双边滤波matlab代码

%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.');endif ~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;endw = 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Fdim = 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-widthsigma = [3 0.1]; % bilateral filter standard deviationsI1=bfilter2(I,w,sigma);subplot(1,2,1);imshow(I);subplot(1,2,2);imshow(I1)

实验结果：

第二种实现

　双边滤波模板主要有两个模板生成，第一个是高斯模板，第二个是以灰度级的差值作为函数系数生成的模板。然后这两个模板点乘就得到了最终的双边滤波模板。

　　第一个模板是全局模板，所以只需要生成一次。第二个模板需要对每个像素都计算一次，所以需要放到循环的里面来生成，这很像表面模糊啊。哦，表面模糊就是用了一个截尾滤波器。

　　这里的公式我参考了这里，不过她给的第二个好像不是截尾均值滤波器，而是以灰度差值为自变量的高斯滤波器。截尾均值滤波器这里有一些理论和实现，

代码如下：

clear all;close all;clc;img=imread('lena.jpg');img=mat2gray(img);[m n]=size(img);imshow(img);r=10;        %模板半径imgn=zeros(m+2*r+1,n+2*r+1);imgn(r+1:m+r,r+1:n+r)=img;imgn(1:r,r+1:n+r)=img(1:r,1:n);                 %扩展上边界imgn(1:m+r,n+r+1:n+2*r+1)=imgn(1:m+r,n:n+r);    %扩展右边界imgn(m+r+1:m+2*r+1,r+1:n+2*r+1)=imgn(m:m+r,r+1:n+2*r+1);    %扩展下边界imgn(1:m+2*r+1,1:r)=imgn(1:m+2*r+1,r+1:2*r);       %扩展左边界sigma_d=2;sigma_r=0.1;[x,y] = meshgrid(-r:r,-r:r);w1=exp(-(x.^2+y.^2)/(2*sigma_d^2));     %以距离作为自变量高斯滤波器h=waitbar(0,'wait...');for i=r+1:m+r    for j=r+1:n+r                w2=exp(-(imgn(i-r:i+r,j-r:j+r)-imgn(i,j)).^2/(2*sigma_r^2)); %以周围和当前像素灰度差值作为自变量的高斯滤波器        w=w1.*w2;                s=imgn(i-r:i+r,j-r:j+r).*w;        imgn(i,j)=sum(sum(s))/sum(sum(w));        end    waitbar(i/m);endclose(h)figure;imshow(mat2gray(imgn(r+1:m+r,r+1:n+r)));

