OSTU C++实现：
#include <assert.h>
#include "cv.h"
#include "highgui.h"
#include <math.h>
#include <iostream>
using namespace std;
// implementation of otsu algorithm
// author: onezeros(@yahoo.cn)
// reference: Rafael C. Gonzalez. Digital Image Processing Using MATLAB
void cvThresholdOtsu(IplImage* src, IplImage* dst)
{
int height=src->height;
int width=src->width;
//histogram
float histogram[256]={0};
for(int i=0;i<height;i++) {
unsigned char* p=(unsigned char*)src->imageData+src->widthStep*i;
for(int j=0;j<width;j++) {
histogram[*p++]++;
}
}
//normalize histogram
int size=height*width;
for(int i=0;i<256;i++) {
histogram[i]=histogram[i]/size;
}
//average pixel value
float avgValue=0;
for(int i=0;i<256;i++) {
avgValue+=i*histogram[i];
}
int threshold;
float maxVariance=0;
float w=0,u=0;
for(int i=0;i<256;i++) {
w+=histogram[i];
u+=i*histogram[i];
float t=avgValue*w-u;
float variance=t*t/(w*(1-w));
if(variance>maxVariance) {
maxVariance=variance;
threshold=i;
}
}
cvThreshold(src,dst,threshold,255,CV_THRESH_BINARY);
}
// implementation of otsu algorithm
// author: onezeros(@yahoo.cn)
// reference: Rafael C. Gonzalez. Digital Image Processing Using MATLAB
int cvThresholdOtsu(IplImage* src)
{
int height=src->height;
int width=src->width;
//histogram
float histogram[256]={0};
for(int i=0;i<height;i++) {
unsigned char* p=(unsigned char*)src->imageData+src->widthStep*i;
for(int j=0;j<width;j++) {
histogram[*p++]++;
}
}
//normalize histogram
int size=height*width;
for(int i=0;i<256;i++) {
histogram[i]=histogram[i]/size;
}
//average pixel value
float avgValue=0;
for(int i=0;i<256;i++) {
avgValue+=i*histogram[i];
}
int threshold;
float maxVariance=0;
float w=0,u=0;
for(int i=0;i<256;i++) {
w+=histogram[i];
u+=i*histogram[i];
float t=avgValue*w-u;
float variance=t*t/(w*(1-w));
if(variance>maxVariance) {
maxVariance=variance;
threshold=i;
}
}
return threshold;
}
#include <cv.h>
#include <cxcore.h>
#include <highgui.h>
#pragma comment(lib,"cv210d.lib")
#pragma comment(lib,"cxcore210d.lib")
#pragma comment(lib,"highgui210d.lib")
#include <iostream>
using namespace std;
int main()
{
int threshold=-1;
IplImage* img =cvLoadImage("E:\\test.jpg");
cvShowImage("video",img);
cvCvtColor(img,img,CV_RGB2YCrCb);
IplImage* imgCb=cvCreateImage(cvGetSize(img),8,1);
cvSplit(img,NULL,NULL,imgCb,NULL);
if (threshold<0){
threshold=cvThresholdOtsu(imgCb);
}
//cvThresholdOtsu(imgCb,imgCb);
cvThreshold(imgCb,imgCb,threshold,255,CV_THRESH_BINARY);
cvSaveImage("E:\\imgCb.bmp",imgCb);
cvShowImage("object",imgCb);
cvReleaseImage(&imgCb);
return 0;
}
迭代阈值分割 mtalab实现：
%基于贝叶斯分类算法的图像阈值分割
clear
clc;
Init = imread('E:\\test.jpg');
Im=rgb2gray(Init);
figure(1)
imhist(Im),title('直方图') ;
[x,y]=size(Im); % 求出图象大小
b=double(Im);
zd=double(max(Im)) % 求出图象中最大的灰度
zx=double(min(Im)) % 最小的灰度
T=double((zd+zx))/2; % T赋初值，为最大值和最小值的平均值
count=double(0); % 记录几次循环
