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域滤波：方框、高斯、中值、双边滤波
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鄰域?yàn)V波（卷積）
鄰域算子值利用給定像素周?chē)袼氐闹禌Q定此像素的最終輸出。如圖左邊圖像與中間圖像卷積禪城右邊圖像。目標(biāo)圖像中綠色的像素由原圖像中藍(lán)色標(biāo)記的像素計(jì)算得到。
通用線性鄰域?yàn)V波是一種常用的鄰域算子，輸入像素加權(quán)得到輸出像素：
其中權(quán)重核???為“濾波系數(shù)
【方框?yàn)V波】
最簡(jiǎn)單的線性濾波是移動(dòng)平均或方框?yàn)V波，用?窗口中的像素值平均后輸出，核函數(shù)為：
其實(shí)等價(jià)于圖像與全部元素值為1的核函數(shù)進(jìn)行卷積再進(jìn)行尺度縮放。
代碼
OpenCV中的 blur函數(shù)是進(jìn)行標(biāo)準(zhǔn)方框?yàn)V波：
[cpp] ?view plaincopy
void ?cv::blur(?InputArray?src,?OutputArray?dst,?? ???????????Size?ksize,?Point?anchor,?int ?borderType?)?? {?? ????boxFilter(?src,?dst,?-1,?ksize,?anchor,?true ,?borderType?);?? }?? 而boxFilter函數(shù)源碼如下：
[cpp] ?view plaincopy
cv::Ptr<cv::FilterEngine>?cv::createBoxFilter(? int ?srcType,? int ?dstType,?Size?ksize,?? ????????????????????Point?anchor,?bool ?normalize,? int ?borderType?)?? {?? ????int ?sdepth?=?CV_MAT_DEPTH(srcType);?? ????int ?cn?=?CV_MAT_CN(srcType),?sumType?=?CV_64F;?? ????if (?sdepth?<=?CV_32S?&&?(!normalize?||?? ????????ksize.width*ksize.height?<=?(sdepth?==?CV_8U???(1<<23)?:?? ????????????sdepth?==?CV_16U???(1?<<?15)?:?(1?<<?16)))?)?? ????????sumType?=?CV_32S;?? ????sumType?=?CV_MAKETYPE(?sumType,?cn?);?? ?? ????Ptr<BaseRowFilter>?rowFilter?=?getRowSumFilter(srcType,?sumType,?ksize.width,?anchor.x?);?? ????Ptr<BaseColumnFilter>?columnFilter?=?getColumnSumFilter(sumType,?? ????????dstType,?ksize.height,?anchor.y,?normalize???1./(ksize.width*ksize.height)?:?1);?? ?? ????return ?Ptr<FilterEngine>( new ?FilterEngine(Ptr<BaseFilter>(0),?rowFilter,?columnFilter,?? ???????????srcType,?dstType,?sumType,?borderType?));?? }?? 這里 blur 和 boxFilter 的區(qū)別是，blur是標(biāo)準(zhǔn)化后的 boxFilter，即boxFilter的核函數(shù)：
其中，
[cpp] ?view plaincopy
blur(?src,?dst,?Size(?1,?1?),?Point(-1,-1));?? blur(?src,?dst,?Size(?4,?4?),?Point(-1,-1));?? blur(?src,?dst,?Size(?8,?8?),?Point(-1,-1));?? blur(?src,?dst,?Size(?16,?16?),?Point(-1,-1));??
實(shí)驗(yàn)結(jié)果 下圖是對(duì)一幅圖像分別用1*1,4*4,8*8,16*16標(biāo)準(zhǔn)方框?yàn)V波后的圖像： ??????
