【MATLAB图像处理3】 canny边缘检测 （附源码）

canny边缘检测，相对于sobel是较为复杂的一种检测算法，也是迄今为止最优秀的一种边缘检测算法，但是不可否认，它也带来了大量的运算。

 

canny分四步：

1.对灰度图进行高斯滤波  （很简单）

2.. 求出梯度的幅值图像和角度图像（一般用sobel求，简单）

3.对梯度幅值图形进行非最大值抑制，并进行双阈值处理。（难）

4.连接分析来检测并连接边缘。（很难）

 

 

1、高斯滤波。

使用二维高斯公式，产生高斯滤波模版。公式就不写，源码里会有。然后用模版和图像进行卷积。这一步很简单，就不多说了

 

2、求梯度的赋值和角度

用sobel算子，x方向为[-1,-2,-1;               y方向的算子为x方向的转置。然后分别用这两个算子和图像做卷积。然后用公式 A=sqrt(x.^2+y.^2)就是梯度幅值图了。

                                            0, 0, 0

                                            1, 2, 1 ]

 

然后是求角度，没一点的角度为arctan[y/x],求出梯度角度图；

 

3、利用求出的梯度角度图，把各个梯度分别划分到水平，垂直，45°，-45°，四个方向上。然后把赋值图按所划分的四个方向，分别同邻近的两个点比较，若为最大值则保留，若不是，则变为0；这样就得到非最大值抑制图，然后设置一个大阈值和一个小阈值，再用小阈值图减去大阈值图。得到阈值图。

 

4、在大阈值图中定位下一个非0像素P；在小阈值图中用8连通的方式，连接到P，如此递归，连接所有连线。

 

下面是源码

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%函数功能：canny边缘检测%%%%%%%%%%%%%%%%%%%%%
%%作者：张小胖疯了%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%时间：2013.9.28%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all;close all; clc;
src=imread('D:\Documents\Desktop\lenna.JPG');  %读入图形
[m,n,q]=size(src);
src_gray=my_gray(src);                         %变为灰度图

src_gaussion=my_gaussian(src_gray,3,9);         %高斯滤波

[src_sobel,src_sobel_x,src_sobel_y]=my_sobel(src_gaussion);   %%%%%%%sobel梯度检测
figure(1);
imshow(src_sobel);

%%%%%%%%%%%%%%把梯度划分为4个方向%%%%%%%%%%%%%%%%%%%%%%%
 new_angel_img=zeros(m,n);
for i=1:m
    for j=1:n
        Mx=src_sobel_x(i,j);
        My=src_sobel_y(i,j);

        if My~=0
            o=atan(Mx/My);      %边缘的法线弧度
        elseif My==0 && Mx>0
            o=pi/2;
        else
            o=-pi/2;
        end

        if( ( o>=( -22.5/180*pi ) && o<( 22.5/180*pi ) ) || ( o>=( 157.5/180*pi ) && o<=pi ) || ( o<=( -157.5/180*pi ) && o>=-pi ) )
            d1=0;
        elseif (  ( o>= ( 22.5/180*pi ) && o<( 67.5/180*pi ) ) ||  (   o>=( -157.5/180*pi ) && o<(-112.5/180*pi )  )   )
            d1=-45;
        elseif ( ( o>=(67.5/180*pi) && o<(112.5/180*pi) ) || ( o>=(-112.5/180*pi) && o<-67.5/180*pi ) )
            d1=90;
        else
            d1=45;
         end
            new_angel_img(i,j)=d1;
    end
end


canny_dst=src_sobel;
%%%%%%%%%%%%%%%%%%非最大值抑制%%%%%%%%%%%%%%%%%%%%%%%5
for i=3:m-2
    for j=3:n-2
        if( new_angel_img(i,j)==0 )
            A=[canny_dst(i-1,j),canny_dst(i+1,j)];
            if( abs(canny_dst(i,j))< max( abs(A) ) )
                canny_dst(i,j)=0;
            end
        elseif( new_angel_img(i,j)==-45 )
            A=[canny_dst(i-1,j-1),canny_dst(i+1,j+1)];
            if( abs(canny_dst(i,j))< max( abs(A) ))
                canny_dst(i,j)=0;
            end
        elseif( new_angel_img(i,j)==90 )
            A=[canny_dst(i,j-1),canny_dst(i,j+1)];
            if( abs(canny_dst(i,j))< max( abs(A) ) )
                canny_dst(i,j)=0;
            end
        elseif( new_angel_img(i,j)==45 )
            A=[canny_dst(i-1,j+1),canny_dst(i+1,j-1)];
            if( abs(canny_dst(i,j))< max( abs(A) ) )
               canny_dst(i,j)=0;
            end
        end
    end
end

