例：先用雙邊濾波器（BF）對原圖像進行濾波得到低頻部分，原圖和低頻作差后得到高頻分量，高頻分量和低頻分量分別增強后再進行合成。

雙邊濾波的特點是保邊去噪，相較于高斯濾波，在平滑圖像的同時，增加了對圖像邊緣的保護，其主要原因是由于該濾波器由兩部分組成，一部分與像素空間距離相關，另一部分與像素點的像素差值相關。

下面結合公式來說說為什么雙邊濾波在模糊圖像的時候具有保邊功能，雙邊濾波器公式為：

其中，空間鄰近度因子為

亮度相似度因子為

雙邊濾波器的權重等于空間鄰近度因子和亮度相似度因子的乘積

空間鄰近度因子為高斯濾波器系數，像素距離越遠，權重越小，當越大時，平滑效果越明顯。

亮度相似度因子與空間像素差值相關，像素差值越大，權重越小，這也是為什么雙邊濾波器能夠保邊去噪的原因。當?越大時，對同等灰度差的像素平滑作用越大，保邊效果越差，論文中給出的參考是?一般取高斯噪聲標準差的2倍。

下面列出matlab代碼，這部分代碼既可以處理灰度圖像，也可以處理彩色圖像，代碼下載地址，需要有Mathworks賬號：

https://cn.mathworks.com/matlabcentral/fileexchange/12191-bilateral-filtering

雙邊濾波器

function?B?=?bfilter2(A,w,sigma)???? %A為給定圖像，歸一化到[0,1]的double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)??? %????This?function?implements?2-D?bilateral?filtering?using?? %????the?method?outlined?in:?? %?? %???????C.?Tomasi?and?R.?Manduchi.?Bilateral?Filtering?for??? %???????Gray?and?Color?Images.?In?Proceedings?of?the?IEEE??? %???????International?Conference?on?Computer?Vision,?1998.??? %?? %????B?=?bfilter2(A,W,SIGMA)?performs?2-D?bilateral?filtering?? %????for?the?grayscale?or?color?image?A.?A?should?be?a?double?? %????precision?matrix?of?size?NxMx1?or?NxMx3?(i.e.,?grayscale?? %????or?color?images,?respectively)?with?normalized?values?in?? %????the?closed?interval?[0,1].?The?half-size?of?the?Gaussian?? %????bilateral?filter?window?is?defined?by?W.?The?standard?? %????deviations?of?the?bilateral?filter?are?given?by?SIGMA,?? %????where?the?spatial-domain?standard?deviation?is?given?by?? %????SIGMA(1)?and?the?intensity-domain?standard?deviation?is?? %????given?by?SIGMA(2).?? %?? %?Douglas?R.?Lanman,?Brown?University,?September?2006.?? %?dlanman@brown.edu,?http://mesh.brown.edu/dlanman??%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%?? %?Pre-process?input?and?select?appropriate?filter.??%?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????%計算數組中的元素個數??w?=?5;?? end?? w?=?ceil(w);????%大于w的最小整數??%?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???????%如果輸入圖像為灰度圖像，則調用灰度圖像濾波方法??B?=?bfltGray(A,w,sigma(1),sigma(2));?? else????????????????????%如果輸入圖像為彩色圖像，則調用彩色圖像濾波方法??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.計算過程比較慢，創建waitbar可實時看到進度?? 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);??????%得到輸入圖像的width和height?? 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); ?

主函數：

?

clear?all;?? Image_pri?=?imread('academy.jpg');?? Image_normalized?=?im2double(Image_pri);?? w?=?5;??????%窗口大小?? sigma?=?[3?0.1];????%方差?? Image_bf?=?bfilter2(Image_normalized,w,sigma);?? Image_bfOut?=?uint8(Image_bf*255);?? figure(1);?? subplot(1,2,1);?? imshow(Image_pri);?? subplot(1,2,2);?? imshow(Image_bfOut);??filter_gaussian?=?fspecial('gaussian',[5,5],3);???%生成gaussian空間波波器?? gaussian_image?=?imfilter(Image_pri,filter_gaussian,'replicate');?? figure(2);?? subplot(1,2,1);?? imshow(Image_pri);?? subplot(1,2,2);?? imshow(gaussian_image); ?

?

輸入圖像為512×512的Lena灰度圖像

雙邊濾波

高斯濾波

輸入圖像為512×512的Lena彩色圖像

雙邊濾波

高斯濾波

注意看雙邊濾波圖像，帽子邊緣，模糊的效果很明顯，但皮膚和背景處，仍然比較清晰，說明起到了保邊平滑的作用。

下面給出一些測試結果

輸入圖像為256×256 Einstein灰度圖像

雙邊濾波，濾波后黑色領帶與白色襯衫區域輪廓清晰。

高斯濾波，濾波后圖像整體模糊。

?

輸入圖像為256×256 大沸沸彩色圖像

雙邊濾波

高斯濾波

?

輸入圖像為400×300的彩色圖像

雙邊濾波

高斯濾波

此處代碼運算速度很慢，2007年，麻省理工學院學者提出了快速雙邊濾波算法，并且給出了matlab代碼，下載地址：

http://people.csail.mit.edu/jiawen/#code

?

參考資料：

1.?http://blog.csdn.net/abcjennifer/article/details/7616663

2.?http://blog.csdn.net/bugrunner/article/details/7170471

3. Bilateral Filtering for Gray and Color Images

4. Fast Bilateral Filtering for the Display of High-Dynamic-Range Images ? ? ??

總結

以上是生活随笔為你收集整理的双边滤波器—— Matlab实现的全部內容，希望文章能夠幫你解決所遇到的問題。

如果覺得生活随笔網站內容還不錯，歡迎將生活随笔推薦給好友。