while 1 % 迭代最佳阈值分割算法
count=count+1;
S0=0.0; n0=0.0; %为计算灰度大于阈值的元素的灰度总值、个数赋值
S1=0.0; n1=0.0; %为计算灰度小于阈值的元素的灰度总值、个数赋值
for i=1:x
for j=1:y
if double(Im(i,j))>=T
S1=S1+double(Im(i,j)); %大于阈域值图像点灰度值累加
n1=n1+1; %大于阈域值图像点个数累加
else
S0=S0+double(Im(i,j)); %小于阈域值图像点灰度值累加
n0=n0+1; %小于阀域值图像点个数累加
end
end
end
T0=S0/n0; %求小于阀域值均值
T1=S1/n1; %求大于阀域值均值
if abs(T-((T0+T1)/2))<0.1 %迭代至 前后两次阀域值相差几乎为0时 停止迭代。
break;
else
T=(T0+T1)/2; %在阈值T下，迭代阈值的计算过程
end
end
count %显示运行次数
T
i1=im2bw(Im,T/255); % 图像在最佳阈值下二值化
figure(2)
imshow(i1,'border','tight','InitialMagnification','fit')
title('实验结果') ;
其他的见下面代码，阈值需要自己测试设定（C++实现）：
*===============================图像分割=====================================*/
*---------------------------------------------------------------------------*/
#include <assert.h>
#include "cv.h"
#include "highgui.h"
#include <math.h>
#include <iostream>
using namespace std;
int HistogramBins = 256;
float HistogramRange1[2]={0,255};
float *HistogramRange[1]={&HistogramRange1[0]};
typedef
enum {back,object} entropy_state;
*======================================================================*/
* 迭代法*/
*======================================================================*/
// nMaxIter：最大迭代次数；nDiffRec：使用给定阀值确定的亮区与暗区平均灰度差异值
int DetectThreshold(IplImage*img, int nMaxIter, int& iDiffRec) //阀值分割：迭代法
{
//图像信息
int height = img->height;
int width = img->width;
int step = img->widthStep/sizeof(uchar);
uchar *data = (uchar*)img->imageData;
iDiffRec =0;
int F[256]={ 0 }; //直方图数组
int iTotalGray=0;//灰度值和
int iTotalPixel =0;//像素数和
byte bt;//某点的像素值
uchar iThrehold,iNewThrehold;//阀值、新阀值
uchar iMaxGrayValue=0,iMinGrayValue=255;//原图像中的最大灰度值和最小灰度值
uchar iMeanGrayValue1,iMeanGrayValue2;
//获取(i,j)的值，存于直方图数组F
for(int i=0;i<width;i++)
{
for(int j=0;j<height;j++)
{
bt = data[i*step+j];
if(bt<iMinGrayValue)
iMinGrayValue = bt;
if(bt>iMaxGrayValue)
iMaxGrayValue = bt;
F[bt]++;
}
}
iThrehold =0;//
iNewThrehold = (iMinGrayValue+iMaxGrayValue)/2;//初始阀值
iDiffRec = iMaxGrayValue - iMinGrayValue;
for(int a=0;(abs(iThrehold-iNewThrehold)>0.5)&&a<nMaxIter;a++)//迭代中止条件
{
iThrehold = iNewThrehold;
//小于当前阀值部分的平均灰度值
for(int i=iMinGrayValue;i<iThrehold;i++)
{
iTotalGray += F[i]*i;//F[]存储图像信息
iTotalPixel += F[i];
}
iMeanGrayValue1 = (uchar)(iTotalGray/iTotalPixel);
//大于当前阀值部分的平均灰度值
iTotalPixel =0;
iTotalGray =0;
for(int j=iThrehold+1;j<iMaxGrayValue;j++)
{
iTotalGray += F[j]*j;//F[]存储图像信息
iTotalPixel += F[j];
}
iMeanGrayValue2 = (uchar)(iTotalGray/iTotalPixel);
iNewThrehold = (iMeanGrayValue2+iMeanGrayValue1)/2; //新阀值
iDiffRec = abs(iMeanGrayValue2 - iMeanGrayValue1);
}
//cout<<"The Threshold of this Image in imgIteration is:"<<iThrehold<<endl;
return iThrehold;
}
*======================================================================*/
/* OTSU global thresholding routine */
/* takes a 2D unsigned char array pointer, number of rows, and */
