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域滤波：方框、高斯、中值、双边滤波
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鄰域濾波（卷積）
鄰域算子值利用給定像素周圍像素的值決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。目標圖像中綠色的像素由原圖像中藍色標記的像素計算得到。
通用線性鄰域濾波是一種常用的鄰域算子，輸入像素加權得到輸出像素：
其中權重核???為“濾波系數
【方框濾波】
最簡單的線性濾波是移動平均或方框濾波，用?窗口中的像素值平均后輸出，核函數為：
其實等價于圖像與全部元素值為1的核函數進行卷積再進行尺度縮放。
代碼
OpenCV中的 blur函數是進行標準方框濾波：
[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 的區別是，blur是標準化后的 boxFilter，即boxFilter的核函數：
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));??
實驗結果 下圖是對一幅圖像分別用1*1,4*4,8*8,16*16標準方框濾波后的圖像： ??????
【高斯濾波】
高斯濾波器是一類根據高斯函數的形狀來選擇權值的線性平滑濾波器。它對去除服從正態分布的噪聲很有效。
常用的零均值離散高斯濾波器函數：
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?);?? }?? 實驗結果 下圖是對一幅圖像分別用1*1,3*3,5*5,9*9標準方框濾波后的圖像： ??????
非線性濾波
線性濾波易于構造，且易于從頻率響應的角度分析，但如果噪聲是散粒噪聲而非高斯噪聲時線性濾波不能去除噪聲。如圖像突然出現很大的值，線性濾波只是轉換為柔和但仍可見的散粒。這時需要非線性濾波。
簡單的非線性濾波有?中值濾波 ，?-截尾均值濾波 ，定義域濾波? 和值域濾波? 。
中值濾波選擇每個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；定義域濾波中沿著邊界的數字是像素的距離；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?);?? 中值濾波實驗 下圖是對一幅圖像分別用3*3,5*5,7*7,9*9（這里必須是奇數）標準方框濾波后的圖像：
??????
【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，輸出像素值依賴于鄰域像素值的加權合：
權重系數 取決于定義域核
和依賴于數據的值域核
的乘積。相乘后會產生依賴于數據的雙邊權重函數：
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 表示濾波時像素鄰域直徑，d為負時由 sigaColor計算得到；d>5時不能實時處理。
sigmaColor、sigmaSpace非別表示顏色空間和坐標空間的濾波系數sigma。可以簡單的賦值為相同的值。<10時幾乎沒有效果；>150時為油畫的效果。
borderType可以不指定。
雙邊濾波實驗 用sigma為10，150,240,480時效果如下： ???????
參考文獻：
Richard Szeliski 《Computer Vision: Algorithms and Applications》
轉載請注明出處：http://blog.csdn.net/xiaowei_cqu/article/details/7785365
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