1 内容介绍
在图像阈值分割方法中,Renyi熵法因其显著效能而得到大量应用.为了更好地发挥Renyi熵在图像分割中的应用,提出把Renyi熵法扩展到图像多级阈值化问题.然而,由于计算时间复杂度上的高要求,很难把这种有效的技术推广到复杂图像多级阈值化问题.为减少本方法的计算时间,应用灰狼优化算法实施最佳阈值的搜索.实验结果表明,本方法能有效地对图像进行多级分割,并且显著降低计算时间.
2 部分代码
% Grey Wolf Optimizer
function [Alpha_score,Alpha_pos,Convergence_curve]=GWO(SearchAgents_no,Max_iter,lb,ub,dim,fhandle,fnonlin)
% 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,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=Fun(fhandle,fnonlin,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]聂方彦, 张平凤, 潘梅森,等. 基于Renyi熵与PSO算法的图像多级阈值分割[J]. 湖南文理学院学报：自然科学版, 2013, 25(3):6.