【高斯濾波】
高斯濾波器是一類(lèi)根據(jù)高斯函數(shù)的形狀來(lái)選擇權(quán)值的線性平滑濾波器。它對(duì)去除服從正態(tài)分布的噪聲很有效。
常用的零均值離散高斯濾波器函數(shù)：
2D圖像中表示為：
代碼 [cpp] ?view plaincopy
? ? ?? ?? cv::Mat?cv::getGaussianKernel(?int ?n,? double ?sigma,? int ?ktype?)?? {?? ????const ? int ?SMALL_GAUSSIAN_SIZE?=?7;?? ????static ? const ? float ?small_gaussian_tab[][SMALL_GAUSSIAN_SIZE]?=?? ????{?? ????????{1.f},?? ????????{0.25f,?0.5f,?0.25f},?? ????????{0.0625f,?0.25f,?0.375f,?0.25f,?0.0625f},?? ????????{0.03125f,?0.109375f,?0.21875f,?0.28125f,?0.21875f,?0.109375f,?0.03125f}?? ????};?? ?? ????const ? float *?fixed_kernel?=?n?%?2?==?1?&&?n?<=?SMALL_GAUSSIAN_SIZE?&&?sigma?<=?0???? ????????small_gaussian_tab[n>>1]?:?0;?? ?? ????CV_Assert(?ktype?==?CV_32F?||?ktype?==?CV_64F?);?? ????Mat?kernel(n,?1,?ktype);?? ????float *?cf?=?( float *)kernel.data;?? ????double *?cd?=?( double *)kernel.data;?? ?? ????double ?sigmaX?=?sigma?>?0???sigma?:?((n-1)*0.5?-?1)*0.3?+?0.8;?? ????double ?scale2X?=?-0.5/(sigmaX*sigmaX);?? ????double ?sum?=?0;?? ?? ????int ?i;?? ????for (?i?=?0;?i?<?n;?i++?)?? ????{?? ????????double ?x?=?i?-?(n-1)*0.5;?? ????????double ?t?=?fixed_kernel???( double )fixed_kernel[i]?:?std::exp(scale2X*x*x);?? ????????if (?ktype?==?CV_32F?)?? ????????{?? ????????????cf[i]?=?(float )t;?? ????????????sum?+=?cf[i];?? ????????}?? ????????else ?? ????????{?? ????????????cd[i]?=?t;?? ????????????sum?+=?cd[i];?? ????????}?? ????}?? ?? ????sum?=?1./sum;?? ????for (?i?=?0;?i?<?n;?i++?)?? ????{?? ????????if (?ktype?==?CV_32F?)?? ????????????cf[i]?=?(float )(cf[i]*sum);?? ????????else ?? ????????????cd[i]?*=?sum;?? ????}?? ?? ????return ?kernel;?? }?? ?? ?? cv::Ptr<cv::FilterEngine>?cv::createGaussianFilter(?int ?type,?Size?ksize,?? ????????????????????????????????????????double ?sigma1,? double ?sigma2,?? ????????????????????????????????????????int ?borderType?)?? {?? ????int ?depth?=?CV_MAT_DEPTH(type);?? ????if (?sigma2?<=?0?)?? ????????sigma2?=?sigma1;?? ?? ?????? ????if (?ksize.width?<=?0?&&?sigma1?>?0?)?? ????????ksize.width?=?cvRound(sigma1*(depth?==?CV_8U???3?:?4)*2?+?1)|1;?? ????if (?ksize.height?<=?0?&&?sigma2?>?0?)?? ????????ksize.height?=?cvRound(sigma2*(depth?==?CV_8U???3?:?4)*2?+?1)|1;?? ?? ????CV_Assert(?ksize.width?>?0?&&?ksize.width?%?2?==?1?&&?? ????????ksize.height?>?0?&&?ksize.height?%?2?==?1?);?? ?? ????sigma1?=?std::max(?sigma1,?0.?);?? ????sigma2?=?std::max(?sigma2,?0.?);?? ?? ????Mat?kx?=?getGaussianKernel(?ksize.width,?sigma1,?std::max(depth,?CV_32F)?);?? ????Mat?ky;?? ????if (?ksize.height?==?ksize.width?&&?std::abs(sigma1?-?sigma2)?<?DBL_EPSILON?)?? ????????ky?=?kx;?? ????else ?? ????????ky?=?getGaussianKernel(?ksize.height,?sigma2,?std::max(depth,?CV_32F)?);?? ?? ????return ?createSeparableLinearFilter(?type,?type,?kx,?ky,?Point(-1,-1),?0,?borderType?);?? }?? ?? ?? void ?cv::GaussianBlur(?InputArray?_src,?OutputArray?_dst,?Size?ksize,?? ???????????????????double ?sigma1,? double ?sigma2,?? ???????????????????int ?borderType?)?? {?? ????Mat?src?=?_src.getMat();?? ????_dst.create(?src.size(),?src.type()?);?? ????Mat?dst?=?_dst.getMat();?? ?? ????if (?borderType?!=?BORDER_CONSTANT?)?? ????{?? ????????if (?src.rows?==?1?)?? ????????????ksize.height?=?1;?? ????????if (?src.cols?==?1?)?? ????????????ksize.width?=?1;?? ????}?? ?? ????if (?ksize.width?==?1?&&?ksize.height?==?1?)?? ????{?? ????????src.copyTo(dst);?? ????????return ;?? ????}?? ?? #ifdef?HAVE_TEGRA_OPTIMIZATION ?? ????if (sigma1?==?0?&&?sigma2?==?0?&&?tegra::gaussian(src,?dst,?ksize,?borderType))?? ????????return ;?? #endif ?? ?? ????Ptr<FilterEngine>?f?=?createGaussianFilter(?src.type(),?ksize,?sigma1,?sigma2,?borderType?);?? ????f->apply(?src,?dst?);?? }?? 實(shí)驗(yàn)結(jié)果 下圖是對(duì)一幅圖像分別用1*1,3*3,5*5,9*9標(biāo)準(zhǔn)方框?yàn)V波后的圖像： ??????
