matlab 霍夫变换—检测圆

 function [hough_space,hough_circle,para] = hough_circle(BW,step_r,step_angle,r_min,r_max,p)

 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % input
 % BW:二值图像；
 % step_r:检测的圆半径步长
 % step_angle:角度步长，单位为弧度
 % r_min:最小圆半径
 % r_max:最大圆半径
 % p:阈值，0，1之间的数 通过调此值可以得到图中圆的圆心和半径
 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % output
 % hough_space:参数空间，h(a,b,r)表示圆心在(a,b)半径为r的圆上的点数
 % hough_circl:二值图像，检测到的圆
 % para:检测到的圆的圆心、半径

 circleParaXYR=[];
 para=[];

 [m,n] = size(BW);
 size_r = round((r_max-r_min)/step_r)+1;%四舍五入
 size_angle = round(2*pi/step_angle);

 hough_space = zeros(m,n,size_r);

 [rows,cols] = find(BW);%查找非零元素的行列坐标
 ecount = size(rows);%非零坐标的个数

 % Hough变换
 % 将图像空间(x,y)对应到参数空间(a,b,r)

 % a = x-r*cos(angle)
 % b = y-r*sin(angle)

 for i=1:ecount
     for r=1:size_r %半径步长数
         for k=1:size_angle %按一定弧度把圆几等分
             a = round(rows(i)-(r_min+(r-1)*step_r)*cos(k*step_angle));
             b = round(cols(i)-(r_min+(r-1)*step_r)*sin(k*step_angle));
             if(a>0&a<=m&b>0&b<=n)
             hough_space(a,b,r) = hough_space(a,b,r)+1;%h(a,b,r)的坐标，圆心和半径
             end
         end
     end
 end


 % 搜索超过阈值的聚集点。对于多个圆的检测，阈值要设的小一点！通过调此值，可以求出所有圆的圆心和半径
 max_para = max(max(max(hough_space)));%返回值就是这个矩阵的最大值
 index = find(hough_space>=max_para*p);%一个矩阵中，想找到其中大于max_para*p数的位置
 length = size(index);%符合阈值的个数
 hough_circle = false(m,n);
 %hough_circle = zeros(m,n);
 %通过位置求半径和圆心。
 for i=1:ecount
     for k=1:length
         par3 = floor(index(k)/(m*n))+1;
         par2 = floor((index(k)-(par3-1)*(m*n))/m)+1;
         par1 = index(k)-(par3-1)*(m*n)-(par2-1)*m;
         if((rows(i)-par1)^2+(cols(i)-par2)^2<(r_min+(par3-1)*step_r)^2+5&...
                 (rows(i)-par1)^2+(cols(i)-par2)^2>(r_min+(par3-1)*step_r)^2-5)
               hough_circle(rows(i),cols(i)) = true;   %检测的圆
         end
     end
 end

 % 从超过峰值阈值中得到
 for k=1:length
     par3 = floor(index(k)/(m*n))+1;%取整
     par2 = floor((index(k)-(par3-1)*(m*n))/m)+1;
     par1 = index(k)-(par3-1)*(m*n)-(par2-1)*m;
     circleParaXYR = [circleParaXYR;par1,par2,par3];
     hough_circle(par1,par2)= true; %这时得到好多圆心和半径，不同的圆的圆心处聚集好多点，这是因为所给的圆不是标准的圆
     %fprintf(1,'test1:Center %d %d \n',par1,par2);
 end

