization(SearchAgents_no,dim,ub,lb);

Convergence_curve=zeros(1,Max_iter);

l=0;% Loop counter

% Main loop

while l<Max_iter

for i=1:size(Positions,1)

% Return back the search agents that go beyond the boundaries of the search space

Flag4ub=Positions(i,:)>ub;

Flag4lb=Positions(i,:)<lb;

Positions(i,:)=(Positions(i,:).*(~(Flag4ub+Flag4lb)))+ub.*Flag4ub+lb.*Flag4lb;

% Calculate objective function for each search agent

fitness=fobj(Positions(i,:));

% Update Alpha, Beta, and Delta

if fitness<Alpha_score

Alpha_score=fitness; % Update alpha

Alpha_pos=Positions(i,:);

end

if fitness>Alpha_score && fitness<Beta_score

Beta_score=fitness; % Update beta

Beta_pos=Positions(i,:);

end

if fitness>Alpha_score && fitness>Beta_score && fitness<Delta_score

Delta_score=fitness; % Update delta

Delta_pos=Positions(i,:);

end

end

a=2-l*((2)/Max_iter); % a decreases linearly fron 2 to 0

% Update the Position of search agents including omegas

for i=1:size(Positions,1)

for j=1:size(Positions,2)

r1=rand(); % r1 is a random number in [0,1]

r2=rand(); % r2 is a random number in [0,1]

A1=2*a*r1-a; % Equation (3.3)

C1=2*r2; % Equation (3.4)

D_alpha=abs(C1*Alpha_pos(j)-Positions(i,j)); % Equation (3.5)-part 1

X1=Alpha_pos(j)-A1*D_alpha; % Equation (3.6)-part 1

r1=rand();

r2=rand();

A2=2*a*r1-a; % Equation (3.3)

C2=2*r2; % Equation (3.4)

D_beta=abs(C2*Beta_pos(j)-Positions(i,j)); % Equation (3.5)-part 2

X2=Beta_pos(j)-A2*D_beta; % Equation (3.6)-part 2

r1=rand();

r2=rand();

A3=2*a*r1-a; % Equation (3.3)

C3=2*r2; % Equation (3.4)

D_delta=abs(C3*Delta_pos(j)-Positions(i,j)); % Equation (3.5)-part 3

X3=Delta_pos(j)-A3*D_delta; % Equation (3.5)-part 3

Positions(i,j)=(X1+X2+X3)/3;% Equation (3.7)

end

end

l=l+1;

Convergence_curve(l)=Alpha_score;

end

3 运行结果

4 参考文献

[1]赵勇, 方宗德, 庞辉,等. 基于量子粒子群优化算法的最小交叉熵多阈值图像分割[J]. 计算机应用研究, 2008, 25(4):3.

[2]李薇, 胡晓辉, 王鸿闯. 基于改进BBO算法的二维交叉熵多阈值图像分割（英文）[J]. Journal of Measurement Science and Instrumentation, 2018, v.9;No.33(01):46-53.

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