figure(2);
imshow(canny_dst);

gh=zeros(m,n);
gl=zeros(m,n);
gl1=zeros(m,n);
for i=1:m
   for j=1:n
       if( canny_dst(i,j)>=100 )
            gh(i,j)=1;
        else
          gh(i,j)=0;
      end
        if( canny_dst(i,j)>=30)
           gl(i,j)=1;
        else
           gl(i,j)=0;
       end
  end
end
gl1=gl;
gl1=logical(gl1);
gh=logical(gh);
figure(3);
imshow(gl1);


figure(4);
imshow(gh);
%%%%%%%%%%%%%%%%%%%%%%%%递归连接%%%%%%%%%%%%%%%%%%%
up=100;     %上阈值
low=33;    %下阈值
set(0,'RecursionLimit',10000);  %设置最大递归深度
for i=1:m
    for j=1:n
      if canny_dst(i,j)>up &&canny_dst(i,j)~=255  %判断上阈值
            canny_dst(i,j)=255;
            canny_dst=connect(canny_dst,i,j,low);
      end
    end
end
figure(5);
imshow(canny_dst==255);

 BW2 = edge(src_gaussion,'canny');
figure(6);
imshow(BW2);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%函数功能：canny边缘检测%%%%%%%%%%%%%%%%%%%%%
%%作者：张小胖疯了%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%时间：2013.9.28%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all;close all; clc;
src=imread('D:\Documents\Desktop\lenna.JPG');  %读入图形
[m,n,q]=size(src);
src_gray=my_gray(src);                         %变为灰度图

src_gaussion=my_gaussian(src_gray,3,9);         %高斯滤波

[src_sobel,src_sobel_x,src_sobel_y]=my_sobel(src_gaussion);   %%%%%%%sobel梯度检测
figure(1);
imshow(src_sobel);

%%%%%%%%%%%%%%把梯度划分为4个方向%%%%%%%%%%%%%%%%%%%%%%%
 new_angel_img=zeros(m,n);                              
for i=1:m
    for j=1:n
        Mx=src_sobel_x(i,j);
        My=src_sobel_y(i,j);
        
        if My~=0
            o=atan(Mx/My);      %边缘的法线弧度
        elseif My==0 && Mx>0
            o=pi/2;
        else
            o=-pi/2;            
        end
        
        if( ( o>=( -22.5/180*pi ) && o<( 22.5/180*pi ) ) || ( o>=( 157.5/180*pi ) && o<=pi ) || ( o<=( -157.5/180*pi ) && o>=-pi ) )
            d1=0;
        elseif (  ( o>= ( 22.5/180*pi ) && o<( 67.5/180*pi ) ) ||  (   o>=( -157.5/180*pi ) && o<(-112.5/180*pi )  )   )
            d1=-45;
        elseif ( ( o>=(67.5/180*pi) && o<(112.5/180*pi) ) || ( o>=(-112.5/180*pi) && o<-67.5/180*pi ) )   
            d1=90;
        else      
            d1=45;
         end
            new_angel_img(i,j)=d1;
    end
end


canny_dst=src_sobel;
%%%%%%%%%%%%%%%%%%非最大值抑制%%%%%%%%%%%%%%%%%%%%%%%5
for i=3:m-2
    for j=3:n-2
        if( new_angel_img(i,j)==0 )
            A=[canny_dst(i-1,j),canny_dst(i+1,j)];
            if( abs(canny_dst(i,j))< max( abs(A) ) )
                canny_dst(i,j)=0;
            end
        elseif( new_angel_img(i,j)==-45 )
            A=[canny_dst(i-1,j-1),canny_dst(i+1,j+1)];
            if( abs(canny_dst(i,j))< max( abs(A) ))
                canny_dst(i,j)=0;
            end
        elseif( new_angel_img(i,j)==90 )
            A=[canny_dst(i,j-1),canny_dst(i,j+1)];
            if( abs(canny_dst(i,j))< max( abs(A) ) )
                canny_dst(i,j)=0;
            end            
        elseif( new_angel_img(i,j)==45 )
            A=[canny_dst(i-1,j+1),canny_dst(i+1,j-1)];
            if( abs(canny_dst(i,j))< max( abs(A) ) )
               canny_dst(i,j)=0;
            end  
        end
    end
end

figure(2);
imshow(canny_dst);

gh=zeros(m,n);
gl=zeros(m,n);
gl1=zeros(m,n);
for i=1:m
   for j=1:n
       if( canny_dst(i,j)>=100 )
            gh(i,j)=1;
        else
          gh(i,j)=0;
      end
        if( canny_dst(i,j)>=30)
           gl(i,j)=1;
        else
           gl(i,j)=0;
       end
  end
end
gl1=gl;
gl1=logical(gl1);
gh=logical(gh);
figure(3);
imshow(gl1);


