高斯混合模型

高斯混合模型 看高斯混合模型的论文的时候感觉一头雾水，主要是那些概率 公式 小学单位换算公式大全免费下载公式下载行测公式大全下载excel公式下载逻辑回归公式下载 比较难懂，看了几遍论文 和代码才有了一点感觉，以下是个人的对混合高斯背景模型代码的理解，后面会通过进一步 理解不断对此贴修正..... 注:本人对该代码的理解也有很多不到位的地方，希望以后会慢慢矫正。程序中代码的实现 与论文中公式有些出入，不过不影响对全局的把握和理解。 ////////////////////////cvCreateGaussianBGModel/////////////////////////////////////////// CV_IMPL CvBGStatModel *cvCreateGaussianBGModel( IplImage*first_frame,CvGaussBGStatModelParams* parameters ) { CvGaussBGModel* bg_model = 0; CV_FUNCNAME( "cvCreateGaussianBGModel" ); __BEGIN__; double var_init; CvGaussBGStatModelParams params; int i, j, k, m, n; // init parameters if( parameters == NULL ) { params.win_size = CV_BGFG_MOG_WINDOW_SIZE; // 初始化阶段的帧数;用户 自定义模型学 习率a=1/win_size; params.bg_threshold = CV_BGFG_MOG_BACKGROUND_THRESHOLD; params.std_threshold = CV_BGFG_MOG_STD_THRESHOLD; params.weight_init = CV_BGFG_MOG_WEIGHT_INIT; params.variance_init = CV_BGFG_MOG_SIGMA_INIT*CV_BGFG_MOG_SIGMA_INIT; //方差 params.minArea = CV_BGFG_MOG_MINAREA; params.n_gauss = CV_BGFG_MOG_NGAUSSIANS; //高斯分布函数的个数 } else { params = *parameters; //用户自定义参数 } if( !CV_IS_IMAGE(first_frame) ) CV_ERROR( CV_StsBadArg, "Invalid or NULL first_frame parameter" ); CV_CALL( bg_model = (CvGaussBGModel*)cvAlloc( sizeof(*bg_model) )); memset( bg_model, 0, sizeof(*bg_model) ); bg_model->type = CV_BG_MODEL_MOG; //CV_BG_MODEL_MOG为高斯背景模型 bg_model->release = (CvReleaseBGStatModel)icvReleaseGaussianBGModel; bg_model->update = (CvUpdateBGStatModel)icvUpdateGaussianBGModel; bg_model->params = params; //prepare storages CV_CALL( bg_model->g_point = (CvGaussBGPoint*)cvAlloc(sizeof(CvGaussBGPoint)* ((first_frame->width*first_frame->height) + 256))); CV_CALL( bg_model->background = cvCreateImage(cvSize(first_frame->width, first_frame->height), IPL_DEPTH_8U, first_frame->nChannels)); CV_CALL( bg_model->foreground = cvCreateImage(cvSize(first_frame->width, first_frame->height), IPL_DEPTH_8U, 1)); CV_CALL( bg_model->storage = cvCreateMemStorage()); //initializing var_init = 2 * params.std_threshold * params.std_threshold; //初始化方差 CV_CALL( bg_model->g_point[0].g_values = (CvGaussBGValues*)cvAlloc( sizeof(CvGaussBGValues)*params.n_gauss* (first_frame->width*first_frame->height + 128))); for( i = 0, n = 0; i < first_frame->height; i++ ) //行 { for( j = 0; j < first_frame->width; j++, n++ ) //列 { const int p = i*first_frame->widthStep+j*first_frame->nChannels; //以下几步是对第一个高斯函数做初始化 bg_model->g_point[n].g_values = bg_model->g_point[0].g_values + n*params.n_gauss; bg_model->g_point[n].g_values[0].weight = 1; //权值赋为1 bg_model->g_point[n].g_values[0].match_sum = 1; //高斯函数被匹配的次数 for( m = 0; m < first_frame->nChannels; m++) { bg_model->g_point[n].g_values[0].variance[m] = var_init; //均值赋为当前像素的值 bg_model->g_point[n].g_values[0].mean[m] = (unsigned char)first_frame->imageData[p + m]; } //除第一以外的高斯分布函数的初始化(均值、权值和匹配次数都置零) for( k = 1; k < params.n_gauss; k++) { bg_model->g_point[n].g_values[k].weight = 0; bg_model->g_point[n].g_values[k].match_sum = 0; for( m = 0; m < first_frame->nChannels; m++){ bg_model->g_point[n].g_values[k].variance[m] = var_init; bg_model->g_point[n].g_values[k].mean[m] = 0; } } } } //g_point[]:像素，g_values[]:高斯分布函数，mean[]:通道 bg_model->countFrames = 0; __END__; if( cvGetErrStatus() < 0 ) { CvBGStatModel* base_ptr = (CvBGStatModel*)bg_model; if( bg_model && bg_model->release ) bg_model->release( &base_ptr ); else cvFree( &bg_model ); bg_model = 0; } return (CvBGStatModel*)bg_model; } cvUpdateBGStatModel(videoFrame,bgModel); typedef int (CV_CDECL * CvUpdateBGStatModel)( IplImage* curr_frame, struct CvBGStatModel* bg_model ); /////////////////////////cvUpdateBGStatModel////////////////////////////////// //函数功能:背景模型的更新，不仅要更新高斯分布函数的参数，还要更新各高斯函数的权 重 static int CV_CDECL icvUpdateGaussianBGModel( IplImage* curr_frame, CvGaussBGModel* bg_model ) { int i, j, k, n; int region_count = 0; CvSeq *first_seq = NULL, *prev_seq = NULL, *seq = NULL; bg_model->countFrames++; for( i = 0, n = 0; i < curr_frame->height; i++ ) { for( j = 0; j < curr_frame->width; j++, n++ ) { int match[CV_BGFG_MOG_MAX_NGAUSSIANS]; //对高斯函数做标记， match[m]=1 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 示函数m为匹配的高斯分布函数 double sort_key[CV_BGFG_MOG_MAX_NGAUSSIANS]; //此数组存贮每个高斯函数 的均值与方差比值 const int nChannels = curr_frame->nChannels; const int p = curr_frame->widthStep*i+j*nChannels; CvGaussBGPoint* g_point = &bg_model->g_point[n]; const CvGaussBGStatModelParams bg_model_params = bg_model->params; double pixel[4]; // pixel[]存贮当前像素的各通道RGB值 int no_match; for( k = 0; k < nChannels; k++ ) pixel[k] = (uchar)curr_frame->imageData[p+k]; no_match = icvMatchTest( pixel, nChannels, match, g_point, &bg_model_params ); //检 查是否有与当前像素匹配的高斯函数 if( bg_model->countFrames >= bg_model->params.win_size ) ,,,,,,,,,,,,, { icvUpdateFullWindow( pixel, nChannels, match, g_point, &bg_model->params ); if( no_match == -1) icvUpdateFullNoMatch( curr_frame, p, match, g_point, &bg_model_params ); } else { icvUpdatePartialWindow( pixel, nChannels, match, g_point, &bg_model_params ); if( no_match == -1) icvUpdatePartialNoMatch( pixel, nChannels, match, g_point, &bg_model_params ); } icvGetSortKey( nChannels, sort_key, g_point, &bg_model_params ); icvInsertionSortGaussians( g_point, sort_key, (CvGaussBGStatModelParams *)&bg_model_params ); icvBackgroundTest( nChannels, n, i, j, match, bg_model ); } } //foreground filtering //filter small regions cvClearMemStorage(bg_model->storage); //cvMorphologyEx( bg_model->foreground, bg_model->foreground, 0, 0, CV_MOP_OPEN, 1 ); //cvMorphologyEx( bg_model->foreground, bg_model->foreground, 0, 0, CV_MOP_CLOSE, 1 ); cvFindContours( bg_model->foreground, bg_model->storage, &first_seq, sizeof(CvContour), CV_RETR_LIST ); for( seq = first_seq; seq; seq = seq->h_next ) { CvContour* cnt = (CvContour*)seq; if( cnt->rect.width * cnt->rect.height < bg_model->params.minArea ) { //delete small contour prev_seq = seq->h_prev; if( prev_seq ) { prev_seq->h_next = seq->h_next; if( seq->h_next ) seq->h_next->h_prev = prev_seq; } else { first_seq = seq->h_next; if( seq->h_next ) seq->h_next->h_prev = NULL; } } else { region_count++; } } bg_model->foreground_regions = first_seq; cvZero(bg_model->foreground); cvDrawContours(bg_model->foreground, first_seq, CV_RGB(0, 0, 255), CV_RGB(0, 0, 255), 10, -1); return region_count; } /////////////////////////////////////icvMatchTest////////////////////////////////////////// //函数功能:拿当前像素的值与已存在的高斯分布函数比较，查找是否存在匹配的的高斯分 布函数，如果有则返回 k值(高斯分布函数的序号) static int icvMatchTest( double* src_pixel, int nChannels, int* match, const CvGaussBGPoint* g_point, const CvGaussBGStatModelParams *bg_model_params ) { //参数的传递:src_pixel为piexl[]:即当前像素的各通道值 int k; int matchPosition=-1; for ( k = 0; k < bg_model_params->n_gauss; k++) match[k]=0; for ( k = 0; k < bg_model_params->n_gauss; k++) if (g_point->g_values[k].match_sum > 0) { double sum_d2 = 0.0; double var_threshold = 0.0; for(int m = 0; m < nChannels; m++) { double d = g_point->g_values[k].mean[m]- src_pixel[m]; //通道m的原始模型值与当前 像素的值之差 sum_d2 += (d*d); var_threshold += g_point->g_values[k].variance[m]; } //当前sum_d2为d0,d1,d2的平方和，var_threshold的值为像素各通道方差之和 var_threshold = bg_model_params->std_threshold* bg_model_params- >std_threshold*var_threshold; if(sum_d2 < var_threshold) //查看是否可以与某高斯分布匹 配 ,,,,,,,,,,,,,,,, { match[k] = 1; matchPosition = k; break; //如果和第k个高斯函数匹配，则终止与后续函数的匹配 } } return matchPosition; } ///////////////////////icvUpdateFullWindow//////////////////////////////////////// //函数功能:更新每个高斯分布的权值(对匹配的高斯函数k加大权值，其余的则减小权值)， 如果前面的结果中存在匹配的高斯分布函数k,则需要再对第k个高斯分布函数的均值mean 和方差variance做修正 static void icvUpdateFullWindow( double* src_pixel, int nChannels, int* match, CvGaussBGPoint* g_point, const CvGaussBGStatModelParams *bg_model_params ) { //参数的传递:src_pixel为piexl[]:即当前帧中该像素的RGB值 const double learning_rate_weight = (1.0/(double)bg_model_params->win_size); //用户自定 义模型学习率a for(int k = 0; k < bg_model_params->n_gauss; k++) { //对每个高斯分布的权值做修正:w=(1-a)w+a*m (a:模型学习率，m是匹配，匹配就是1， 不匹配就是0) g_point->g_values[k].weight = g_point->g_values[k].weight + (learning_rate_weight*((double)match[k] -g_point->g_values[k].weight)); if(match[k]) //如果存在匹配的高斯分布函数k(当前像素为背景像素),则需要再对第k 个高斯分布函数的均值mean和方差variance更新 { double learning_rate_gaussian = (double)match[k]/(g_point->g_values[k].weight* (double)bg_model_params->win_size); //参数学习率p(p=a/w) for(int m = 0; m < nChannels; m++) { //参数更新公式:u=(1-p)*u0+p*x; o*o=(1-p)*o*o+p*tmpDiff*tmpDiff const double tmpDiff = src_pixel[m] - g_point->g_values[k].mean[m]; //当前像素的通 道m的值与原始模型值之差 g_point->g_values[k].mean[m] = g_point->g_values[k].mean[m] + (learning_rate_gaussian * tmpDiff); g_point->g_values[k].variance[m] = g_point->g_values[k].variance[m]+ (learning_rate_gaussian*((tmpDiff*tmpDiff) - g_point->g_values[k].variance[m])); } } } } /////////////////////////icvUpdatePartialWindow///////////////////////////// //函数功能:对所有的高斯分布函数做更新.