觉得这篇介绍OTSU方法挺清楚的。自己又加了一些，希望对初学者有帮助哦~

OTSU

1. OTSU算法原理简介

对于一幅图像，设当前景与背景的分割阈值为t时，前景点占图像比例为w0，均值为u0，背景点占图像比例为w1，均值为u1。则整个图像的均值为u = w0*u0+w1*u1。建立目标函数g(t)=w0*(u0-u)^2+w1*(u1-u)^2，g(t)就是当分割阈值为t时的类间方差表达式。OTSU算法使得g(t)取得全局最大值，当g(t)为最大时所对应的t称为最佳阈值。OTSU算法又称为最大类间方差法。

OSTU大津法算法思想：

一幅有depth个灰度级，根据每个灰度级t，可以将一幅图分为前景和背景。

前景指所有灰度级低于等于t的像素点，背景指大于t的像素点。

w0指前景像素个数；w1指背景像素个数；u0指前景加权平均，即

temp=0;

for i=1:t

temp=temp+i*hist(i)

end

u0=temp/w0;

其中w0=hist(0)+hist(1)+……+hist(t)

hist指各个灰度级上的像素个数

u1对应是背景加权平均

u对应整幅图的加权平均

u=u0*w0+u1*w1.(*)

大津法的结果指使得g最大的t值：

g=w0*(u0-u)^2+w1*(u1-u)^2=w0*w1*(u1-u0)^2 (代入*式可得)2.matlab提供算法

function [level em] = graythresh(I)

%GRAYTHRESH Global image threshold using Otsu's method.

%   LEVEL = GRAYTHRESH(I) computes a global threshold (LEVEL) that can be

%   used to convert an intensity image to a binary image with IM2BW. LEVEL

%   is a normalized intensity value that lies in the range [0, 1].

%   GRAYTHRESH uses Otsu's method, which chooses the threshold to minimize

%   the intraclass variance of the thresholded black and white pixels.

%

%   [LEVEL EM] = GRAYTHRESH(I) returns effectiveness metric, EM, as the

%   second output argument. It indicates the effectiveness of thresholding

%   of the input image and it is in the range [0, 1]. The lower bound is

%   attainable only by images having a single gray level, and the upper

%   bound is attainable only by two-valued images.

function level = Mygraythresh(I)

%GRAYTHRESH Global image threshold using Otsu's method.

% LEVEL = Mygraythresh(I) computes a global threshold (LEVEL) that can be

% used to convert an intensity image to a binary image with IM2BW. LEVEL

% is a normalized intensity value that lies in the range [0, 1].

% GRAYTHRESH uses Otsu's method, which chooses the threshold to minimize

% the intraclass variance of the thresholded black and white pixels.

%

% Example

% -------

% I = imread('coins.png');

% level = Mygraythresh(I);

% BW = im2bw(I,level);

% figure, imshow(BW)

%

% See also IM2BW.

%I=rgb2gray(I);

I=im2uint8(I(:));

depth=256;

counts=imhist(I,depth);

w=cumsum(counts);

ut=counts .* (1:depth)';

u=cumsum(ut);

MAX=0;

level=0;

for t=1:depth

u0=u(t,1)/w(t,1);

u1=(u(depth,1)-u(t,1))/(w(depth,1)-w(t,1));

w0=w(t,1);

w1=w(depth,1)-w0;

g=w0*w1*(u1-u0)*(u1-u0);

if g > MAX

MAX=g;

level = t;

end

end

level=level/256;

3.OTSU算法例程-C

下面是OSTU算法的C语言代码及其测试，代码基于opencv。

#include

#include

int otsu(IplImage *image)

{

assert(NULL != image);

int width = image->width;

int height = image->height;

int x=0,y=0;

int pixelCount[256];

float pixelPro[256];

int i, j, pixelSum = width * height, threshold = 0;

uchar* data = (uchar*)image->imageData;

//初始化

for(i = 0; i < 256; i++)

{

pixelCount[i] = 0;

pixelPro[i] = 0;

}

//统计灰度级中每个像素在整幅图像中的个数

for(i = y; i < height; i++)

{

for(j = x;j

{

pixelCount[data[i * image->widthStep + j]]++;

}

}

//计算每个像素在整幅图像中的比例

for(i = 0; i < 256; i++)

{

pixelPro[i] = (float)(pixelCount[i]) / (float)(pixelSum);

}

//经典ostu算法,得到前景和背景的分割

//遍历灰度级[0,255],计算出方差最大的灰度值,为最佳阈值

float w0, w1, u0tmp, u1tmp, u0, u1, u,deltaTmp, deltaMax = 0;

for(i = 0; i < 256; i++)

{

w0 = w1 = u0tmp = u1tmp = u0 = u1 = u = deltaTmp = 0;

for(j = 0; j < 256; j++)

{

if(j <= i) //背景部分

{

//以i为阈值分类，第一类总的概率

w0 += pixelPro[j];

u0tmp += j * pixelPro[j];

}

else //前景部分

{

//以i为阈值分类，第二类总的概率

w1 += pixelPro[j];

u1tmp += j * pixelPro[j];

}

}

u0 = u0tmp / w0;//第一类的平均灰度

u1 = u1tmp / w1;//第二类的平均灰度

u = u0tmp + u1tmp;//整幅图像的平均灰度

//计算类间方差

deltaTmp = w0 * (u0 - u)*(u0 - u) + w1 * (u1 - u)*(u1 - u);

//找出最大类间方差以及对应的阈值

if(deltaTmp > deltaMax)

{

deltaMax = deltaTmp;

threshold = i;

}

}

//返回最佳阈值;

return threshold;

}

int main(int argc, char* argv[])

{

IplImage* srcImage = cvLoadImage("D:\\technology\\CV\\Database\\image\\rice.png",0);

assert(NULL != srcImage);

cvNamedWindow("src");

cvShowImage("src",srcImage);

IplImage* biImage = cvCreateImage(cvGetSize(srcImage),8,1);

//计算最佳阈值

int threshold = otsu(srcImage);

//对图像二值化

cvThreshold(srcImage,biImage,threshold,255,CV_THRESH_BINARY);

cvNamedWindow("binary");

cvShowImage("binary",biImage);

cvWaitKey(0);

cvReleaseImage(&srcImage);

cvReleaseImage(&biImage);

cvDestroyWindow("src");

cvDestroyWindow("binary");

return 0;

}

下面是上述代码的运行结果图片。其中左边为原图像，右边为使用OTSU算法进行二值化后的图像。