双边滤波Matlab实现<The Bilateral Filter>

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.