【图像分割】基于回溯搜索优化算法实现图像聚类分割附matlab代码

1 内容介绍

阈值法是一种简单且有效的图像分割技术.但是随着阈值数目的增加,求解阈值的计算量增大并且实时性降低,这给多阈值图像分割带来了很大的困难.为了克服这一困难,把多阈值分割看作一个优化问题.将最大类间方差法当作要优化的函数,用回溯搜索优化算法求解要优化的函数,从而实现多阈值图像分割.将提出的多阈值算法应用于基准测试图像上,并与传统阈值分割法比较.实验结果表明:回溯搜索优化算法很好的解决了最大类间方差算法求解多阈值分割实时性差的问题,并验证了该算法应用在图像分割上是可行的.

2 仿真代码

%{

Backtracking Search Optimization Algorithm (BSA)

Platform: Matlab 2013a   

Cite this algorithm as;

[1]  P. Civicioglu, "Backtracking Search Optimization Algorithm for 

numerical optimization problems", Applied Mathematics and Computation, 219, 8121?144, 2013.

Copyright Notice

Copyright (c) 2012, Pinar Civicioglu

All rights reserved.

Redistribution and use in source and binary forms, with or without 

modification, are permitted provided that the following conditions are 

met:

    * Redistributions of source code must retain the above copyright 

      notice, this list of conditions and the following disclaimer.

    * Redistributions in binary form must reproduce the copyright 

      notice, this list of conditions and the following disclaimer in 

      the documentation and/or other materials provided with the distribution

      

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 

AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 

IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 

ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 

LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 

CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 

SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 

INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 

CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 

ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 

POSSIBILITY OF SUCH DAMAGE.

%}

function bsa(fnc,mydata,popsize,dim,DIM_RATE,low,up,epoch)

%INITIALIZATION

if numel(low)==1, low=low*ones(1,dim); up=up*ones(1,dim); end % this line must be adapted to your problem

pop=GeneratePopulation(popsize,dim,low,up); % see Eq.1 in [1]

fitnesspop=feval(fnc,pop,mydata);

historical_pop=GeneratePopulation(popsize,dim,low,up); % see Eq.2 in [1]

% historical_pop  is swarm-memory of BSA as mentioned in [1].

% ------------------------------------------------------------------------------------------ 

for epk=1:epoch

    %SELECTION-I

    if rand

    historical_pop=historical_pop(randperm(popsize),:); % see Eq.4 in [1]

    F=get_scale_factor; % see Eq.5 in [1], you can other F generation strategies 

    map=zeros(popsize,dim); % see Algorithm-2 in [1]         

    if rand

        for i=1:popsize,  u=randperm(dim); map(i,u(1:ceil(DIM_RATE*rand*dim)))=1; end

    else

        for i=1:popsize,  map(i,randi(dim))=1; end

    end

    % RECOMBINATION (MUTATION+CROSSOVER)   

    offsprings=pop+(map.*F).*(historical_pop-pop);   % see Eq.5 in [1]    

    offsprings=BoundaryControl(offsprings,low,up); % see Algorithm-3 in [1]

    % SELECTON-II

    fitnessoffsprings=feval(fnc,offsprings,mydata);

    ind=fitnessoffsprings

    fitnesspop(ind)=fitnessoffsprings(ind);

    pop(ind,:)=offsprings(ind,:);

    [globalminimum,ind]=min(fitnesspop);    

    globalminimizer=pop(ind,:);

    % EXPORT SOLUTIONS 

    assignin('base','globalminimizer',globalminimizer);

    assignin('base','globalminimum',globalminimum);

    fprintf('BSA|%5.0f -----> %9.16f\n',epk,globalminimum);

end

return

function pop=GeneratePopulation(popsize,dim,low,up)

pop=ones(popsize,dim);

for i=1:popsize

    for j=1:dim

        pop(i,j)=rand*(up(j)-low(j))+low(j);

    end

end

return

function pop=BoundaryControl(pop,low,up)

[popsize,dim]=size(pop);

for i=1:popsize

    for j=1:dim                

        k=rand

        if pop(i,j)

        if pop(i,j)>up(j),  if k, pop(i,j)=up(j);  else pop(i,j)=rand*(up(j)-low(j))+low(j); end, end        

    end

end

return

function F=get_scale_factor % you can change generation strategy of scale-factor,F    

     F=3*randn; % STANDARD brownian-walk

    % F=4*randg;  % brownian-walk    

    % F=lognrnd(rand,5*rand);  % brownian-walk              

    % F=1/normrnd(0,5);        % pseudo-stable walk (levy-like)

    % F=1./gamrnd(1,0.5);      % pseudo-stable walk (levy-like, simulates inverse gamma distribution; levy-distiribution)   

return

3 运行结果

4 参考文献

[1]LI Sheng-jie. 基于回溯搜索优化算法的图像分割[J]. 新一代信息技术, 2019, 2(11):7.

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