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雙邊濾波器是什麼？
雙邊濾波器中，輸出像素的值依賴于鄰域像素的值的權重組合，
權重系數w(i,j,k,l)取決于定義域核
和值域核
的乘積
同時考慮了空間域與值域的差别，而Gaussian Filter和α均值濾波分别隻考慮了空間域和值域差别。
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雙邊濾波器的實作（MATLAB）：function B = bfilter2(A,w,sigma)
CopyRight：
% Douglas R. Lanman, Brown University, September 2006.
% [email protected], http://mesh.brown.edu/dlanman
具體請見function B = bfltGray(A,w,sigma_d,sigma_r)函數說明。
%簡單地說:
%A為給定圖像，歸一化到[0,1]的矩陣
%W為雙邊濾波器（核）的邊長/2
%定義域方差σd記為SIGMA(1),值域方差σr記為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].']);
% Verify bilateral filter window size.
if ~exist('w','var') || isempty(w) || ...
numel(w) ~= 1 || w < 1
w = 5;
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];
% 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));
% 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);
%建立核距離矩陣，e.g.
% [x,y]=meshgrid(-1:1,-1:1)
%
% x =
% -1 0 1
% y =
% -1 -1 -1
% 0 0 0
% 1 1 1
%計算定義域核
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.
%計算值域核H 并與定義域核G 乘積得到雙邊權重函數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));
%定義目前核所作用的區域為(iMin:iMax,jMin:jMax)
I = A(iMin:iMax,jMin:jMax);%提取該區域的源圖像值賦給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));
% 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'));
A = colorspace('Lab<-RGB',A);
% Pre-compute Gaussian domain weights.
% Rescale range variance (using maximum luminance).
sigma_r = 100*sigma_r;
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));
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;
% Convert filtered image back to sRGB color space.
B = applycform(B,makecform('lab2srgb'));
else
B = colorspace('RGB<-Lab',B);
調用方法：
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)
實驗結果：
參考資料：
1.《Computer Vision Algorithms and Applications》
5. http://mesh.brown.edu/dlanman