非線性濾波
線性濾波易于構(gòu)造，且易于從頻率響應(yīng)的角度分析，但如果噪聲是散粒噪聲而非高斯噪聲時(shí)線性濾波不能去除噪聲。如圖像突然出現(xiàn)很大的值，線性濾波只是轉(zhuǎn)換為柔和但仍可見(jiàn)的散粒。這時(shí)需要非線性濾波。
簡(jiǎn)單的非線性濾波有?中值濾波 ，?-截尾均值濾波 ，定義域?yàn)V波? 和值域?yàn)V波? 。
中值濾波選擇每個(gè)鄰域像素的中值輸出；?-截尾均值濾波是指去掉百分率為?的最小值和最大值；定義域?yàn)V波中沿著邊界的數(shù)字是像素的距離；值域就是去掉值域外的像素值。
中值濾波代碼
[cpp] ?view plaincopy
medianBlur?(?src,?dst,?i?);?? 中值濾波實(shí)驗(yàn) 下圖是對(duì)一幅圖像分別用3*3,5*5,7*7,9*9（這里必須是奇數(shù)）標(biāo)準(zhǔn)方框?yàn)V波后的圖像：
??????
【雙邊濾波】
雙邊濾波的思想是抑制與中心像素值差別太大的像素，輸出像素值依賴(lài)于鄰域像素值的加權(quán)合：
權(quán)重系數(shù) 取決于定義域核
和依賴(lài)于數(shù)據(jù)的值域核
的乘積。相乘后會(huì)產(chǎn)生依賴(lài)于數(shù)據(jù)的雙邊權(quán)重函數(shù)：
雙邊濾波源碼
[cpp] ?view plaincopy
? ? ?? ?? namespace ?cv?? {?? ?? static ? void ?? bilateralFilter_8u(?const ?Mat&?src,?Mat&?dst,? int ?d,?? ????????????????????double ?sigma_color,? double ?sigma_space,?? ????????????????????int ?borderType?)?? {?? ????int ?cn?=?src.channels();?? ????int ?i,?j,?k,?maxk,?radius;?? ????Size?size?=?src.size();?? ?? ????CV_Assert(?(src.type()?==?CV_8UC1?||?src.type()?==?CV_8UC3)?&&?? ????????src.type()?==?dst.type()?&&?src.size()?==?dst.size()?&&?? ????????src.data?!=?dst.data?);?? ?? ????if (?sigma_color?<=?0?)?? ????????sigma_color?=?1;?? ????if (?sigma_space?<=?0?)?? ????????sigma_space?=?1;?? ?? ????double ?gauss_color_coeff?=?-0.5/(sigma_color*sigma_color);?? ????double ?gauss_space_coeff?=?-0.5/(sigma_space*sigma_space);?? ?? ????if (?d?<=?0?)?? ????????radius?=?cvRound(sigma_space*1.5);?? ????else ?? ????????radius?=?d/2;?? ????radius?=?MAX(radius,?1);?? ????d?=?radius*2?+?1;?? ?? ????Mat?temp;?? ????copyMakeBorder(?src,?temp,?radius,?radius,?radius,?radius,?borderType?);?? ?? ????vector<float >?_color_weight(cn*256);?? ????vector<float >?_space_weight(d*d);?? ????vector<int >?_space_ofs(d*d);?? ????float *?color_weight?=?&_color_weight[0];?? ????float *?space_weight?=?&_space_weight[0];?? ????int *?space_ofs?=?&_space_ofs[0];?? ?? ?????? ????for (?i?=?0;?i?<?256*cn;?i++?)?? ????????color_weight[i]?=?(float )std::exp(i*i*gauss_color_coeff);?? ?? ?????? ????for (?i?=?-radius,?maxk?=?0;?i?<=?radius;?i++?)?? ????????for (?j?=?-radius;?j?<=?radius;?j++?)?? ????????{?? ????????????double ?r?=?std::sqrt(( double )i*i?+?( double )j*j);?? ????????????if (?r?>?radius?)?? ????????????????continue ;?? ????????????space_weight[maxk]?=?(float )std::exp(r*r*gauss_space_coeff);?? ????????????space_ofs[maxk++]?=?(int )(i*temp.step?+?j*cn);?? ????????}?? ?? ????for (?i?=?0;?i?