/* number of cols in the array. returns the value of the threshold */
/*parameter:
*image --- buffer for image
rows, cols --- size of image
x0, y0, dx, dy --- region of vector used for computing threshold
vvv --- debug option, is 0, no debug information outputed
*/
/*
OTSU 算法可以说是自适应计算单阈值（用来转换灰度图像为二值图像）的简单高效方法。
下面的代码最早由 Ryan Dibble提供，此后经过多人Joerg.Schulenburg, R.Z.Liu 等修改，补正。
算法对输入的灰度图像的直方图进行分析，将直方图分成两个部分，使得两部分之间的距离最大。
划分点就是求得的阈值。
*/
/*======================================================================*/
int otsu (unsigned char*image, int rows, int cols, int x0, int y0, int dx, int dy, int vvv)
{
unsigned char*np; // 图像指针
int thresholdValue=1; // 阈值
int ihist[256]; // 图像直方图，256个点
int i, j, k; // various counters
int n, n1, n2, gmin, gmax;
double m1, m2, sum, csum, fmax, sb;
// 对直方图置零
memset(ihist, 0, sizeof(ihist));
gmin=255; gmax=0;
// 生成直方图
for (i = y0 +1; i < y0 + dy -1; i++)
{
np = (unsigned char*)image[i*cols+x0+1];
for (j = x0 +1; j < x0 + dx -1; j++)
{
ihist[*np]++;
if(*np > gmax) gmax=*np;
if(*np < gmin) gmin=*np;
np++; /* next pixel */
}
}
// set up everything
sum = csum =0.0;
n =0;
for (k =0; k <=255; k++)
{
sum += (double) k * (double) ihist[k]; /* x*f(x) 质量矩*/
n += ihist[k]; /* f(x) 质量 */
}
if (!n)
{
// if n has no value, there is problems...
fprintf (stderr, "NOT NORMAL thresholdValue = 160\n");
return (160);
}
// do the otsu global thresholding method
fmax =-1.0;
n1 =0;
for (k =0; k <255; k++)
{
n1 += ihist[k];
if (!n1)
{
continue;
}
n2 = n - n1;
if (n2 ==0)
{
break;
}
csum += (double) k *ihist[k];
m1 = csum / n1;
m2 = (sum - csum) / n2;
sb = (double) n1 *(double) n2 *(m1 - m2) * (m1 - m2);
/* bbg: note: can be optimized. */
if (sb > fmax)
{
fmax = sb;
thresholdValue = k;
}
}
// at this point we have our thresholding value
// debug code to display thresholding values
if ( vvv &1 )
fprintf(stderr,"# OTSU: thresholdValue = %d gmin=%d gmax=%d\n",
thresholdValue, gmin, gmax);
return(thresholdValue);
}
/*======================================================================*/
/* OTSU global thresholding routine */
/*======================================================================*/
int otsu2 (IplImage *image)
{
int w = image->width;
int h = image->height;
unsigned char*np; // 图像指针
unsigned char pixel;
int thresholdValue=1; // 阈值
int ihist[256]; // 图像直方图，256个点
int i, j, k; // various counters
int n, n1, n2, gmin, gmax;
double m1, m2, sum, csum, fmax, sb;
// 对直方图置零...
memset(ihist, 0, sizeof(ihist));
gmin=255; gmax=0;
// 生成直方图
for (i =0; i < h; i++)
{
np = (unsigned char*)(image->imageData + image->widthStep*i);
for (j =0; j < w; j++)
{
pixel = np[j];
ihist[ pixel]++;
if(pixel > gmax) gmax= pixel;
if(pixel < gmin) gmin= pixel;
}
}
// set up everything
sum = csum =0.0;
n =0;
for (k =0; k <=255; k++)
{
sum += k * ihist[k]; /* x*f(x) 质量矩*/
n += ihist[k]; /* f(x) 质量 */
}
if (!n)
{
// if n has no value, there is problems...