至少每个高斯分布的权值必须修正，如果前面的 结果中存在匹配的高斯分布函数k,则需要再对第k个高斯分布函数的match_sum修改，最 终对那些匹配的高斯分布函数k的参数match_sum>0的做均值mean和方差variance修正 static void icvUpdatePartialWindow( double* src_pixel, int nChannels, int* match, CvGaussBGPoint* g_point, const CvGaussBGStatModelParams *bg_model_params ) { int k, m; int window_current = 0; for( k = 0; k < bg_model_params->n_gauss; k++ ) window_current += g_point->g_values[k].match_sum; //window_current为k个高斯分布 函数的match_sum值之和 for( k = 0; k < bg_model_params->n_gauss; k++ ) { g_point->g_values[k].match_sum += match[k]; //修正匹配的高斯分布函数k的 match_sum值 double learning_rate_weight = (1.0/((double)window_current + 1.0)); //increased by one since sum //修正每个高斯分布的权值 g_point->g_values[k].weight = g_point->g_values[k].weight + (learning_rate_weight*((double)match[k] - g_point->g_values[k].weight)); if( g_point->g_values[k].match_sum > 0 && match[k] ) { double learning_rate_gaussian = (double)match[k]/((double)g_point->g_values[k].match_sum); for( m = 0; m < nChannels; m++ ) { const double tmpDiff = src_pixel[m] - g_point->g_values[k].mean[m]; g_point->g_values[k].mean[m] = g_point->g_values[k].mean[m] + (learning_rate_gaussian*tmpDiff); g_point->g_values[k].variance[m] = g_point->g_values[k].variance[m]+ (learning_rate_gaussian*((tmpDiff*tmpDiff) - g_point->g_values[k].variance[m])); } } } } //////////////////////////icvUpdateFullNoMatch////////////////////////// //函数功能:当所有的高斯函数均不匹配时，说明有新的分布出现，需要将原高斯函数中 sort_key最小的替换为新的高斯函数(权值小，方差大),其余的高斯函数对应的只需更新权值 static void icvUpdateFullNoMatch( IplImage* gm_image, int p, int* match, CvGaussBGPoint* g_point, const CvGaussBGStatModelParams *bg_model_params) { //参数的传递:gm_image为当前帧curr_frame int k, m; double alpha; int match_sum_total = 0; g_point->g_values[bg_model_params->n_gauss - 1].match_sum = 1; //将新的高斯分布函 数的match_sum置为1 for( k = 0; k < bg_model_params->n_gauss ; k++ ) match_sum_total += g_point->g_values[k].match_sum; g_point->g_values[bg_model_params->n_gauss - 1].weight = 1./(double)match_sum_total; // 要给新的高斯分布函数赋一个较小的权值 //将新的高斯分布函数的variance[m]全部置为variance_init;mean[m]的值置为当前像素各 通道的值 for( m = 0; m < gm_image->nChannels ; m++ ) { g_point->g_values[bg_model_params->n_gauss - 1].variance[m] = bg_model_params->variance_init; g_point->g_values[bg_model_params->n_gauss - 1].mean[m] = (unsigned char)gm_image->imageData[p + m]; } //对其他的高斯分布函数做权值更新:w=(1-a)*w+a*m (a:模型学习率，m是匹配，匹配就是 1，不匹配就是0) alpha = 1.0 - (1.0/bg_model_params->win_size); //alpha=1-a; for( k = 0; k < bg_model_params->n_gauss - 1; k++ ) { g_point->g_values[k].weight *= alpha; if( match[k] ) g_point->g_values[k].weight += alpha; } } ////////////////////////////icvUpdatePartialNoMatch//////////////////////////////// static void icvUpdatePartialNoMatch(double *pixel, int nChannels, int* /*match*/, CvGaussBGPoint* g_point, const