第三种实现

双边滤波与一般的高斯滤波的不同就是：双边滤波既利用了位置信息<or 几何信息——高斯滤波只用了位置信息>又利用了像素信息来定义滤波窗口的权重。

像素值越接近，权重越大。双边滤波会去除图像的细节信息，又能保持边界。

对于彩色图像，像素值的接近与否不能使用RGB空间值，双边滤波的原始文献建议使用CIE颜色空间。

代码如下：

function resultI = BilateralFilt2(I,d,sigma)%%%%Author：LiFeiteng%Version：1.0——灰色图像  Time：2013/05/01%Version：1.1——灰色/彩色图像  Time：2013/05/02  2013/05/05%d 半窗口宽度I = double(I);if size(I,3)==1    resultI = BilateralFiltGray(I,d,sigma);elseif size(I,3)==3    resultI = BilateralFiltColor(I,d,sigma);else     error('Incorrect image size')    endendfunction resultI = BilateralFiltGray(I,d,sigma)[m n] = size(I);newI = ReflectEdge(I,d);resultI = zeros(m,n);width = 2*d+1;%DistanceD = fspecial('gaussian',[width,width],sigma(1));S = zeros(width,width);%pix Similarityh = waitbar(0,'Applying bilateral filter...');set(h,'Name','Bilateral Filter Progress');for i=1+d:m+d    for j=1+d:n+d        pixValue = newI(i-d:i+d,j-d:j+d);        subValue = pixValue-newI(i,j);        S = exp(-subValue.^2/(2*sigma(2)^2));        H = S.*D;        resultI(i-d,j-d) = sum(pixValue(:).*H(:))/sum(H(:));     end    waitbar(i/m);endclose(h);endfunction resultI = BilateralFiltColor(I,d,sigma)I = applycform(I,makecform('srgb2lab'));[m n ~] = size(I);newI = ReflectEdge(I,d);resultI = zeros(m,n,3);width = 2*d+1;%DistanceD = fspecial('gaussian',[width,width],sigma(1));% [X,Y] = meshgrid(-d:d,-d:d);% D = exp(-(X.^2+Y.^2)/(2*sigma(1)^2));S = zeros(width,width);%pix Similarityh = waitbar(0,'Applying bilateral filter...');set(h,'Name','Bilateral Filter Progress');sigma_r = 100*sigma(2);for i=1+d:m+d    for j=1+d:n+d        pixValue = newI(i-d:i+d,j-d:j+d,1:3);        %subValue = pixValue-repmat(newI(i,j,1:3),width,width);        dL = pixValue(:,:,1)-newI(i,j,1);        da = pixValue(:,:,2)-newI(i,j,2);        db = pixValue(:,:,3)-newI(i,j,3);        S = exp(-(dL.^2+da.^2+db.^2)/(2*sigma_r^2));        H = S.*D;        H = H./sum(H(:));        resultI(i-d,j-d,1) = sum(sum(pixValue(:,:,1).*H));         resultI(i-d,j-d,2) = sum(sum(pixValue(:,:,2).*H));            resultI(i-d,j-d,3) = sum(sum(pixValue(:,:,3).*H));        end    waitbar(i/m);endclose(h);resultI = applycform(resultI,makecform('lab2srgb'));end

其中newI = ReflectEdge(I,d); %对称地扩展边界，在原始图像I的边界处镜像映射像素值 

function newI = ReflectEdge(I,d)%Version：1.0——灰色图像  Time：2013/05/01%Version：1.1——灰色/彩色图像  Time：2013/05/02%考虑到实用性，决定不添加更多的边界处理选择，统一使用：reflect across edgeif size(I,3)==1    newI = ReflectEdgeGray(I,d);elseif size(I,3)==3    newI = ReflectEdgeColor(I,d);else     error('Incorrect image size')    endendfunction newI = ReflectEdgeGray(I,d)[m n] = size(I);newI = zeros(m+2*d,n+2*d);%中间部分newI(d+1:d+m,d+1:d+n) = I;%上newI(1:d,d+1:d+n) = I(d:-1:1,:);%下newI(end-d:end,d+1:d+n) = I(end:-1:end-d,:);%左newI(:,1:d) = newI(:,2*d:-1:d+1);%右newI(:,m+d+1:m+2*d) = newI(:,m+d:-1:m+1);endfunction newI = ReflectEdgeColor(I,d)%扩展图像边界[m n ~] = size(I);newI = zeros(m+2*d,n+2*d,3);%中间部分newI(d+1:d+m,d+1:d+n,1:3) = I;%上newI(1:d,d+1:d+n,1:3) = I(d:-1:1,:,1:3);%下newI(end-d:end,d+1:d+n,1:3) = I(end:-1:end-d,:,1:3);%左newI(:,1:d,1:3) = newI(:,2*d:-1:d+1,1:3);%右newI(:,m+d+1:m+2*d,1:3) = newI(:,m+d:-1:m+1,1:3);end

测试用例：

img = imread('.\lena.tif');%%img = imread('.\images\lena_gray.tif');img = double(img)/255;img = img+0.05*randn(size(img));img(img<0) = 0; img(img>1) = 1;%img = imnoise(img,'gaussian');figure, imshow(img,[])title('原始图像')d = 6;sigma = [3 0.1];resultI = BilateralFilt2(double(img), d, sigma);figure, imshow(resultI,[])title('双边滤波后的图像')

结果：