//fprintf (stderr, "NOT NORMAL thresholdValue = 160\n");
thresholdValue =160;
goto L;
}
// do the otsu global thresholding method
fmax =-1.0;
n1 =0;
for (k =0; k <255; k++)
{
n1 += ihist[k];
if (!n1) { continue; }
n2 = n - n1;
if (n2 ==0) { break; }
csum += k *ihist[k];
m1 = csum / n1;
m2 = (sum - csum) / n2;
sb = n1 * n2 *(m1 - m2) * (m1 - m2);
/* bbg: note: can be optimized. */
if (sb > fmax)
{
fmax = sb;
thresholdValue = k;
}
}
L:
for (i =0; i < h; i++)
{
np = (unsigned char*)(image->imageData + image->widthStep*i);
for (j =0; j < w; j++)
{
if(np[j] >= thresholdValue)
np[j] =255;
else np[j] =0;
}
}
//cout<<"The Threshold of this Image in Otsu is:"<<thresholdValue<<endl;
return(thresholdValue);
}
/*============================================================================
= 代码内容：最大熵阈值分割
= 修改日期:2009-3-3
= 作者:crond123
= 博客:http://blog.csdn.net/crond123/
= E_Mail:crond123@163.com
===============================================================================*/
// 计算当前位置的能量熵
double caculateCurrentEntropy(CvHistogram * Histogram1,int cur_threshold,entropy_state state)
{
int start,end;
int total =0;
double cur_entropy =0.0;
if(state == back)
{
start =0;
end = cur_threshold;
}
else
{
start = cur_threshold;
end =256;
}
for(int i=start;i<end;i++)
{
total += (int)cvQueryHistValue_1D(Histogram1,i);//查询直方块的值 P304
}
for(int j=start;j<end;j++)
{
if((int)cvQueryHistValue_1D(Histogram1,j)==0)
continue;
double percentage = cvQueryHistValue_1D(Histogram1,j)/total;
/*熵的定义公式*/
cur_entropy +=-percentage*logf(percentage);
/*根据泰勒展式去掉高次项得到的熵的近似计算公式
cur_entropy += percentage*percentage;*/
}
return cur_entropy;
// return (1-cur_entropy);
}
//寻找最大熵阈值并分割
void MaxEntropy(IplImage *src,IplImage *dst)
{
assert(src != NULL);
assert(src->depth ==8&& dst->depth ==8);
assert(src->nChannels ==1);
CvHistogram * hist = cvCreateHist(1,&HistogramBins,CV_HIST_ARRAY,HistogramRange);//创建一个指定尺寸的直方图
//参数含义：直方图包含的维数、直方图维数尺寸的数组、直方图的表示格式、方块范围数组、归一化标志
cvCalcHist(&src,hist);//计算直方图
double maxentropy =-1.0;
int max_index =-1;
// 循环测试每个分割点，寻找到最大的阈值分割点
for(int i=0;i<HistogramBins;i++)
{
double cur_entropy = caculateCurrentEntropy(hist,i,object)+caculateCurrentEntropy(hist,i,back);
if(cur_entropy>maxentropy)
{
maxentropy = cur_entropy;
max_index = i;
}
}
cout<<"The Threshold of this Image in MaxEntropy is:"<<max_index<<endl;
cvThreshold(src, dst, (double)max_index,255, CV_THRESH_BINARY);
cvReleaseHist(&hist);
}
/*============================================================================
= 代码内容：基本全局阈值法
==============================================================================*/
int BasicGlobalThreshold(int*pg,int start,int end)
{ // 基本全局阈值法
int i,t,t1,t2,k1,k2;
double u,u1,u2;
t=0;
u=0;
for (i=start;i<end;i++)
{
t+=pg[i];
u+=i*pg[i];
}
k2=(int) (u/t); // 计算此范围灰度的平均值
do
{
k1=k2;
t1=0;
u1=0;
for (i=start;i<=k1;i++)
{ // 计算低灰度组的累加和
t1+=pg[i];
u1+=i*pg[i];
}
t2=t-t1;
u2=u-u1;
if (t1)
u1=u1/t1; // 计算低灰度组的平均值
else
u1=0;
if (t2)
u2=u2/t2; // 计算高灰度组的平均值
else
u2=0;
k2=(int) ((u1+u2)/2); // 得到新的阈值估计值
}
while(k1!=k2); // 数据未稳定，继续
