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: http://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.