【转】七种常见阈值分割代码(Otsu、最大熵、迭代法、自适应阀值、手动、迭代法、基本全局阈值法)

http://blog.csdn.net/xw20084898/article/details/17564957

一、工具：VC+OpenCV

二、语言：C++

三、原理

otsu法（最大类间方差法，有时也称之为大津算法）使用的是聚类的思想，把图像的灰度数按灰度级分成2个部分，使得两个部分之间的灰度值差异最大，每个部分之间的灰度差异最小，通过方差的计算来寻找一个合适的灰度级别来划分。所以可以在二值化的时候采用otsu算法来自动选取阈值进行二值化。otsu算法被认为是图像分割中阈值选取的最佳算法，计算简单，不受图像亮度和对比度的影响。因此,使类间方差最大的分割意味着错分概率最小。

设t为设定的阈值。

wo：分开后前景像素点数占图像的比例

uo：分开后前景像素点的平均灰度

w1：分开后被景像素点数占图像的比例

u1：分开后被景像素点的平均灰度

u=w0*u0 + w1*u1 :图像总平均灰度

从L个灰度级遍历t，使得t为某个值的时候，前景和背景的方差最大，则这个 t 值便是我们要求得的阈值。

其中，方差的计算公式如下：

g=wo * (uo - u) * (uo - u) + w1 * (u1 - u) * (u1 - u)

[ 此公式计算量较大，可以采用： g = wo * w1 * (uo - u1) * (uo - u1) ]

由于otsu算法是对图像的灰度级进行聚类，so 在执行otsu算法之前，需要计算该图像的灰度直方图。

迭代法原理：迭代选择法是首先猜测一个初始阈值，然后再通过对图像的多趟计算对阈值进行改进的过程。重复地对图像进行阈值操作，将图像分割为对象类和背景类，然后来利用每一个类中的灰阶级别对阈值进行改进。

图像阈值分割---迭代算法

1 .处理流程：

1.为全局阈值选择一个初始估计值T(图像的平均灰度)。
2.用T分割图像。产生两组像素：G1有灰度值大于T的像素组成，G2有小于等于T像素组成。
3.计算G1和G2像素的平均灰度值m1和m2；
4.计算一个新的阈值:T = (m1 + m2) / 2;
5.重复步骤2和4,直到连续迭代中的T值间的差小于一个预定义参数为止。

适合图像直方图有明显波谷

四、程序

主程序(核心部分)

