图像处理（四）——快速均值滤波（MATLAB实现）

均值滤波是典型的线性滤波算法，它是指在图像上对目标像素给一个模板，该模板包括了其周围的临近像素（以目标像素为中心的周围8个像素，构成一个滤波模板，即去掉目标像素本身），再用模板中的全体像素的平均值来代替原来像素值。

快速均值滤波要求：

在这里就要先解释一下积分图的概念了。


在实现均值滤波的过程中也要特别注意边界问题，以免在处理边界上点的像素值时发生越界。

%边界处理
for v=1:ncols-w
    for i=1:w+1
        for j=0:w
            RR(i,v+j)=Sr(i,v+j)/(i*(v+j));
            GG(i,v+j)=Sg(i,v+j)/(i*(v+j));
            BB(i,v+j)=Sb(i,v+j)/(i*(v+j));            
        end        
    end    
end
for v=1:ncols-w+1
    for i=nrows-w+1:nrows
        for j=0:w-1
            RR(i,v+j)=Sr(i,v+j)/(i*(v+j));
            GG(i,v+j)=Sg(i,v+j)/(i*(v+j));
            BB(i,v+j)=Sb(i,v+j)/(i*(v+j));
        end        
    end    
end
for u=w+2:nrows-w-w
    for i=0:w
        for j=1:w+1
            RR(u+i,j)=Sr(u+i,j)/((u+i)*j);
            GG(u+i,j)=Sg(u+i,j)/((u+i)*j);
            BB(u+i,j)=Sb(u+i,j)/((u+i)*j);
        end
    end
end
for u=w+2:nrows-w-w+1
    for i=0:w-1
        for j=ncols-w+1:ncols
            RR(u+i,j)=Sr(u+i,j)/((u+i)*j);
            GG(u+i,j)=Sg(u+i,j)/((u+i)*j);
            BB(u+i,j)=Sb(u+i,j)/((u+i)*j);
        end
    end
end

最终结果为：

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---

代码自取：

clear;
A1=imread('E:\C++\CVE4\res\img.jpg');
w=str2double(inputdlg('请输入滤波窗口大小', 'INPUT scale factor', 1, {'2'}));
z=(2*w+1)*(2*w+1);
%A2=imnoise(A1,'salt & pepper',0.01);
%A2=rgb2gray(A2);
[nrows,ncols,ncoms]=size(A1);
OUT = uint8(zeros(nrows,ncols,ncoms));%输出图像
if(ncoms==1)
    S=zeros(nrows,ncols);
    S(1,1)=A1(1,1);
    for u=2:nrows
        S(u,1)=S(1,1)+A1(u,1);
    end    
    for u=1:nrows
       for v=2:ncols
         S(u,v)=S(u,v-1)+sum(A1(1:u,v));          
       end
    end
    t=S(3,2)/6;
  for v=1:ncols-w
      for i=1:w+1
        for j=0:w
            OUT(i,v+j)=S(i,v+j)/(i*(v+j));            
        end        
      end    
  end
for v=1:ncols-w+1
    for i=nrows-w+1:nrows
        for j=0:w-1
           OUT(i,v+j)=S(i,v+j)/(i*(v+j));            
        end        
    end    
end
for u=w+2:nrows-w-w
    for i=0:w
        for j=1:w+1
            OUT(u+i,j)=S(u+i,j)/((u+i)*j);            
        end
    end
end
for u=w+2:nrows-w-w+1
    for i=0:w-1
        for j=ncols-w+1:ncols
            OUT(u+i,j)=S(u+i,j)/((u+i)*j);            
        end
    end
end
for u=w+2:nrows-w
    for v=w+2:ncols-w
        OUT(u,v)=(1/z)*(S(u+w,v+w)+S(u-w-1,v-w-1)-S(u+w,v-w-1)-S(u-w-1,v+w));        
    end
end
end
 
 
if(ncoms==3)
R = A1(:,:,1);
G = A1(:,:,2);
B = A1(:,:,3);
%输出图像的RGB分量
RR = uint8(zeros(nrows,ncols));
GG = uint8(zeros(nrows,ncols));
BB = uint8(zeros(nrows,ncols));
%各分量上的积分量
Sr =zeros(nrows,ncols);
Sg =zeros(nrows,ncols);
Sb =zeros(nrows,ncols);
Sr(1,1)=R(1,1);
Sg(1,1)=G(1,1);
Sb(1,1)=B(1,1);
for u=2:nrows
    Sr(u,1)=Sr(u-1,1)+R(u,1);
    Sg(u,1)=Sg(u-1,1)+G(u,1);
    Sb(u,1)=Sb(u-1,1)+B(u,1);
end
for u=1:nrows
    for v=2:ncols
        Sr(u,v)=Sr(u,v-1)+sum(R(1:u,v));
        Sg(u,v)=Sg(u,v-1)+sum(G(1:u,v));
        Sb(u,v)=Sb(u,v-1)+sum(B(1:u,v));        
    end
end
%边界处理
for v=1:ncols-w
    for i=1:w+1
        for j=0:w
            RR(i,v+j)=Sr(i,v+j)/(i*(v+j));
            GG(i,v+j)=Sg(i,v+j)/(i*(v+j));
            BB(i,v+j)=Sb(i,v+j)/(i*(v+j));            
        end        
    end    
end
for v=1:ncols-w+1
    for i=nrows-w+1:nrows
        for j=0:w-1
            RR(i,v+j)=Sr(i,v+j)/(i*(v+j));
            GG(i,v+j)=Sg(i,v+j)/(i*(v+j));
            BB(i,v+j)=Sb(i,v+j)/(i*(v+j));
        end        
    end    
end
for u=w+2:nrows-w-w
    for i=0:w
        for j=1:w+1
            RR(u+i,j)=Sr(u+i,j)/((u+i)*j);
            GG(u+i,j)=Sg(u+i,j)/((u+i)*j);
            BB(u+i,j)=Sb(u+i,j)/((u+i)*j);
        end
    end
end
for u=w+2:nrows-w-w+1
    for i=0:w-1
        for j=ncols-w+1:ncols
            RR(u+i,j)=Sr(u+i,j)/((u+i)*j);
            GG(u+i,j)=Sg(u+i,j)/((u+i)*j);
            BB(u+i,j)=Sb(u+i,j)/((u+i)*j);
        end
    end
end
for u=w+2:nrows-w
    for v=w+2:ncols-w
        RR(u,v)=(1/z)*(Sr(u+w,v+w)+Sr(u-w-1,v-w-1)-Sr(u+w,v-w-1)-Sr(u-w-1,v+w));
        GG(u,v)=(1/z)*(Sg(u+w,v+w)+Sg(u-w-1,v-w-1)-Sg(u+w,v-w-1)-Sg(u-w-1,v+w));
        BB(u,v)=(1/z)*(Sb(u+w,v+w)+Sb(u-w-1,v-w-1)-Sb(u+w,v-w-1)-Sb(u-w-1,v+w));
    end
end
OUT(:,:,1) = RR;
OUT(:,:,2) = GG;
OUT(:,:,3) = BB;
end
imshow(A1),title('原图');
figure;
%imshow(A1),title('加噪声后的图片');
%figure;
imshow(OUT),title('均值滤波后的图片');