//cout<<"The Threshold of this Image in BasicGlobalThreshold is:"<<k1<<endl;
return(k1); // 返回阈值
}
int main()
{
/*手动设置阀值*/
IplImage* smoothImgGauss = cvLoadImage("E:\\test.jpg", CV_LOAD_IMAGE_GRAYSCALE);
IplImage* imgGrey = cvCreateImage(cvGetSize(smoothImgGauss),IPL_DEPTH_8U, 1);
int w = smoothImgGauss->width, h = smoothImgGauss->height;
IplImage* binaryImg = cvCreateImage(cvGetSize(smoothImgGauss),IPL_DEPTH_8U, 1);
cvThreshold(smoothImgGauss,binaryImg,71,255,CV_THRESH_BINARY);
//cvNamedWindow("cvThreshold", CV_WINDOW_AUTOSIZE );
//cvShowImage( "cvThreshold", binaryImg );
cvSaveImage("E:\\手动设置阀值.bmp",binaryImg);
cvReleaseImage(&binaryImg);
/*---------------------------------------------------------------------------*/
/*自适应阀值 //计算像域邻域的平均灰度，来决定二值化的值*/
IplImage* adThresImg = cvCreateImage(cvGetSize(smoothImgGauss),IPL_DEPTH_8U, 1);
double max_value=255;
int adpative_method=CV_ADAPTIVE_THRESH_GAUSSIAN_C;//CV_ADAPTIVE_THRESH_MEAN_C
int threshold_type=CV_THRESH_BINARY;
int block_size=3;//阈值的象素邻域大小
int offset=5;//窗口尺寸
cvAdaptiveThreshold(smoothImgGauss,adThresImg,max_value,adpative_method,threshold_type,block_size,offset);
//cvNamedWindow("cvAdaptiveThreshold", CV_WINDOW_AUTOSIZE );
cvSaveImage("E:\\自适应阀值.bmp",adThresImg);
//cvShowImage( "cvAdaptiveThreshold", adThresImg );
cvReleaseImage(&adThresImg);
/*---------------------------------------------------------------------------*/
/*最大熵阀值分割法*/
IplImage* imgMaxEntropy = cvCreateImage(cvGetSize(imgGrey),IPL_DEPTH_8U,1);
MaxEntropy(smoothImgGauss,imgMaxEntropy);
//cvNamedWindow("MaxEntroyThreshold", CV_WINDOW_AUTOSIZE );
//cvShowImage( "MaxEntroyThreshold", imgMaxEntropy );//显示图像
cvSaveImage("E:\\最大熵阀值分割.bmp",imgMaxEntropy);
cvReleaseImage(&imgMaxEntropy );
/*---------------------------------------------------------------------------*/
/*基本全局阀值法*/
IplImage* imgBasicGlobalThreshold = cvCreateImage(cvGetSize(imgGrey),IPL_DEPTH_8U,1);
IplImage* srcImgGrey = cvCreateImage(cvGetSize(imgGrey),IPL_DEPTH_8U,1);
cvCopyImage(srcImgGrey,imgBasicGlobalThreshold);
int pg[256],i,thre;
for (i=0;i<256;i++) pg[i]=0;
for (i=0;i<imgBasicGlobalThreshold->imageSize;i++) // 直方图统计
pg[(BYTE)imgBasicGlobalThreshold->imageData[i]]++;
thre = BasicGlobalThreshold(pg,0,256); // 确定阈值
cout<<"The Threshold of this Image in BasicGlobalThreshold is:"<<thre<<endl;//输出显示阀值
cvThreshold(imgBasicGlobalThreshold,imgBasicGlobalThreshold,thre,200,CV_THRESH_BINARY); // 二值化
//cvNamedWindow("BasicGlobalThreshold", CV_WINDOW_AUTOSIZE );
//cvShowImage( "BasicGlobalThreshold", imgBasicGlobalThreshold);//显示图像
cvSaveImage("E:\\基本全局阀值法.bmp",imgBasicGlobalThreshold);
cvReleaseImage(&imgBasicGlobalThreshold);
/*---------------------------------------------------------------------------*/
/*OTSU*/
IplImage* imgOtsu = cvCreateImage(cvGetSize(imgGrey),IPL_DEPTH_8U,1);
cvCopyImage(srcImgGrey,imgOtsu);
int thre2;
thre2 = otsu2(imgOtsu);
cout<<"The Threshold of this Image in Otsu is:"<<thre2<<endl;//输出显示阀值
cvThreshold(imgOtsu,imgOtsu,thre2,200,CV_THRESH_BINARY); // 二值化
//cvNamedWindow("imgOtsu", CV_WINDOW_AUTOSIZE );
