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这个老兄的地址是：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Gaussian Filter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。
- %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-process input and select appropriate filter.
- function B = bfilter2(A,w,sigma)
- % Verify that the input image exists and is valid.
- if ~exist('A','var') || isempty(A)
- error('Input image A is undefined or invalid.');
- end
- if ~isfloat(A) || ~sum([1,3] == size(A,3)) || ...
- min(A(:)) < 0 || max(A(:)) > 1
- error(['Input image A must be a double precision ',...
- 'matrix of size NxMx1 or NxMx3 on the closed ',...
- 'interval [0,1].']);
- end
- % Verify bilateral filter window size.
- if ~exist('w','var') || isempty(w) || ...
- numel(w) ~= 1 || w < 1
- w = 5;
- end
- w = ceil(w);
- % Verify bilateral filter standard deviations.
- if ~exist('sigma','var') || isempty(sigma) || ...
- numel(sigma) ~= 2 || sigma(1) <= 0 || sigma(2) <= 0
- sigma = [3 0.1];
- end
- % Apply either grayscale or color bilateral filtering.
- if size(A,3) == 1
- B = bfltGray(A,w,sigma(1),sigma(2));
- else
- B = bfltColor(A,w,sigma(1),sigma(2));
- end
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- % Implements bilateral filtering for grayscale images.
- function B = bfltGray(A,w,sigma_d,sigma_r)
- % Pre-compute Gaussian distance weights.
- [X,Y] = meshgrid(-w:w,-w:w);
- %创建核距离矩阵，e.g.
- % [x,y]=meshgrid(-1:1,-1:1)
- %
- % x =
- %
- % -1 0 1
- % -1 0 1
- % -1 0 1
- %
- %
- % y =
- %
- % -1 -1 -1
- % 0 0 0
- % 1 1 1
- %计算定义域核
- G = exp(-(X.^2+Y.^2)/(2*sigma_d^2));
- % Create waitbar.
- h = waitbar(0,'Applying bilateral filter...');
- set(h,'Name','Bilateral Filter Progress');
- % Apply bilateral filter.
- %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);
- for i = 1:dim(1)
- for j = 1:dim(2)
- % Extract local region.
- 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
- % Compute Gaussian intensity weights.
- H = exp(-(I-A(i,j)).^2/(2*sigma_r^2));
- % Calculate bilateral filter response.
- 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
- % Close waitbar.
- close(h);
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- % Implements bilateral filter for color images.
- function B = bfltColor(A,w,sigma_d,sigma_r)
- % Convert input sRGB image to CIELab color space.
- if exist('applycform','file')
- A = applycform(A,makecform('srgb2lab'));
- else
- A = colorspace('Lab<-RGB',A);
- end
- % Pre-compute Gaussian domain weights.
- [X,Y] = meshgrid(-w:w,-w:w);
- G = exp(-(X.^2+Y.^2)/(2*sigma_d^2));
- % Rescale range variance (using maximum luminance).
- sigma_r = 100*sigma_r;
- % Create waitbar.
- h = waitbar(0,'Applying bilateral filter...');
- set(h,'Name','Bilateral Filter Progress');
- % Apply bilateral filter.
- dim = size(A);
- B = zeros(dim);
- for i = 1:dim(1)
- for j = 1:dim(2)
- % Extract local region.
- 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,:);
- % Compute Gaussian range weights.
- 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));
- % Calculate bilateral filter response.
- 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
- % Convert filtered image back to sRGB color space.
- if exist('applycform','file')
- B = applycform(B,makecform('lab2srgb'));
- else
- B = colorspace('RGB<-Lab',B);
- end
- % Close waitbar.
- close(h);
调用方法：
- I=imread('einstein.jpg');
- I=double(I)/255;
- w = 5; % bilateral filter half-width
- sigma = [3 0.1]; % bilateral filter standard deviations
- 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 and Applications》
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