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.');
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) 
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);
end
close(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
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
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);
endimg = 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：