[cpp] view plain copy

阈值分割
1 /*===============================图像分割=====================================*/
2 /*---------------------------------------------------------------------------*/
3 /*手动设置阀值*/
4 IplImage* binaryImg = cvCreateImage(cvSize(w, h),IPL_DEPTH_8U, 1);
5 cvThreshold(smoothImgGauss,binaryImg,71,255,CV_THRESH_BINARY);
6 cvNamedWindow("cvThreshold", CV_WINDOW_AUTOSIZE );
7 cvShowImage( "cvThreshold", binaryImg );
8 //cvReleaseImage(&binaryImg);
9 /*---------------------------------------------------------------------------*/
10 /*自适应阀值 //计算像域邻域的平均灰度，来决定二值化的值*/
11 IplImage* adThresImg = cvCreateImage(cvSize(w, h),IPL_DEPTH_8U, 1);
12 double max_value=255;
13 int adpative_method=CV_ADAPTIVE_THRESH_GAUSSIAN_C;//CV_ADAPTIVE_THRESH_MEAN_C
14 int threshold_type=CV_THRESH_BINARY;
15 int block_size=3;//阈值的象素邻域大小
16 int offset=5;//窗口尺寸
17 cvAdaptiveThreshold(smoothImgGauss,adThresImg,max_value,adpative_method,threshold_type,block_size,offset);
18 cvNamedWindow("cvAdaptiveThreshold", CV_WINDOW_AUTOSIZE );
19 cvShowImage( "cvAdaptiveThreshold", adThresImg );
20 cvReleaseImage(&adThresImg);
21 /*---------------------------------------------------------------------------*/
22 /*最大熵阀值分割法*/
23 IplImage* imgMaxEntropy = cvCreateImage(cvGetSize(imgGrey),IPL_DEPTH_8U,1);
24 MaxEntropy(smoothImgGauss,imgMaxEntropy);
25 cvNamedWindow("MaxEntroyThreshold", CV_WINDOW_AUTOSIZE );
26 cvShowImage( "MaxEntroyThreshold", imgMaxEntropy );//显示图像
27 cvReleaseImage(&imgMaxEntropy );
28 /*---------------------------------------------------------------------------*/
29 /*基本全局阀值法*/
30 IplImage* imgBasicGlobalThreshold = cvCreateImage(cvGetSize(imgGrey),IPL_DEPTH_8U,1);
31 cvCopyImage(srcImgGrey,imgBasicGlobalThreshold);
32 int pg[256],i,thre;
33 for (i=0;i<256;i++) pg[i]=0;
34 for (i=0;i<imgBasicGlobalThreshold->imageSize;i++) // 直方图统计
35 pg[(BYTE)imgBasicGlobalThreshold->imageData[i]]++;
36 thre = BasicGlobalThreshold(pg,0,256); // 确定阈值
37 cout<<"The Threshold of this Image in BasicGlobalThreshold is:"<<thre<<endl;//输出显示阀值
38 cvThreshold(imgBasicGlobalThreshold,imgBasicGlobalThreshold,thre,255,CV_THRESH_BINARY); // 二值化
39 cvNamedWindow("BasicGlobalThreshold", CV_WINDOW_AUTOSIZE );
40 cvShowImage( "BasicGlobalThreshold", imgBasicGlobalThreshold);//显示图像
41 cvReleaseImage(&imgBasicGlobalThreshold);
42 /*---------------------------------------------------------------------------*/
43 /*OTSU*/
44 IplImage* imgOtsu = cvCreateImage(cvGetSize(imgGrey),IPL_DEPTH_8U,1);
45 cvCopyImage(srcImgGrey,imgOtsu);
46 int thre2;
47 thre2 = otsu2(imgOtsu);
48 cout<<"The Threshold of this Image in Otsu is:"<<thre2<<endl;//输出显示阀值
49 cvThreshold(imgOtsu,imgOtsu,thre2,255,CV_THRESH_BINARY); // 二值化
50 cvNamedWindow("imgOtsu", CV_WINDOW_AUTOSIZE );
51 cvShowImage( "imgOtsu", imgOtsu);//显示图像
52 cvReleaseImage(&imgOtsu);
53 /*---------------------------------------------------------------------------*/
54 /*上下阀值法：利用正态分布求可信区间*/
55 IplImage* imgTopDown = cvCreateImage( cvGetSize(imgGrey), IPL_DEPTH_8U, 1 );
56 cvCopyImage(srcImgGrey,imgTopDown);
57 CvScalar mean ,std_dev;//平均值、标准差
58 double u_threshold,d_threshold;
59 cvAvgSdv(imgTopDown,&mean,&std_dev,NULL);
60 u_threshold = mean.val[0] +2.5* std_dev.val[0];//上阀值
61 d_threshold = mean.val[0] -2.5* std_dev.val[0];//下阀值
62 //u_threshold = mean + 2.5 * std_dev; //错误
