差分进化算法在图像处理中的应用研究（Matlab代码实现）

    目录

1 概述

2 运行结果

3 参考文献

‍4 Matlab代码

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1 概述

本文为Storn和Price制定的著名差分进化计算智能算法的实现。该算法使用Otsu准则作为适应度函数，可用于使用多个阈值对灰度图像进行阈值设置。

该程序旨在生成任何灰度图像的0到255级直方图，然后尝试找到阈值，在该阈值下，图像可以最佳地分离为属于图像前景的像素和属于图像背景的像素。最佳阈值的评估使用Otsu标准进行，阈值的Otsu适应度作为“类间方差”返回。值越高，适合度越好。差分进化保持生成1到256范围内的阈值，并评估图像的阈值的适合性。使用突变和交叉，一代又一代地选择更为理想的阈值。用户可以选择运行多个试验，并选择这些试验中的最佳阈值，并显示分割图像以及直方图和阈值的位置。

2 运行结果

3 参考文献

[1]刘波,王凌,金以慧.差分进化算法研究进展[J].控制与决策,2007(07):721-729.DOI:10.13195/j.cd.2007.07.3.liub.001.

‍4 Matlab代码

主函数部分代码：

% This is the main file for running Differential Evolution

clc;clear all;close all;

images = {'lena_gray.png', 'barbara_gray.bmp'};

imgName = char(images(1));

infor = imfinfo(imgName);

disp(infor);

[I, colormap] = imread(imgName);

if isempty(colormap), I = rgb2gray(I); else I = ind2gray(I, colormap);end

I = im2uint8(I);

searchSpace = imhist(I);

%-----Control panel

thresh = 8;%the number of thresholds

population = 30;%the number of vectors

masterBeta = 2.0;%beta is real number belongs to [0 -> 2]

cr = 0.3;%crossover probability range [0 -> 1]

generations = 200;

numTrials = 1;

if population < 4, disp('Population should be more than 3');return;end

minThresh = 1; maxThresh = numel(searchSpace);

figNum = 1;

figure(figNum);clf;figNum=figNum+1;imshow(I);title('Original image');

%figure(figNum);clf;figNum=figNum+1;imhist(I);title(strcat('histogram of : ',imgName));

%OtsuThreshold = graythresh(I);II = im2bw(I);imshow(II);title('Otsu thresholded image');

runtime = [];

fitStore = [];

bestThresholdAmongTrials = [];

bestFitnessAmongTrials = 0;

tempBestFitnessAmongTrials = 0;

fastestGenerationForBestFitness = 0;

for aTrial = 1:numTrials  

tic;

tempFitStore = [];

vBeta = masterBeta;%variable beta

fprintf('Trial: %d\n', aTrial);

X = floor(minThresh + (maxThresh - minThresh) * rand(thresh, population));

U = X;

generationAtBestFit = [0 0];%stores generation and best fitness

spaceSize = size(searchSpace, 1);

totalPixels = sum(searchSpace);

normProba = searchSpace ./ totalPixels;%normalized probabilities

if thresh < 1 || thresh > spaceSize, disp('Thresholds should be in a range of 1 to 256');return;end

%-----Get an initial Fitness

[fitnessX, X] = OtsuFitness(X, spaceSize, totalPixels, normProba);

[val, fittest] = max(fitnessX);