双边滤波Matlab实现

原文：http://blog.csdn.net/lifeitengup/article/details/8902326#comments

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')
 end
 end

 function resultI = BilateralFiltGray(I,d,sigma)

 [m n] = size(I);
 newI = ReflectEdge(I,d);
 resultI = zeros(m,n);
 width = 2*d+1;
 %Distance
 D = fspecial('gaussian',[width,width],sigma(1));
 S = zeros(width,width);%pix Similarity
 h = 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);
 end
 close(h);
 end

 function 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;
 %Distance
 D = 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 Similarity
 h = 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);
 end
 close(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 edge

 if size(I,3)==1
     newI = ReflectEdgeGray(I,d);
 elseif size(I,3)==3
     newI = ReflectEdgeColor(I,d);
 else
     error('Incorrect image size')
 end
 end

 function 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(:,n+d+1:n+2*d) = newI(:,n+d:-1:n+1);
 end

 function 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(:,n+d+1:n+2*d,1:3) = newI(:,n+d:-1:n+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：

Reference：

1.C Tomasi, R Manduchi.Bilateral Filtering for Gray and Color Images, - Computer Vision, 1998.

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')
 end
 end

 function resultI = BilateralFiltGray(I,d,sigma)

 [m n] = size(I);
 newI = ReflectEdge(I,d);
 resultI = zeros(m,n);
 width = 2*d+1;
 %Distance
 D = fspecial('gaussian',[width,width],sigma(1));
 S = zeros(width,width);%pix Similarity
 h = 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);
 end
 close(h);
 end

 function 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;
 %Distance
 D = 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 Similarity
 h = 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);
 end
 close(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 edge

 if size(I,3)==1
     newI = ReflectEdgeGray(I,d);
 elseif size(I,3)==3
     newI = ReflectEdgeColor(I,d);
 else
     error('Incorrect image size')
 end
 end

 function 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);
 end

 function 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：

Reference：

1.C Tomasi, R Manduchi.Bilateral Filtering for Gray and Color Images, - Computer Vision, 1998.