63 //d_threshold = mean - 2.5 * std_dev;
64 cout<<"The TopThreshold of this Image in TopDown is:"<<d_threshold<<endl;//输出显示阀值
65 cout<<"The DownThreshold of this Image in TopDown is:"<<u_threshold<<endl;
66 cvThreshold(imgTopDown,imgTopDown,d_threshold,u_threshold,CV_THRESH_BINARY_INV);//上下阀值
67 cvNamedWindow("imgTopDown", CV_WINDOW_AUTOSIZE );
68 cvShowImage( "imgTopDown", imgTopDown);//显示图像
69 cvReleaseImage(&imgTopDown);
70 /*---------------------------------------------------------------------------*/
71 /*迭代法*/
72 IplImage* imgIteration = cvCreateImage( cvGetSize(imgGrey), IPL_DEPTH_8U, 1 );
73 cvCopyImage(srcImgGrey,imgIteration);
74 int thre3,nDiffRec;
75 thre3 =DetectThreshold(imgIteration, 100, nDiffRec);
76 cout<<"The Threshold of this Image in imgIteration is:"<<thre3<<endl;//输出显示阀值
77 cvThreshold(imgIteration,imgIteration,thre3,255,CV_THRESH_BINARY_INV);//上下阀值
78 cvNamedWindow("imgIteration", CV_WINDOW_AUTOSIZE );
79 cvShowImage( "imgIteration", imgIteration);
80 cvReleaseImage(&imgIteration);
迭代
1 /*======================================================================*/
2 /* 迭代法*/
3 /*======================================================================*/
4 // 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
5 int DetectThreshold(IplImage*img, int nMaxIter, int& iDiffRec) //阀值分割：迭代法
6 {
7 //图像信息
8 int height = img->height;
9 int width = img->width;
10 int step = img->widthStep/sizeof(uchar);
11 uchar *data = (uchar*)img->imageData;
12
13 iDiffRec =0;
14 int F[256]={ 0 }; //直方图数组
15 int iTotalGray=0;//灰度值和
16 int iTotalPixel =0;//像素数和
17 byte bt;//某点的像素值
18
19 uchar iThrehold,iNewThrehold;//阀值、新阀值
20 uchar iMaxGrayValue=0,iMinGrayValue=255;//原图像中的最大灰度值和最小灰度值
21 uchar iMeanGrayValue1,iMeanGrayValue2;
22
23 //获取(i,j)的值，存于直方图数组F
24 for(int i=0;i<width;i++)
25 {
26 for(int j=0;j<height;j++)
27 {
28 bt = data[i*step+j];
29 if(bt<iMinGrayValue)
30 iMinGrayValue = bt;
31 if(bt>iMaxGrayValue)
32 iMaxGrayValue = bt;
33 F[bt]++;
34 }
35 }
36
37 iThrehold =0;//
38 iNewThrehold = (iMinGrayValue+iMaxGrayValue)/2;//初始阀值
39 iDiffRec = iMaxGrayValue - iMinGrayValue;
40
41 for(int a=0;(abs(iThrehold-iNewThrehold)>0.5)&&a<nMaxIter;a++)//迭代中止条件
42 {
43 iThrehold = iNewThrehold;
44 //小于当前阀值部分的平均灰度值
45 for(int i=iMinGrayValue;i<iThrehold;i++)
46 {
47 iTotalGray += F[i]*i;//F[]存储图像信息
48 iTotalPixel += F[i];
49 }
50 iMeanGrayValue1 = (uchar)(iTotalGray/iTotalPixel);
51 //大于当前阀值部分的平均灰度值
52 iTotalPixel =0;
53 iTotalGray =0;
54 for(int j=iThrehold+1;j<iMaxGrayValue;j++)
55 {
56 iTotalGray += F[j]*j;//F[]存储图像信息
57 iTotalPixel += F[j];
58 }
59 iMeanGrayValue2 = (uchar)(iTotalGray/iTotalPixel);
60
61 iNewThrehold = (iMeanGrayValue2+iMeanGrayValue1)/2; //新阀值
62 iDiffRec = abs(iMeanGrayValue2 - iMeanGrayValue1);
63 }
64
65 //cout<<"The Threshold of this Image in imgIteration is:"<<iThrehold<<endl;
66 return iThrehold;
67 }
68
Otsu代码一
1 /*======================================================================*/
2 /* OTSU global thresholding routine */
3 /* takes a 2D unsigned char array pointer, number of rows, and */
4 /* number of cols in the array. returns the value of the threshold */
5 /*parameter:
6 *image --- buffer for image
7 rows, cols --- size of image
8 x0, y0, dx, dy --- region of vector used for computing threshold
9 vvv --- debug option, is 0, no debug information outputed
10 */
11 /*
