前面介紹了 數字圖像灰度直方圖,現在來嘗試直方圖的應用。
直方圖均衡化
直方圖均衡化(Histogram Equalization)是直方圖最典型的應用,是圖像點運算的一種。對於一幅輸入圖像,通過運算產生一幅輸出圖像,點運算是指輸出圖像的每個像素點的灰度值由輸入像素點決定,即:
直方圖均衡化是通過灰度變換將一幅圖像轉換爲另一幅具有均衡直方圖,即在每個灰度級上都具有相同的象素點數過程。從分佈圖上的理解就是希望原始圖像中y軸的值在新的分佈中儘可能的展開。變換過程是利用累積分佈函數對原始分佈進行映射,生成新的均勻拉伸的分佈。因此對應每個點的操作是尋找原始分佈中y值在均勻分佈中的位置,如下圖是理想的單純高斯分佈映射的示意圖:
(圖片來源:《Learnning OpenCV》 p189)
OpenCV中的cvEqualizeHist
OpenCV中有灰度直方圖均衡化的函數cvEqualizeHist,接口很明朗:
- void cvEqualizeHist( const CvArr* src, CvArr* dst );
注意此函數只能處理單通道的灰色圖像,對於彩色圖像,我們可以把每個信道分別均衡化,再Merge爲彩色圖像。
實踐:圖像直方圖均衡化
- int main()
- {
- IplImage * image= cvLoadImage("baboon.jpg");
- //顯示原圖及直方圖
- myShowHist("Source",image);
- IplImage* eqlimage=cvCreateImage(cvGetSize(image),image->depth,3);
- //分別均衡化每個信道
- IplImage* redImage=cvCreateImage(cvGetSize(image),image->depth,1);
- IplImage* greenImage=cvCreateImage(cvGetSize(image),image->depth,1);
- IplImage* blueImage=cvCreateImage(cvGetSize(image),image->depth,1);
- cvSplit(image,blueImage,greenImage,redImage,NULL);
- cvEqualizeHist(redImage,redImage);
- cvEqualizeHist(greenImage,greenImage);
- cvEqualizeHist(blueImage,blueImage);
- //均衡化後的圖像
- cvMerge(blueImage,greenImage,redImage,NULL,eqlimage);
- myShowHist("Equalized",eqlimage);
- }
均衡化後的直方圖:
直方圖匹配
參考shlkl99上傳的直方圖匹配代碼,將圖像規定化爲高斯分佈函數。
- //將圖像與特定函數分佈histv[]匹配
- void myHistMatch(IplImage *img,double histv[])
- {
- int bins = 256;
- int sizes[] = {bins};
- CvHistogram *hist = cvCreateHist(1,sizes,CV_HIST_ARRAY);
- cvCalcHist(&img,hist);
- cvNormalizeHist(hist,1);
- double val_1 = 0.0;
- double val_2 = 0.0;
- uchar T[256] = {0};
- double S[256] = {0};
- double G[256] = {0};
- for (int index = 0; index<256; ++index)
- {
- val_1 += cvQueryHistValue_1D(hist,index);
- val_2 += histv[index];
- G[index] = val_2;
- S[index] = val_1;
- }
- double min_val = 0.0;
- int PG = 0;
- for ( int i = 0; i<256; ++i)
- {
- min_val = 1.0;
- for(int j = 0;j<256; ++j)
- {
- if( (G[j] - S[i]) < min_val && (G[j] - S[i]) >= 0)
- {
- min_val = (G[j] - S[i]);
- PG = j;
- }
- }
- T[i] = (uchar)PG;
- }
- uchar *p = NULL;
- for (int x = 0; x<img->height;++x)
- {
- p = (uchar*)(img->imageData + img->widthStep*x);
- for (int y = 0; y<img->width;++y)
- {
- p[y] = T[p[y]];
- }
- }
- }
- // 生成高斯分佈
- void GenerateGaussModel(double model[])
- {
- double m1,m2,sigma1,sigma2,A1,A2,K;
- m1 = 0.15;
- m2 = 0.75;
- sigma1 = 0.05;
- sigma2 = 0.05;
- A1 = 1;
- A2 = 0.07;
- K = 0.002;
- double c1 = A1*(1.0/(sqrt(2*CV_PI))*sigma1);
- double k1 = 2*sigma1*sigma1;
- double c2 = A2*(1.0/(sqrt(2*CV_PI))*sigma2);
- double k2 = 2*sigma2*sigma2;
- double p = 0.0,val= 0.0,z = 0.0;
- for (int zt = 0;zt < 256;++zt)
- {
- val = K + c1*exp(-(z-m1)*(z-m1)/k1) + c2*exp(-(z-m2)*(z-m2)/k2);
- model[zt] = val;
- p = p +val;
- z = z + 1.0/256;
- }
- for (int i = 0;i<256; ++i)
- {
- model[i] = model[i]/p;
- }
- }
實踐:直方圖匹配
對示例圖片每個信道分別進行匹配處理
對比直方圖
- double cvCompareHist(
- const CvHistogram* hist1, //直方圖1
- const CvHistogram* hist2, //直方圖2
- int method//對比方法
- );
- int main()
- {
- IplImage * image= cvLoadImage("myhand1.jpg");
- IplImage * image2= cvLoadImage("myhand2.jpg");
- int hist_size=256;
- float range[] = {0,255};
- float* ranges[]={range};
- IplImage* gray_plane = cvCreateImage(cvGetSize(image),8,1);
- cvCvtColor(image,gray_plane,CV_BGR2GRAY);
- CvHistogram* gray_hist = cvCreateHist(1,&hist_size,CV_HIST_ARRAY,ranges,1);
- cvCalcHist(&gray_plane,gray_hist,0,0);
- IplImage* gray_plane2 = cvCreateImage(cvGetSize(image2),8,1);
- cvCvtColor(image2,gray_plane2,CV_BGR2GRAY);
- CvHistogram* gray_hist2 = cvCreateHist(1,&hist_size,CV_HIST_ARRAY,ranges,1);
- cvCalcHist(&gray_plane2,gray_hist2,0,0);
- //相關:CV_COMP_CORREL
- //卡方:CV_COMP_CHISQR
- //直方圖相交:CV_COMP_INTERSECT
- //Bhattacharyya距離:CV_COMP_BHATTACHARYYA
- double com=cvCompareHist(gray_hist,gray_hist2,CV_COMP_BHATTACHARYYA);
- cout<<com<<endl;
- }
輸出結果爲:0.396814
表明兩幅圖的匹配度變高了。