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<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')
 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<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')
 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.