12 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。
13 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。
14 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。
15 划分点就是求得的阈值。
16 */
17 /*======================================================================*/
18 int otsu (unsigned char*image, int rows, int cols, int x0, int y0, int dx, int dy, int vvv)
19 {
20
21 unsigned char*np; // 图像指针
22 int thresholdValue=1; // 阈值
23 int ihist[256]; // 图像直方图，256个点
24
25 int i, j, k; // various counters
26 int n, n1, n2, gmin, gmax;
27 double m1, m2, sum, csum, fmax, sb;
28
29 // 对直方图置零
30 memset(ihist, 0, sizeof(ihist));
31
32 gmin=255; gmax=0;
33 // 生成直方图
34 for (i = y0 +1; i < y0 + dy -1; i++)
35 {
36 np = (unsigned char*)image[i*cols+x0+1];
37 for (j = x0 +1; j < x0 + dx -1; j++)
38 {
39 ihist[*np]++;
40 if(*np > gmax) gmax=*np;
41 if(*np < gmin) gmin=*np;
42 np++; /* next pixel */
43 }
44 }
45
46 // set up everything
47 sum = csum =0.0;
48 n =0;
49
50 for (k =0; k <=255; k++)
51 {
52 sum += (double) k * (double) ihist[k]; /* x*f(x) 质量矩*/
53 n += ihist[k]; /* f(x) 质量 */
54 }
55
56 if (!n)
57 {
58 // if n has no value, there is problems...
59 fprintf (stderr, "NOT NORMAL thresholdValue = 160 ");
60 return (160);
61 }
62
63 // do the otsu global thresholding method
64 fmax =-1.0;
65 n1 =0;
66 for (k =0; k <255; k++)
67 {
68 n1 += ihist[k];
69 if (!n1)
70 {
71 continue;
72 }
73 n2 = n - n1;
74 if (n2 ==0)
75 {
76 break;
77 }
78 csum += (double) k *ihist[k];
79 m1 = csum / n1;
80 m2 = (sum - csum) / n2;
81 sb = (double) n1 *(double) n2 *(m1 - m2) * (m1 - m2);
82 /* bbg: note: can be optimized. */
83 if (sb > fmax)
84 {
85 fmax = sb;
86 thresholdValue = k;
87 }
88 }
89
90 // at this point we have our thresholding value
91
92 // debug code to display thresholding values
93 if ( vvv &1 )
94 fprintf(stderr,"# OTSU: thresholdValue = %d gmin=%d gmax=%d ",
95 thresholdValue, gmin, gmax);
96
97 return(thresholdValue);
98 }
Otsu代码二
1 /*======================================================================*/
2 /* OTSU global thresholding routine */
3 /*======================================================================*/
4 int otsu2 (IplImage *image)
5 {
6 int w = image->width;
7 int h = image->height;
8
9 unsigned char*np; // 图像指针
10 unsigned char pixel;
11 int thresholdValue=1; // 阈值
12 int ihist[256]; // 图像直方图，256个点
13
14 int i, j, k; // various counters
15 int n, n1, n2, gmin, gmax;
16 double m1, m2, sum, csum, fmax, sb;
17
18 // 对直方图置零...
19 memset(ihist, 0, sizeof(ihist));
20
21 gmin=255; gmax=0;
22 // 生成直方图
23 for (i =0; i < h; i++)
24 {
25 np = (unsigned char*)(image->imageData + image->widthStep*i);
26 for (j =0; j < w; j++)
27 {
28 pixel = np[j];
29 ihist[ pixel]++;
30 if(pixel > gmax) gmax= pixel;
31 if(pixel < gmin) gmin= pixel;
32 }
33 }
34
35 // set up everything
36 sum = csum =0.0;
37 n =0;
38
39 for (k =0; k <=255; k++)
40 {
41 sum += k * ihist[k]; /* x*f(x) 质量矩*/
42 n += ihist[k]; /* f(x) 质量 */
43 }
44
45 if (!n)
46 {
47 // if n has no value, there is problems...
48 //fprintf (stderr, "NOT NORMAL thresholdValue = 160 ");
49 thresholdValue =160;
50 goto L;
51 }
52
53 // do the otsu global thresholding method
54 fmax =-1.0;
55 n1 =0;
56 for (k =0; k <255; k++)
57 {
58 n1 += ihist[k];
59 if (!n1) { continue; }
60 n2 = n - n1;
61 if (n2 ==0) { break; }
62 csum += k *ihist[k];
63 m1 = csum / n1;