<?size.height;?i++?)?? ????{?? ????????const ?uchar*?sptr?=?temp.data?+?(i+radius)*temp.step?+?radius*cn;?? ????????uchar*?dptr?=?dst.data?+?i*dst.step;?? ?? ????????if (?cn?==?1?)?? ????????{?? ????????????for (?j?=?0;?j?<?size.width;?j++?)?? ????????????{?? ????????????????float ?sum?=?0,?wsum?=?0;?? ????????????????int ?val0?=?sptr[j];?? ????????????????for (?k?=?0;?k?<?maxk;?k++?)?? ????????????????{?? ????????????????????int ?val?=?sptr[j?+?space_ofs[k]];?? ????????????????????float ?w?=?space_weight[k]*color_weight[std::abs(val?-?val0)];?? ????????????????????sum?+=?val*w;?? ????????????????????wsum?+=?w;?? ????????????????}?? ?????????????????? ????????????????dptr[j]?=?(uchar)cvRound(sum/wsum);?? ????????????}?? ????????}?? ????????else ?? ????????{?? ????????????assert(?cn?==?3?);?? ????????????for (?j?=?0;?j?<?size.width*3;?j?+=?3?)?? ????????????{?? ????????????????float ?sum_b?=?0,?sum_g?=?0,?sum_r?=?0,?wsum?=?0;?? ????????????????int ?b0?=?sptr[j],?g0?=?sptr[j+1],?r0?=?sptr[j+2];?? ????????????????for (?k?=?0;?k?<?maxk;?k++?)?? ????????????????{?? ????????????????????const ?uchar*?sptr_k?=?sptr?+?j?+?space_ofs[k];?? ????????????????????int ?b?=?sptr_k[0],?g?=?sptr_k[1],?r?=?sptr_k[2];?? ????????????????????float ?w?=?space_weight[k]*color_weight[std::abs(b?-?b0)?+?? ????????????????????????std::abs(g?-?g0)?+?std::abs(r?-?r0)];?? ????????????????????sum_b?+=?b*w;?sum_g?+=?g*w;?sum_r?+=?r*w;?? ????????????????????wsum?+=?w;?? ????????????????}?? ????????????????wsum?=?1.f/wsum;?? ????????????????b0?=?cvRound(sum_b*wsum);?? ????????????????g0?=?cvRound(sum_g*wsum);?? ????????????????r0?=?cvRound(sum_r*wsum);?? ????????????????dptr[j]?=?(uchar)b0;?dptr[j+1]?=?(uchar)g0;?dptr[j+2]?=?(uchar)r0;?? ????????????}?? ????????}?? ????}?? }??
雙邊濾波調(diào)用
[cpp] ?view plaincopy
bilateralFilter(InputArray?src,?OutputArray?dst,? int ?d,? double ?sigmaColor,? double ?sigmaSpace,?? ??????????????????????int ?borderType=BORDER_DEFAULT?)；?? d 表示濾波時(shí)像素鄰域直徑，d為負(fù)時(shí)由 sigaColor計(jì)算得到；d>5時(shí)不能實(shí)時(shí)處理。
sigmaColor、sigmaSpace非別表示顏色空間和坐標(biāo)空間的濾波系數(shù)sigma。可以簡(jiǎn)單的賦值為相同的值。<10時(shí)幾乎沒(méi)有效果；>150時(shí)為油畫(huà)的效果。
borderType可以不指定。
雙邊濾波實(shí)驗(yàn) 用sigma為10，150,240,480時(shí)效果如下： ???????
參考文獻(xiàn)：
Richard Szeliski 《Computer Vision: Algorithms and Applications》
轉(zhuǎn)載請(qǐng)注明出處：http://blog.csdn.net/xiaowei_cqu/article/details/7785365
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