CvGaussBGStatModelParams *bg_model_params) { int k, m; //new value of last one g_point->g_values[bg_model_params->n_gauss - 1].match_sum = 1; //get sum of all but last value of match_sum int match_sum_total = 0; for(k = 0; k < bg_model_params->n_gauss ; k++) match_sum_total += g_point->g_values[k].match_sum; for(m = 0; m < nChannels; m++) { //first pass mean is image value g_point->g_values[bg_model_params->n_gauss - 1].variance[m] = bg_model_params->variance_init; g_point->g_values[bg_model_params->n_gauss - 1].mean[m] = pixel[m]; } for(k = 0; k < bg_model_params->n_gauss; k++) { //更新所有高斯分布的权值 g_point->g_values[k].weight = (double)g_point->g_values[k].match_sum / (double)match_sum_total; } } /////////////////////////////////icvGetSortKey/////////////////////////////////// //函数功能:计算各个高斯分布weight/sqrt(variance_sum)的值，后面将对该值进行排序(该 值越大则表示背景的可能性就越大) static void icvGetSortKey( const int nChannels, double* sort_key, const CvGaussBGPoint* g_point,const CvGaussBGStatModelParams *bg_model_params ) { int k, m; for( k = 0; k < bg_model_params->n_gauss; k++ ) { // Avoid division by zero if( g_point->g_values[k].match_sum > 0 ) { // Independence assumption between components double variance_sum = 0.0; for( m = 0; m < nChannels; m++ ) variance_sum += g_point->g_values[k].variance[m]; sort_key[k] = g_point->g_values[k].weight/sqrt(variance_sum); //sort_key=w/(o*o) } else sort_key[k]= 0.0; } } //////////////////////////////icvInsertionSortGaussians//////////////////////////// static void icvInsertionSortGaussians( CvGaussBGPoint* g_point, double* sort_key, CvGaussBGStatModelParams *bg_model_params ) { int i, j; for( i = 1; i < bg_model_params->n_gauss; i++ ) { double index = sort_key[i]; for( j = i; j > 0 && sort_key[j-1] < index; j-- ) //对sort_key[]按降序排序 { double temp_sort_key = sort_key[j]; sort_key[j] = sort_key[j-1]; sort_key[j-1] = temp_sort_key; CvGaussBGValues temp_gauss_values = g_point->g_values[j]; g_point->g_values[j] = g_point->g_values[j-1]; g_point->g_values[j-1] = temp_gauss_values; } // sort_key[j] = index; } } ///////////////////////////////////icvBackgroundTest///////////////////////// static void icvBackgroundTest( const int nChannels, int n, int i, int j, int *match, CvGaussBGModel* bg_model ) { int m, b; uchar pixelValue = (uchar)255; // 像素默认都为前景 double weight_sum = 0.0; CvGaussBGPoint* g_point = bg_model->g_point; for( m = 0; m < nChannels; m++),,,,,,,,,,,,, bg_model->background->imageData[ bg_model->background->widthStep*i + j*nChannels + m] = (unsigned char)(g_point[n].g_values[0].mean[m]+0.5); for( b = 0; b < bg_model->params.n_gauss; b++) { weight_sum += g_point[n].g_values[b].weight; if( match[b] ) pixelValue = 0; //if为真，说明该像素已与某高斯函数匹配，该像素为背景 if( weight_sum > bg_model->params.bg_threshold ) break; //如果if语句为真，则前b个高斯分布被选为描述背景的函数 } bg_model->foreground->imageData[ bg_model->foreground->widthStep*i + j] = pixelValue; }