64 m2 = (sum - csum) / n2;
65 sb = n1 * n2 *(m1 - m2) * (m1 - m2);
66 /* bbg: note: can be optimized. */
67 if (sb > fmax)
68 {
69 fmax = sb;
70 thresholdValue = k;
71 }
72 }
73
74 L:
75 for (i =0; i < h; i++)
76 {
77 np = (unsigned char*)(image->imageData + image->widthStep*i);
78 for (j =0; j < w; j++)
79 {
80 if(np[j] >= thresholdValue)
81 np[j] =255;
82 else np[j] =0;
83 }
84 }
85
86 //cout<<"The Threshold of this Image in Otsu is:"<<thresholdValue<<endl;
87 return(thresholdValue);
88 }
最大熵阀值
1 /*============================================================================
2 = 代码内容：最大熵阈值分割
3 = 修改日期:2009-3-3
4 = 作者:crond123
5 = 博客:http://blog.csdn.net/crond123/
6 = E_Mail:crond123@163.com
7 ===============================================================================*/
8 // 计算当前位置的能量熵
9 double caculateCurrentEntropy(CvHistogram * Histogram1,int cur_threshold,entropy_state state)
10 {
11 int start,end;
12 int total =0;
13 double cur_entropy =0.0;
14 if(state == back)
15 {
16 start =0;
17 end = cur_threshold;
18 }
19 else
20 {
21 start = cur_threshold;
22 end =256;
23 }
24 for(int i=start;i<end;i++)
25 {
26 total += (int)cvQueryHistValue_1D(Histogram1,i);//查询直方块的值 P304
27 }
28 for(int j=start;j<end;j++)
29 {
30 if((int)cvQueryHistValue_1D(Histogram1,j)==0)
31 continue;
32 double percentage = cvQueryHistValue_1D(Histogram1,j)/total;
33 /*熵的定义公式*/
34 cur_entropy +=-percentage*logf(percentage);
35 /*根据泰勒展式去掉高次项得到的熵的近似计算公式
36 cur_entropy += percentage*percentage;*/
37 }
38 return cur_entropy;
39 // return (1-cur_entropy);
40 }
41
42 //寻找最大熵阈值并分割
43 void MaxEntropy(IplImage *src,IplImage *dst)
44 {
45 assert(src != NULL);
46 assert(src->depth ==8&& dst->depth ==8);
47 assert(src->nChannels ==1);
48 CvHistogram * hist = cvCreateHist(1,&HistogramBins,CV_HIST_ARRAY,HistogramRange);//创建一个指定尺寸的直方图
49 //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
50 cvCalcHist(&src,hist);//计算直方图
51 double maxentropy =-1.0;
52 int max_index =-1;
53 // 循环测试每个分割点，寻找到最大的阈值分割点
54 for(int i=0;i<HistogramBins;i++)
55 {
56 double cur_entropy = caculateCurrentEntropy(hist,i,object)+caculateCurrentEntropy(hist,i,back);
57 if(cur_entropy>maxentropy)
58 {
59 maxentropy = cur_entropy;
60 max_index = i;
61 }
62 }
63 cout<<"The Threshold of this Image in MaxEntropy is:"<<max_index<<endl;
64 cvThreshold(src, dst, (double)max_index,255, CV_THRESH_BINARY);
65 cvReleaseHist(&hist);
66 }
基本全局阀值法
1 /*============================================================================
2 = 代码内容：基本全局阈值法
3 ==============================================================================*/
4 int BasicGlobalThreshold(int*pg,int start,int end)
5 { // 基本全局阈值法
6 int i,t,t1,t2,k1,k2;
7 double u,u1,u2;
8 t=0;
9 u=0;
10 for (i=start;i<end;i++)
11 {
12 t+=pg[i];
13 u+=i*pg[i];
14 }
15 k2=(int) (u/t); // 计算此范围灰度的平均值
16 do
17 {
18 k1=k2;
19 t1=0;
20 u1=0;
21 for (i=start;i<=k1;i++)
22 { // 计算低灰度组的累加和
23 t1+=pg[i];
24 u1+=i*pg[i];
25 }
26 t2=t-t1;
27 u2=u-u1;
28 if (t1)
29 u1=u1/t1; // 计算低灰度组的平均值
30 else
31 u1=0;
32 if (t2)
33 u2=u2/t2; // 计算高灰度组的平均值
34 else
35 u2=0;
36 k2=(int) ((u1+u2)/2); // 得到新的阈值估计值
37 }
38 while(k1!=k2); // 数据未稳定，继续
39 //cout<<"The Threshold of this Image in BasicGlobalThreshold is:"<<k1<<endl;
40 return(k1); // 返回阈值
41 }

【转】七种常见阈值分割代码(Otsu、最大熵、迭代法、自适应阀值、手动、迭代法、基本全局阈值法)

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