 %集中在各个圆的圆心处的点取平均，得到针对每个圆的精确圆心和半径！
 while size(circleParaXYR,1) >= 1
     num=1;
     XYR=[];
     temp1=circleParaXYR(1,1);
     temp2=circleParaXYR(1,2);
     temp3=circleParaXYR(1,3);
     c1=temp1;
     c2=temp2;
     c3=temp3;
     temp3= r_min+(temp3-1)*step_r;
    if size(circleParaXYR,1)>1
      for k=2:size(circleParaXYR,1)
       if (circleParaXYR(k,1)-temp1)^2+(circleParaXYR(k,2)-temp2)^2 > temp3^2
          XYR=[XYR;circleParaXYR(k,1),circleParaXYR(k,2),circleParaXYR(k,3)];  %保存剩下圆的圆心和半径位置
       else
       c1=c1+circleParaXYR(k,1);
       c2=c2+circleParaXYR(k,2);
       c3=c3+circleParaXYR(k,3);
       num=num+1;
       end
     end
    end
       %fprintf(1,'sum %d %d radius %d\n',c1,c2,r_min+(c3-1)*step_r);
       c1=round(c1/num);
       c2=round(c2/num);
       c3=round(c3/num);
       c3=r_min+(c3-1)*step_r;
       %fprintf(1,'num=%d\n',num)
       %fprintf(1,'Center %d %d radius %d\n',c1,c2,c3);
       para=[para;c1,c2,c3]; %保存各个圆的圆心和半径的值
       circleParaXYR=XYR;
 end

 文件2 main.m
 clc,clear all
 circleParaXYR=[];
 I = imread('h6.jpg');
 [m,n,l] = size(I);
 if l>1
     I = rgb2gray(I);
 end
 BW = edge(I,'sobel');

 step_r = 1;
 step_angle = 0.1;
 minr = 3
 maxr = 30;
 thresh = 0.51;

 [hough_space,hough_circle,para] = hough_circlefu(BW,step_r,step_angle,minr,maxr,thresh);
 figure(1),imshow(I),title('原图')
 figure(2),imshow(BW),title('边缘')
 figure(3),imshow(hough_circle),title('检测结果')

 circleParaXYR=para;

 %输出
 fprintf(1,'\n---------------圆统计----------------\n');
 [r,c]=size(circleParaXYR);%r=size(circleParaXYR,1);
 fprintf(1,'  检测出%d个圆\n',r);%圆的个数
 fprintf(1,'  圆心     半径\n');%圆的个数
 for n=1:r
 fprintf(1,'%d （%d，%d）  %d\n',n,floor(circleParaXYR(n,1)),floor(circleParaXYR(n,2)),floor(circleParaXYR(n,3)));
 end

 %标出圆
 figure(4),imshow(I),title('检测出图中的圆')
 hold on;
  plot(circleParaXYR(:,2), circleParaXYR(:,1), 'r+');
  for k = 1 : size(circleParaXYR, 1)
   t=0:0.01*pi:2*pi;
   x=cos(t).*circleParaXYR(k,3)+circleParaXYR(k,2);y=sin(t).*circleParaXYR(k,3)+circleParaXYR(k,1);
   plot(x,y,'r-');
  end


 R_max=maxr;
 acu=zeros(R_max);
 stor =[];
 for j=1:R_max
   for n=1:r
    if  j == floor(circleParaXYR(n,3))
        acu(j)= acu(j)+1;
    end
   end
    stor=[stor;j,acu(j)];
    %fprintf(1,'%d,%d\n',j,acu(j));
 end

 fprintf(1,'\n------------粒子大小，数目统计---------\n');
 fprintf(1,'粒子半径，粒子个数\n');
 for j=1:R_max
   if acu(j) > 0
    fprintf(1,'%4d %8d\n',stor(j,1),stor(j,2));
   end
 end

 fprintf(1,'----------------------------------------\n');
 figure(5),plot(stor(:,1),stor(:,2),'-k','LineWidth',2),title('粒径谱');
 xlabel('粒子大小');
 ylabel('粒子个数');
 grid on;

 z=[0,10,20,30,40,50,60,70,80,90,11,35,25,42,48,40,20,75,88,94,23,10,20,30,40,78,60,76,84,95,58,10,20,30,40,50,60,70,80,90,100];%给出z的坐标
 Z=z(:);
 S=floor(abs(Z)*1);
 C=floor(abs(Z)*0.5);
 figure(6),scatter3(circleParaXYR(:,1),circleParaXYR(:,2),Z,circleParaXYR(:,3)*7,'filled'),title('构建三维粒子场');

 

 

注：对网上的代码做了改动，使它更能精准检测每个圆的圆心和半径

 2012-5-31