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双边滤波器的原理及实现
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雙邊濾波器是什么？
雙邊濾波（Bilateral filter）是一種可以保邊去噪的濾波器。之所以可以達到此去噪效果，是因為濾波器是由兩個函數構成。一個函數是由幾何空間距離決定濾波器系數。另一個由像素差值決定濾波器系數。可以與其相比較的兩個filter：高斯低通濾波器(http://en.wikipedia.org/wiki/Gaussian_filter)和α-截尾均值濾波器（去掉百分率為α的最小值和最大之后剩下像素的均值作為濾波器），后文中將結合公式做詳細介紹。
雙邊濾波器中，輸出像素的值依賴于鄰域像素的值的加權組合，
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別，而Gaussian Filter和α均值濾波分別只考慮了空間域和值域差別。
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雙邊濾波器的實現（MATLAB）：function B = bfilter2(A,w,sigma)
CopyRight：
% Douglas R. Lanman, Brown University, September 2006.
% dlanman@brown.edu, http://mesh.brown.edu/dlanman
具體請見function B = bfltGray(A,w,sigma_d,sigma_r)函數說明。
[cpp]?view plain
?copy %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].']);???????? 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);?? %創建核距離矩陣，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?? %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));?? ?????????%定義當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));?? 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);??
調用方法：
[cpp]?view plain
?copy 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》
2.?http://de.wikipedia.org/wiki/Bilaterale_Filterung
3.http://www.cs.duke.edu/~tomasi/papers/tomasi/tomasiIccv98.pdf
4.?http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/MANDUCHI1/Bilateral_Filtering.html
5.?http://mesh.brown.edu/dlanman
from:?http://blog.csdn.net/abcjennifer/article/details/7616663
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