高斯滤波器的原理及其实现过程（附模板代码）

void generateGaussianTemplate(double window[][11], int ksize, double sigma){ static const double pi = 3.1415926; int center = ksize / 2; // 模板的中心位置，也就是坐标的原点 double x2, y2; for (int i = 0; i < ksize; i++) { x2 = pow(i - center, 2); for (int j = 0; j < ksize; j++) { y2 = pow(j - center, 2); double g = exp(-(x2 + y2) / (2 * sigma * sigma)); g /= 2 * pi * sigma; window[i][j] = g; } } double k = 1 / window[0][0]; // 将左上角的系数归一化为1 for (int i = 0; i < ksize; i++) { for (int j = 0; j < ksize; j++) { window[i][j] *= k; } }}

void generateGaussianTemplate(double window[][11], int ksize, double sigma){ static const double pi = 3.1415926; int center = ksize / 2; // 模板的中心位置，也就是坐标的原点 double x2, y2; double sum = 0; for (int i = 0; i < ksize; i++) { x2 = pow(i - center, 2); for (int j = 0; j < ksize; j++) { y2 = pow(j - center, 2); double g = exp(-(x2 + y2) / (2 * sigma * sigma)); g /= 2 * pi * sigma; sum += g; window[i][j] = g; } } //double k = 1 / window[0][0]; // 将左上角的系数归一化为1 for (int i = 0; i < ksize; i++) { for (int j = 0; j < ksize; j++) { window[i][j] /= sum; } }}

void GaussianFilter(const Mat &src, Mat &dst, int ksize, double sigma){ CV_Assert(src.channels() || src.channels() == 3); // 只处理单通道或者三通道图像 const static double pi = 3.1415926; // 根据窗口大小和sigma生成高斯滤波器模板 // 申请一个二维数组，存放生成的高斯模板矩阵 double **templateMatrix = new double*[ksize]; for (int i = 0; i < ksize; i++) templateMatrix[i] = new double[ksize]; int origin = ksize / 2; // 以模板的中心为原点 double x2, y2; double sum = 0; for (int i = 0; i < ksize; i++) { x2 = pow(i - origin, 2); for (int j = 0; j < ksize; j++) { y2 = pow(j - origin, 2); // 高斯函数前的常数可以不用计算，会在归一化的过程中给消去 double g = exp(-(x2 + y2) / (2 * sigma * sigma)); sum += g; templateMatrix[i][j] = g; } } for (int i = 0; i < ksize; i++) { for (int j = 0; j < ksize; j++) { templateMatrix[i][j] /= sum; cout << templateMatrix[i][j] << " "; } cout << endl; } // 将模板应用到图像中 int border = ksize / 2; copyMakeBorder(src, dst, border, border, border, border, BorderTypes::BORDER_REFLECT); int channels = dst.channels(); int rows = dst.rows - border; int cols = dst.cols - border; for (int i = border; i < rows; i++) { for (int j = border; j < cols; j++) { double sum[3] = { 0 }; for (int a = -border; a <= border; a++) { for (int b = -border; b <= border; b++) { if (channels == 1) { sum[0] += templateMatrix[border + a][border + b] * dst.at<uchar>(i + a, j + b); } else if (channels == 3) { Vec3b rgb = dst.at<Vec3b>(i + a, j + b); auto k = templateMatrix[border + a][border + b]; sum[0] += k * rgb[0]; sum[1] += k * rgb[1]; sum[2] += k * rgb[2]; } } } for (int k = 0; k < channels; k++) { if (sum[k] < 0) sum[k] = 0; else if (sum[k] > 255) sum[k] = 255; } if (channels == 1) dst.at<uchar>(i, j) = static_cast<uchar>(sum[0]); else if (channels == 3) { Vec3b rgb = { static_cast<uchar>(sum[0]), static_cast<uchar>(sum[1]), static_cast<uchar>(sum[2]) }; dst.at<Vec3b>(i, j) = rgb; } } } // 释放模板数组 for (int i = 0; i < ksize; i++) delete[] templateMatrix[i]; delete[] templateMatrix;}

// 分离的计算void separateGaussianFilter(const Mat &src, Mat &dst, int ksize, double sigma){ CV_Assert(src.channels()==1 || src.channels() == 3); // 只处理单通道或者三通道图像 // 生成一维的高斯滤波模板 double *matrix = new double[ksize]; double sum = 0; int origin = ksize / 2; for (int i = 0; i < ksize; i++) { // 高斯函数前的常数可以不用计算，会在归一化的过程中给消去 double g = exp(-(i - origin) * (i - origin) / (2 * sigma * sigma)); sum += g; matrix[i] = g; } // 归一化 for (int i = 0; i < ksize; i++) matrix[i] /= sum; // 将模板应用到图像中 int border = ksize / 2; copyMakeBorder(src, dst, border, border, border, border, BorderTypes::BORDER_REFLECT); int channels = dst.channels(); int rows = dst.rows - border; int cols = dst.cols - border; // 水平方向 for (int i = border; i < rows; i++) { for (int j = border; j < cols; j++) { double sum[3] = { 0 }; for (int k = -border; k <= border; k++) { if (channels == 1) { sum[0] += matrix[border + k] * dst.at<uchar>(i, j + k); // 行不变，列变化；先做水平方向的卷积 } else if (channels == 3) { Vec3b rgb = dst.at<Vec3b>(i, j + k); sum[0] += matrix[border + k] * rgb[0]; sum[1] += matrix[border + k] * rgb[1]; sum[2] += matrix[border + k] * rgb[2]; } } for (int k = 0; k < channels; k++) { if (sum[k] < 0) sum[k] = 0; else if (sum[k] > 255) sum[k] = 255; } if (channels == 1) dst.at<uchar>(i, j) = static_cast<uchar>(sum[0]); else if (channels == 3) { Vec3b rgb = { static_cast<uchar>(sum[0]), static_cast<uchar>(sum[1]), static_cast<uchar>(sum[2]) }; dst.at<Vec3b>(i, j) = rgb; } } } // 竖直方向 for (int i = border; i < rows; i++) { for (int j = border; j < cols; j++) { double sum[3] = { 0 }; for (int k = -border; k <= border; k++) { if (channels == 1) { sum[0] += matrix[border + k] * dst.at<uchar>(i + k, j); // 列不变，行变化；竖直方向的卷积 } else if (channels == 3) { Vec3b rgb = dst.at<Vec3b>(i + k, j); sum[0] += matrix[border + k] * rgb[0]; sum[1] += matrix[border + k] * rgb[1]; sum[2] += matrix[border + k] * rgb[2]; } } for (int k = 0; k < channels; k++) { if (sum[k] < 0) sum[k] = 0; else if (sum[k] > 255) sum[k] = 255; } if (channels == 1) dst.at<uchar>(i, j) = static_cast<uchar>(sum[0]); else if (channels == 3) { Vec3b rgb = { static_cast<uchar>(sum[0]), static_cast<uchar>(sum[1]), static_cast<uchar>(sum[2]) }; dst.at<Vec3b>(i, j) = rgb; } } } delete[] matrix;}

CV_EXPORTS_W void GaussianBlur( InputArray src, OutputArray dst, Size ksize, double sigmaX, double sigmaY = 0, int borderType = BORDER_DEFAULT );