figure(4);
imshow(gh);
%%%%%%%%%%%%%%%%%%%%%%%%递归连接%%%%%%%%%%%%%%%%%%%
up=100;     %上阈值
low=33;    %下阈值
set(0,'RecursionLimit',10000);  %设置最大递归深度
for i=1:m
    for j=1:n
      if canny_dst(i,j)>up &&canny_dst(i,j)~=255  %判断上阈值
            canny_dst(i,j)=255;
            canny_dst=connect(canny_dst,i,j,low);
      end
    end
end
figure(5);
imshow(canny_dst==255);

 BW2 = edge(src_gaussion,'canny');
figure(6);
imshow(BW2);

%%%%%%%%高斯滤波函数%%%%%%%%%%%%%%%%%%%%%%

 

function d=my_gaussian(src,n,k)

n1=(n+1)/2;                                         %%%%%%%%%%%%%计算高斯滤波模版中心
[m,l]=size(src);
b=zeros(n,n);                                       %%%%%%%%%%%%%空模版
I=zeros(m,l);
d=zeros(m,l);
img=zeros(m,l);
%%%%%%%%%%%%%%%%%计算高斯滤波模版的各个系数
for i=1:n
    for j=1:n
          b(i,j)=(exp(-((i-n1)^2 +(j-n1)^2)/(2*k)))/(2*pi*k);
    end
end

b = b/sum(b(:));   %%%%%%%%%%%%%%%%%%%%%%对系数进行归一化 （这个地方必须归一化，不然整体灰度会底）
I=double(src);
img=conv2(I,b,'same');                %%%%%%%%%%%%图像与高斯滤波模版卷积，输出与输入图像大小相同的图像
d=uint8(img);                             %%%%%%%%%%转为无符号整型，用来显示

end

function d=my_gaussian(src,n,k)

n1=(n+1)/2;                                         %%%%%%%%%%%%%计算高斯滤波模版中心
[m,l]=size(src);
b=zeros(n,n);                                       %%%%%%%%%%%%%空模版  
I=zeros(m,l);
d=zeros(m,l);
img=zeros(m,l);
%%%%%%%%%%%%%%%%%计算高斯滤波模版的各个系数
for i=1:n
    for j=1:n
          b(i,j)=(exp(-((i-n1)^2 +(j-n1)^2)/(2*k)))/(2*pi*k);
    end
end

b = b/sum(b(:));   %%%%%%%%%%%%%%%%%%%%%%对系数进行归一化 （这个地方必须归一化，不然整体灰度会底）    
I=double(src);
img=conv2(I,b,'same');                %%%%%%%%%%%%图像与高斯滤波模版卷积，输出与输入图像大小相同的图像
d=uint8(img);                             %%%%%%%%%%转为无符号整型，用来显示

end

 

%%%%%%%%%%%%%%递归连接%%%%%%%%%%%%%%

function nedge=connect(nedge,y,x,low)       %种子定位后的连通分析
    neighbour=[-1 -1;-1 0;-1 1;0 -1;0 1;1 -1;1 0;1 1];  %八连通搜寻
    [m n]=size(nedge);
    for k=1:8
        yy=y+neighbour(k,1);
        xx=x+neighbour(k,2);
        if yy>=1 &&yy<=m &&xx>=1 && xx<=n
            if nedge(yy,xx)>=low && nedge(yy,xx)~=255   %判断下阈值
                nedge(yy,xx)=255;
                nedge=connect(nedge,yy,xx,low);
            end
        end
    end

end

function nedge=connect(nedge,y,x,low)       %种子定位后的连通分析
    neighbour=[-1 -1;-1 0;-1 1;0 -1;0 1;1 -1;1 0;1 1];  %八连通搜寻
    [m n]=size(nedge);
    for k=1:8
        yy=y+neighbour(k,1);
        xx=x+neighbour(k,2);
        if yy>=1 &&yy<=m &&xx>=1 && xx<=n  
            if nedge(yy,xx)>=low && nedge(yy,xx)~=255   %判断下阈值
                nedge(yy,xx)=255;
                nedge=connect(nedge,yy,xx,low);
            end
        end        
    end 

end

原图：

 

 梯度赋值图：

 

非最大值抑制图：

 

 

阈值化后：

 

连接后：

 

MATLAB自带函数效果：

 

 

很明显自己写的函数跟MATLAB有很大差距，差距主要在非最大值抑制时的细化，和最后的连接。

还有努力啊。