爱华网wiki： http://zh.wikipedia.org/wiki/雙邊濾波器
以下为转载（http://blog.csdn.net/abcjennifer/article/details/7616663）：
双边滤波器是什么？
双边滤波（Bilateral filter）是一种可以保边去噪的滤波器。之所以可以达到此去噪效果，是因为滤波器是由两个函数构成。一个函数是由几何空间距离决定滤波器系数。另一个由像素差值决定滤波器系数。可以与其相比较的两个filter：高斯低通滤波器(http://en.wikipedia.org/wiki/Gaussian_filter)和α-截尾均值滤波器（去掉百分率为α的最小值和最大之后剩下像素的均值作为滤波器），后文中将结合公式做详细介绍。
双边滤波器中，输出像素的值依赖于邻域像素的值的加权组合，
权重系数w(i,j,k,l)取决于定义域核
和值域核
的乘积
同时考虑了空间域与值域的差别，而GaussianFilter和α均值滤波分别只考虑了空间域和值域差别。
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双边滤波器的实现（MATLAB）：function B =bfilter2(A,w,sigma)
CopyRight：
% Douglas R. Lanman, Brown University,September 2006.
% dlanman@brown.edu,http://mesh.brown.edu/dlanman
具体请见function B =bfltGray(A,w,sigma_d,sigma_r)函数说明。
[cpp]viewplaincopy- %简单地说:
- %A为给定图像，归一化到[0,1]的矩阵
- %W为双边滤波器（核）的边长/2
- %定义域方差σd记为SIGMA(1),值域方差σr记为SIGMA(2)
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- %Pre-processinputandselectappropriatefilter.
- functionB=bfilter2(A,w,sigma)
- %Verifythattheinputimageexistsandisvalid.
- if~exist('A','var')||isempty(A)
- error('InputimageAisundefinedorinvalid.');
- end
- if~isfloat(A)||~sum([1,3]==size(A,3))||...
- min(A(:))<0||max(A(:))>1
- error(['InputimageAmustbeadoubleprecision',...
- 'matrixofsizeNxMx1orNxMx3ontheclosed',...
- 'interval[0,1].']);
- end
- %Verifybilateralfilterwindowsize.
- if~exist('w','var')||isempty(w)||...
- numel(w)~=1||w<1
- w=5;
- end
- w=ceil(w);
- %Verifybilateralfilterstandarddeviations.
- if~exist('sigma','var')||isempty(sigma)||...
- numel(sigma)~=2||sigma(1)<=0||sigma(2)<=0
- sigma=[30.1];
- end
- %Applyeithergrayscaleorcolorbilateralfiltering.
- ifsize(A,3)==1
- B=bfltGray(A,w,sigma(1),sigma(2));
- else
- B=bfltColor(A,w,sigma(1),sigma(2));
- end
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- %Implementsbilateralfilteringforgrayscaleimages.
- functionB=bfltGray(A,w,sigma_d,sigma_r)
- %Pre-computeGaussiandistanceweights.
- [X,Y]=meshgrid(-w:w,-w:w);
- %创建核距离矩阵，e.g.
- %[x,y]=meshgrid(-1:1,-1:1)
- %
- %x=
- %
- %-101
- %-101
- %-101
- %
- %
- %y=
- %
- %-1-1-1
- %000
- %111
- %计算定义域核
- G=exp(-(X.^2+Y.^2)/(2*sigma_d^2));
- %Createwaitbar.
- h=waitbar(0,'Applyingbilateralfilter...');
- set(h,'Name','BilateralFilterProgress');
- %Applybilateralfilter.
- %计算值域核H并与定义域核G乘积得到双边权重函数F
- dim=size(A);
- B=zeros(dim);
- fori=1:dim(1)
- forj=1:dim(2)
- %Extractlocalregion.
- iMin=max(i-w,1);
- iMax=min(i+w,dim(1));
- jMin=max(j-w,1);
- jMax=min(j+w,dim(2));
- %定义当前核所作用的区域为(iMin:iMax,jMin:jMax)
- I=A(iMin:iMax,jMin:jMax);%提取该区域的源图像值赋给I
- %ComputeGaussianintensityweights.
- H=exp(-(I-A(i,j)).^2/(2*sigma_r^2));
- %Calculatebilateralfilterresponse.
- F=H.*G((iMin:iMax)-i+w+1,(jMin:jMax)-j+w+1);
- B(i,j)=sum(F(:).*I(:))/sum(F(:));
- end
- waitbar(i/dim(1));
- end
- %Closewaitbar.
- close(h);
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- %Implementsbilateralfilterforcolorimages.
- functionB=bfltColor(A,w,sigma_d,sigma_r)
- %ConvertinputsRGBimagetoCIELabcolorspace.
- ifexist('applycform','file')
- A=applycform(A,makecform('srgb2lab'));
- else
- A=colorspace('Lab<-RGB',A);
- end
- %Pre-computeGaussiandomainweights.
- [X,Y]=meshgrid(-w:w,-w:w);
- G=exp(-(X.^2+Y.^2)/(2*sigma_d^2));
- %Rescalerangevariance(usingmaximumluminance).
- sigma_r=100*sigma_r;
- %Createwaitbar.
- h=waitbar(0,'Applyingbilateralfilter...');
- set(h,'Name','BilateralFilterProgress');
- %Applybilateralfilter.
- dim=size(A);
- B=zeros(dim);
- fori=1:dim(1)
- forj=1:dim(2)
- %Extractlocalregion.
- iMin=max(i-w,1);
- iMax=min(i+w,dim(1));
- jMin=max(j-w,1);
- jMax=min(j+w,dim(2));
- I=A(iMin:iMax,jMin:jMax,:);
- %ComputeGaussianrangeweights.
- dL=I(:,:,1)-A(i,j,1);
- da=I(:,:,2)-A(i,j,2);
- db=I(:,:,3)-A(i,j,3);
- H=exp(-(dL.^2+da.^2+db.^2)/(2*sigma_r^2));
- %Calculatebilateralfilterresponse.
- F=H.*G((iMin:iMax)-i+w+1,(jMin:jMax)-j+w+1);
- norm_F=sum(F(:));
- B(i,j,1)=sum(sum(F.*I(:,:,1)))/norm_F;
- B(i,j,2)=sum(sum(F.*I(:,:,2)))/norm_F;
- B(i,j,3)=sum(sum(F.*I(:,:,3)))/norm_F;
- end
- waitbar(i/dim(1));
- end
- %ConvertfilteredimagebacktosRGBcolorspace.
- ifexist('applycform','file')
- B=applycform(B,makecform('lab2srgb'));
- else
- B=colorspace('RGB<-Lab',B);
- end
- %Closewaitbar.
- close(h);
调用方法：
[cpp]viewplaincopy- I=imread('einstein.jpg');
- I=double(I)/255;
- w=5;%bilateralfilterhalf-width
- sigma=[30.1];%bilateralfilterstandarddeviations
- I1=bfilter2(I,w,sigma);
- subplot(1,2,1);
- imshow(I);
- subplot(1,2,2);
- imshow(I1)
实验结果：
参考资料：
1.《Computer Vision Algorithms andApplications》
2.http://de.wikipedia.org/wiki/Bilaterale_Filterung
3.http://www.cs.duke.edu/~tomasi/papers/tomasi/tomasiIccv98.pdf
4.http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/MANDUCHI1/Bilateral_Filtering.html
5.http://mesh.brown.edu/dlanman