//cvShowImage( "imgOtsu", imgOtsu);//显示图像
cvSaveImage("E:\\OTSU.bmp",imgOtsu);
cvReleaseImage(&imgOtsu);
/*---------------------------------------------------------------------------*/
/*上下阀值法：利用正态分布求可信区间*/
IplImage* imgTopDown = cvCreateImage( cvGetSize(imgGrey), IPL_DEPTH_8U, 1 );
cvCopyImage(srcImgGrey,imgTopDown);
CvScalar mean ,std_dev;//平均值、 标准差
double u_threshold,d_threshold;
cvAvgSdv(imgTopDown,&mean,&std_dev,NULL);
u_threshold = mean.val[0] +2.5* std_dev.val[0];//上阀值
d_threshold = mean.val[0] -2.5* std_dev.val[0];//下阀值
//u_threshold = mean + 2.5 * std_dev; //错误
//d_threshold = mean - 2.5 * std_dev;
cout<<"The TopThreshold of this Image in TopDown is:"<<d_threshold<<endl;//输出显示阀值
cout<<"The DownThreshold of this Image in TopDown is:"<<u_threshold<<endl;
cvThreshold(imgTopDown,imgTopDown,d_threshold,u_threshold,CV_THRESH_BINARY_INV);//上下阀值
//cvNamedWindow("imgTopDown", CV_WINDOW_AUTOSIZE );
//cvShowImage( "imgTopDown", imgTopDown);//显示图像
cvSaveImage("E:\\上下阀值法.bmp",imgTopDown);
cvReleaseImage(&imgTopDown);
}
再次，全局阈值分割C++：
/************************************************************************/
/* 全局阈值分割 自动求取阈值 */
/************************************************************************/
//自动求取阈值，增加对场景的适应性
//只需求取一次，之后就可以一直使用
#include<cv.h>
#include <highgui.h>
#include <iostream>
#include <math.h>
using namespace std;
int main(){
IplImage * image,* image2;
image = cvLoadImage("E:\\111.jpg",0);
cvNamedWindow("image",1);
cvShowImage("image",image);
image2 = cvCreateImage(cvSize(image->width,image->height),image->depth,1);
double T = 0;
double dT0 = 1.0;//阈值求取结束标志
double dT = 255.0;
//求取平均灰度，作为阈值T的初始值T0
int i, j;
double T0 = 0,T1 = 0,T2 = 0;//初始阈值
int count1,count2;
unsigned char * ptr,*dst;
for (i = 0 ; i< image->height ; i++)
{
for (j =0 ; j < image->width;j++)
{
ptr = (unsigned char *)image->imageData + i*image->widthStep + j;
T0 += ((double)(*ptr))/image->width/image->height;
}
}
cout<<"T0: "<<T0<<endl;
T = (int)(T0 + 0.5);
//计算T两侧的灰度平均值，然后把二者的均值赋值给T
while (dT > dT0)
{
T1 = 0;
T2 = 0;
count1 = 0;
count2 = 0;
for (i = 0 ; i< image->height ; i++)
{
for (j =0 ; j < image->width;j++)
{
ptr = (unsigned char *)image->imageData + i*image->widthStep + j;
if (*ptr > T)
{
T1 += ((double)(*ptr))/image->width/image->height;
count1++;
}
else if(*ptr < T)
{
T2 += ((double)(*ptr))/image->width/image->height;
count2++;
}
}
}
T1 = T1*image->width*image->height/count1;
T2 = T2*image->width*image->height/count2;
dT = fabs(T - (T1 + T2)/2);
cout<<"T1"<<T1<<endl;
cout<<"T2"<<T2<<endl;
cout<<"dT " << dT<<endl;
T = (T1 + T2)/2;
cout<<"T: "<<T<<endl;
}
//根据求取的阈值进行分割
for (i = 0 ; i< image2->height ; i++)
{
for (j =0 ; j < image2->width;j++)
{
ptr = (unsigned char *)image->imageData + i*image->widthStep + j;
dst = (unsigned char *)image2->imageData+i*image2->widthStep+j;
if (*ptr > T)
{
*dst = 255;
}
else
{
*dst =0;
}
}
}
cvNamedWindow("image2",1);
cvShowImage("image2",image2);
cvSaveImage("E:\\image\\dowels2.tif",image2);
cvWaitKey(0);
return 0;
}
来源：https://www.cnblogs.com/xiangshancuizhu/archive/2012/03/07/2384197.html